Identifying Rumors and Their Sources in Social Networks

Eunsoo Seoa, Prasant Mohapatrab and Tarek Abdelzahera

aUniversity of Illinois at Urbana-Champaign, Urbana, IL, USA;bUniversity of California at Davis, Davis, CA, USA

ABSTRACT

Information that propagates through social networks can carry a lot of false claims. For example, rumorson certain topics can propagate rapidly leading to a large number of nodes reporting the same (incorrect)observations. In this paper, we describe an approach for finding the rumor source and assessing the likelihoodthat a piece of information is in fact a rumor, in the absence of data provenance information. We model the socialnetwork as a directed graph, where vertices represent individuals and directed edges represent information flow(e.g., who follows whom on Twitter). A number of monitor nodes are injected into the network whose job is toreport data they receive. Our algorithm identifies rumors and their sources by observing which of the monitorsreceived the given piece of information and which did not. We show that, with a sufficient number of monitornodes, it is possible to recognize most rumors and their sources with high accuracy.

Keywords: Social Networks, Rumor Spreading, Epidemics

1. INTRODUCTION

Social networks are popular media for sharing information. Online social networks enable large-scale informationdissemination in a very short time, often not matched by traditional media.1,2 Mis-information and false claimscan also propagate rapidly through social networks. This is exacerbated by the fact that (i) anyone can publish(incorrect) information and (ii) it is hard to tell who the original source of the information is.3

In this paper, we focus on two problems related to mitigation of false claims in social networks. First, westudy the question of identifying sources of rumors in the absence of complete provenance information aboutrumor propagation. Second, we study how rumors (false claims) and non-rumors (true information) can bedifferentiated. Our method is based on an assumption that rumors are initiated from only a small number ofsources, whereas truthful information can be observed and originated by a large number of unrelated individualsconcurrently. Our approach relies on utilizing network monitors; individuals who agree to let us know whether ornot they heard a particular piece of information (from their social neighborhood), although do not agree to let usknow who told them this information or when they learned it. Hence, all we know is which of the monitors hearda particular piece of information. This, in some sense, is the most challenging scenario that offers a worst-casebound on accuracy of rumor detection and source identification. Additional information can only simplify theproblem. We show, that even in the aforementioned worst case, promissing results can be achieved.

The rest of the paper is organized as follows. Section 2 describes the problem of identifying rumors and theirsources and explains our approach. We also explain various ways of selecting monitors. Section 3 presents acase study of a real social network crawled from Twitter. We describe the details of the dataset and comparedifferent monitor selection methods in terms of accuracy of rumor and source identification. In Section 4, weprovide related work and conclude the paper in Section 5.

Further author information: (Send correspondence to Eunsoo Seo.)Eunsoo Seo: E-mail: eseo2@cs.illinois.edu, Telephone: 1 217 265 6793Prasant Mohapatra: E-mail: prasant@cs.ucdavis.edu, Telephone: 1 530 754 8016Tarek Abdelzaher: E-mail: zaher@cs.illinois.edu, Telephone: 1 217 265 6793

2. IDENTIFYING RUMORS AND THEIR SOURCES

2.1 Identifying Rumor Sources

The first question we are studying in this paper is as follows: if a rumor is initiated by a single source in a socialnetwork, how can the source be identified?

A social network is modeled as a directed graph G = (V,E) where V is the set of all people and E is theset of edges where each edge represents information flow between two individuals. We assume that a set of kpre-selected nodes M (M ⊆ V ) are our monitors. For rumor investigation purposes, given a specific piece ofinformation, a monitor reports whether they received it or not. We denote the set of monitor nodes who receivedthe rumor by M+, and the set of monitor nodes who have not received it by M− (where M+,M− ⊆ M). Wecall the former set positive monitors and the latter negative monitors.

To identify the souce of a rumor, we use the intuition that the source must be close to the positive monitorsbut far from the negative monitors. Hence, for each node x, our algorithm calculates the following four metrics:

(1) Reachability to all positive monitors We first calculate how many positive monitors are reachablefrom each node. For a node x to be the rumor source, x must have paths to all monitors in M+. If those pathsdo not exist, x cannot be a rumor source.

(2) Distance to positive monitors Among those nodes that can reach all positive monitors, nodes that arecloser, on average, are preferred. In other words, for each node x, we calculate the total distance∑

m∈M+ and m is reachable from x

d(x,m).

where d(x,m) is the distance from x to m, and sort the suspected sources by increasing total distance frompositive monitors.

(3) Reachability to negative monitors Among the nodes that can reach all nodes in M+ and have thesame total distance to these positive monitors, we use reachability to negative monitors as a third metric. Foreach such node x, we count of monitors in M− that are not reachable from x and prefer larger counts.

(4) Distance to negative monitors As a last metric, we also use the distance to negative monitors. Foreach node x, we calculate the total distance ∑

m∈M− and m is reachable from x

d(x,m).

It is more natural that negative monitors are far from the rumor source, so nodes with large values of totaldistance are preferred.

Using the above four metrics – number of reachable positive monitors, sum of distances to reachable positivemonitors, number of reachable negative monitors, sum of distances to reachable negative monitors –, all nodesin the network are sorted lexicographically. That is, i-th metric is used only when there is a tie in all metricsbefore it. Note that, for the first and last metric, large numbers are preferred while small numbers are preferredfor the second and third. Our implementation converts the sign of first and fourth metrics to make sorting easy.

In the sorted list, the top suspect is the first node. For best accuracy, it is important to choose monitorswisely. In this paper, we compare the following six monitor selection methods.

(1) Random Random selection method selects k monitors randomly. This means that, for any node x ∈ V ,the probability that x is selected as a monitor is k

|V | .

(2) Inter-Monitor Distance (Dist) This requires any pair of monitors to be at least d hops away. To dothat, it first randomly shuffles the list of all nodes. Then, from the first node, it checks whether it is at leastd hops away from all already-selected monitors. If it is, the node is selected as a monitor and the next node ischecked. Note that the first node is always selected as a monitor. This is repeated until k monitors are selectedor it is impossible to select any more monitors. Dist selection method finds the largest d which can choose kmonitors. To do that, it starts with a large value of d and decrements it every time it fails to choose k monitors,starting over with the smaller d until it can find k monitors.

(3) Number of Incoming Edges (NI) In this method, the number of incoming edges of each node is counted.Then, the top k nodes which have largest counts are chosen.

(4) NI+Dist This method combines NI and Dist. Nodes with a large number of incoming edges are preferredas monitors, but the algorithm also considers inter-monitor distance. To do that, it first sorts all nodes in thedescending order by the number of incoming edges of each node, then Dist is used to choose monitors. In otherwords, nodes in the sorted list are examined one by one and a node is chosen as a monitor if it is at least dhops away from all previously selected monitors. As in Dist, this method finds the largest d which can choose kmonitors.

(5) Betweenness Centrality (BC) This method calculates betweenness centrality4 for each node v, whichis defined as

C(v) =∑

s6=t 6=v∈V

σst(v)

σst

where σst is the number of shortest paths from s to t and σst(v) is the number of shortest paths from s to t thatpass through v. Then, the k nodes which have the largest betweenness centrality are chosen as monitors.

(6) BC+Dist This method combines BC and Dist. Nodes are first sorted by their betweenness centrality,then Dist is used to choose monitors.

The above six monitor selection algorithms produce different sets of monitors, which result in differentaccuracy in source finding. Section 3.2 compares these algorithms in detail.

2.2 Identifying Rumors

Given a piece of information, can we determine whether it is a rumor (false claim) or not using the set of monitorsthat received the information? We use the following two metrics for this classification.

2.2.1 Greedy Sources Set Size (GSSS)

If a rumor is initiated by some person intentionally, it is not independently corroborated by others. Hence, inthe absence of collusion, there is only one source of the rumor in the network. If a rumor is initiated by a smallcolluding group of people, the number of independent sources is just the size of the group. Conversely, if apiece of information is not a rumor, there may be many independent sources of the information. Therefore, it isimportant to estimate the number of independent sources correctly.

A set of nodes C is a valid source set if the following is satisfied: for all m ∈ M+, there exists n ∈ Cwhich satisfies d(n,m) 6= ∞. The question is, what is the minimum size of set C? Instead of calculating theexact solution with an exponential algorithm∗, we use the greedy approximation algorithm in Figure 1 to get anapproximate minimal source set. The algorithm calculates the set of candidate sources (C). For each candidatesource x, it also calculates the set of positive monitors (Px) covered by x that are used in Section 2.2.2.

∗For each node m in M+, we define Sm the set of nodes which have a path to m. Then calculating the minimal C isexactly same as the minimal hitting set problem among {Sm}m∈H .

C ← {}For each m ∈ V , Pm ← {}.For each m ∈M+, Sm ← the set of nodes which have a path to m.while M+ 6= {} do

Let x be one of the most frequent elements in all Sm’s where m ∈M+.Add x to C.For each m ∈M+, add m to Px and remove m from M+ if d(x,m) 6=∞.

end while

Figure 1. A Greedy algorithm for calculating an approximate minimal source set.

Initially, C and Pm for all m ∈ V are initialized to empty sets. At each iteration, a node x which can reachthe largest number of elements in M+ is chosen as a source. Node x is considered as one of the candidate sourcesand all monitors in M+ that are reachable from x are assumed to have received the information from x. Thenx is added to C. The reachable monitors are removed from M+ and put into Px. In the final state, C becomesthe Greedy Source Set (GSS), which is an approximate minimal source set. For each node x ∈ C, Px is the setof monitors that are expected to receive the information from x.

12

34

5

67 8

910

Figure 2. Greedy source selection overestimates rumor propagation distance.

2.2.2 Maximal Distance of Greedy Information Propagation (MDGIP)

The previous greedy algorithm tries to assign as many positive monitors as possible to each source, so theresulting greedy information propagation trees tend to become larger than the real ones. Figure 2 shows anexample with three original source nodes (black circles). Information from the sources propagates along the solidarrows. Note that, the dotted edges are not used for the actual rumor propagation. Suppose all nodes (black orwhite) are monitors. The greedy approach in Section 2.2.1 finds that it is possible to cover all positive monitorsusing only one source node. This means that C = {1} and P1 = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. As a result, a newlarge propagation tree is generated instead of the actual three small trees.

To estimate possible disparty between the actual propagation tree and the one constructed by the abovegreedy algorithm, we use a second metric. Namely, given a greedy source set C and the set of nodes thatreceive information from x (Px) for all x ∈ C, we define Maximal Distance of Greedy Information Propagation(MDGIP), calculated as:

maxx∈C,y∈Px

d(x, y)

where d(x, y) is the distance from x to y. Note that, when there are many actual sources, the estimated MDGIPtends to become large since many small propagation trees are combined into one greedy propagation tree.

In this section, we suggested two metrics: Greedy Source Set Size (GSSS) and Maximal Distance of GreedyInformation Propagation (MDGIP). Both metrics increase as the number of actual sources increases. In thefollowing section, we discuss how they can be used for rumor classification using actual social network data.

3. CASE STUDY

3.1 Data set

To apply our algorithm to a real social network, we extracted a social graph from Twitter. First, we obtained159271 tweets written in Dec. 2011 containing a special keyword†. These tweets were written by 39567 twitteraccounts.

In Twitter, tweets are propagated by retweets. When a user y retweets another user x’s tweet (or retweet),we assume that there is an edge from x to y. In total, we obtained 102796 edges from the crawled data. Theundirected version of this graph has 9243 connected components. In this evaluation, we focus on the largestconnected component G which has 30146 nodes and 102608 edges. Maximum in-degree and out-degree amongall nodes in G is 193 and 2264, respectively. The undirected version of G has a diameter of 12 hops.

Besides the topology, we also calculated Retweet probability of each edge x → y as the ratio of “x’s tweetsretweeted by y” to “all tweets of x.” Calculated Retweet probabilities were used to simulate random propagationof rumors.

3.2 Finding Rumor Sources

We first evaluate the accuracy of our approach in finding rumor sources. To simulate random rumor propagation,we did the following: (1) A random rumor source is selected, (2) Using retweet probability of each edge, the rumoris propagated, (3) if the rumor does not reach more than 1% of all nodes, it is considered as a negligible rumor,rumor propagation result is discarded, a new rumor source is selected and the same procedures are repeated. Foreach rumor propagation, we used our rumor source identification algorithm using different number of monitors:20, 40, 80, · · · , 5120 and we repeated this 200 times.

3.2.1 Rank of True Source

Using the method presented in Section 2.1, all nodes are sorted in the likelihood that they are the actual rumorsource. Figure 3 shows the average rank of the actual source in the output. In the ideal case, the rank shouldbe one which means that the top suspect is actually the rumor source. Note that, regardless of the monitorselection method, the rank of the true source generally decreases (i.e., improves by becoming closer to 1) as thenumber of monitors increases. Dist and NI+Dist generally show a bad accuracy. Random also performs poorlywhen the number of monitors is small, but it improves as more monitors are added. NI, BC and BC+Dist showbetter performance than the others. When the number of monitors is very large, the choice of monitor selectiondoes not matter that much anymore, and all algorithms converge.

One of the important factors that affects the accuracy of rumor source identification is the number of positivemonitors. Figure 4 shows the ratio of experiments in which no monitor received the rumor. In all monitorselection methods, the ratio decreases as the number of monitors increases. Among the four methods compared,the Dist selection method has the highest ratio. Dist basically maximizes inter-monitor distance, so it tends tochoose nodes on the boundary of the graph. Therefore, monitors selected by Dist have low probability of hearingrumors. The Random selection method also has a high ratio of negative monitors when the number of monitorsis small. The other methods (NI, NI+Dist, BC, BC+Dist) have small ratio compared to Dist and Random.When no monitor hears the rumor, it is very hard to find the source accurately as shown in Figure 3 (Randomand Dist when the number of monitors is 20, for example).

However, a larger number of positive monitors does not always lead to a more accurate result. Figure 5 showsthe average number of positive monitors when the number of monitors is 160. Figure 3 shows that BC has bestaccuracy, NI has second best, and the others are worse. Note that, the number of positive monitors in NI isalmost double of that in BC, but BC is more accurate. This means that it is not always helpful to have morepositive monitors.

†The actual used keyword is “Kim, Geuntae (in Korean),” a Korean politician who died in Dec. 2011. Instead ofusing Twitter API directly, we downloaded already-crawled tweets from Tweetrend.com. It is a third-party twitter website which shows the trend of popular keywords and the actual tweets in Korean.

20 40 80 160 320 640 1280 2560 5120RandomNIDistNI+DistBCBC+Dist

20591.64 15644.535 9199.785 3658.33 472.670000 9.775000 4.475000 3.765000 3.040000247.830000 47.020000 43.375000 41.635000 35.355000 26.910000 21.370000 15.625000 11.45000023873.88 22386.69 19227.55 16516.805 13809.575 9024.89 7.690000 7.805000 6.7500007896.42 5429.55 2981.365 1619.63 1593.43 974.420000 17.040000 12.755000 9.3050001875.565 180.275000 19.595000 17.270000 18.680000 14.735000 12.995000 10.550000 7.2900003669.07 1692.935 314.705000 159.160000 157.665000 5.615000 5.825000 4.510000 4.205000

1

10

100

1000

10000

100000

20 40 80 160 320 640 1280 2560 5120

Rank

of t

he A

ctua

l Sou

rce

Number of Monitors

RandomNIDistNI+DistBCBC+Dist

Figure 3. Average Rank of Actual Source in the output (out of 30146 nodes)

# Count of cases that No monitor heard the rumorRandomNIDistNI+DistBCBC+Dist

20 40 80 160 320 640 1280 2560 5120

0.6850 0.5200 0.3050 0.1200 0.0150 0.0000 0.0000 0.0000 0.00000.0050 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.00000.7950 0.7450 0.6400 0.5500 0.4600 0.3000 0.0000 0.0000 0.00000.2550 0.1750 0.0950 0.0500 0.0500 0.0300 0.0000 0.0000 0.00000.0600 0.0050 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.00000.1200 0.0550 0.0100 0.0050 0.0050 0.0000 0.0000 0.0000 0.0000

This figure shows the ratio of experiments (out of 200 experiments) that no sensor hears the rumor. In random selection, it decreases as the number of sensors increases.

0

0.25

0.5

0.75

1

20 40 80 160 320 640 1280 2560 5120

Ratio

Number of Monitors

RandomNIDistNI+DistBCBC+Dist

Figure 4. Ratio of experiments in which no monitor receives a rumor (out of 200 experiments)

3.2.2 Distance from Top Suspect to the True Source

Figure 6 shows the distance‡ between the top suspect and the actual source. In the ideal case, the distanceshould be zero, meaning the the top suspect is the source. Figure 6 shows a similar tendency as Figure 3. Thedistance decreases as more monitors are added. Dist shows the largest distance of all monitor selection methods.Random has large distances with a small number of monitors, but the distance decreases drastically as thenumber of monitors increase. BC and BC+Dist generally show the smallest distance between the top suspectand the actual source.

3.3 Identifying Rumors

As discussed in Section 2.2, rumors are usually initiated by a small number of people. In contrast, true informationcan be reported by many people independently. In this evaluation, we assumed that rumors have a small number(1 or 10) of sources and non-rumors have a large number (100 or 1000) of sources and show how their propagationfeatures are different.

For each number of sources (1, 10, 100 and 1000), monitor selection method, and number of monitors (20, 40,80, 160, 320 and 640), we repeated rumor identification 200 times and used the results for rumor identificationonly when there is at least one monitor that heard the rumor.

‡This distance is calculated over the undirected version of the graph.

Number of Heard

Monitors

Average Distance Between

Heard Monitors

BCNIBC+DistNI+DistRandomDist

17.575 1.7864245534.89 1.944263860.335 4.60.76 4.206349212.79 2.479169520.21 5.0

0

10

20

30

40

BC NI BC+Dist NI+Dist Random DistN

umbe

r of H

erad

Mon

itors

Figure 5. Number of Positive Monitors (Number of Monitors: 160)

20 40 80 160 320 640 1280 2560 5120RandomNIDistNI+DistBCBC+Dist

2.470000 2.170000 1.670000 1.135000 0.555000 0.315000 0.180000 0.160000 0.1400001.825000 1.665000 1.560000 1.425000 1.040000 0.755000 0.600000 0.470000 0.3600002.700000 2.610000 2.435000 2.290000 2.125000 1.845000 0.205000 0.175000 0.1400002.110000 1.910000 1.700000 1.505000 1.370000 1.080000 0.525000 0.385000 0.2350001.440000 1.105000 0.890000 0.930000 0.765000 0.550000 0.490000 0.420000 0.1650001.365000 1.385000 0.970000 0.650000 0.665000 0.520000 0.295000 0.150000 0.155000

0

1

2

3

20 40 80 160 320 640 1280 2560 5120

Dist

ance

(hop

s)

Number of Monitors

RandomNIDistNI+DistBCBC+Dist

Figure 6. Average Distance between the top suspect and the actual source

Dist Figure 7 shows average GSSS and MDGIP when Dist monitor selection method is used. Left figure showsthat, as the number of real sources increases, GSSS also increases. Right figure also shows that, as the numberof real sources increases, MDGIP also increases. These two graphs show that GSSS and MDGIP can be used toclassify a piece of information as a rumor or not since it is directly related to the number of sources.

GSSS (Greedy Source Set Size)

Rumor (NumSources=1)Rumor (NumSources=10)NonRumor (NumSources=100)NonRumor (NumSources=1000)MDGIP (Maximal Distance of Greedy Information Propagation)

Rumor (NumSources=1)Rumor (NumSources=10)NonRumor (NumSources=100)NonRumor (NumSources=1000)

20 40 80 160 320 6401.000000 1.000000 1.000000 1.000000 1.000000 1.000000

1.000000 1.000000 1.000000 1.010753 1.048000 1.096154

1.000000 1.039216 1.102273 1.170213 1.489011 2.238579

1.131783 1.392045 2.185930 4.330000 8.620000 17.690000

ms=20 ms=40 ms=80 ms=160 ms=320 ms=6402.414634 2.254902 2.250000 2.511111 2.962963 3.814286

2.352941 2.436364 2.514286 2.666667 3.024000 3.961538

2.866667 2.784314 2.727273 3.439716 4.307692 5.370558

3.790698 4.289773 5.407035 6.365000 7.400000 7.915000

0

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20 40 80 160 320 640

GSSS

GSS

S

Number of Monitors

0

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8

20 40 80 160 320 640

MDGIP

MDG

IP

Number of Monitors

Rumor (NumSources=1)Rumor (NumSources=10)NonRumor (NumSources=100)NonRumor (NumSources=1000)

Figure 7. GSSS and MDGIP (Monitor Selection: Dist)

GSSS (Greedy Source Set Size)

Rumor (NumSources=1)Rumor (NumSources=10)NonRumor (NumSources=100)NonRumor (NumSources=1000)MDGIP (Maximal Distance of Greedy Information Propagation)

Rumor (NumSources=1)Rumor (NumSources=10)NonRumor (NumSources=100)NonRumor (NumSources=1000)

ms=20 ms=40 ms=80 ms=160 ms=320 ms=6401.000000 1.000000 1.000000 1.000000 1.000000 1.000000

1.000000 1.000000 1.000000 1.000000 1.015306 1.025000

1.000000 1.000000 1.006849 1.061111 1.151515 1.430000

1.045161 1.155556 1.351759 2.085000 3.470000 6.405000

ms=20 ms=40 ms=80 ms=160 ms=320 ms=6402.920635 3.052083 3.525180 3.784091 3.761421 3.960000

3.158730 3.419048 3.634483 3.956757 4.051020 4.000000

3.322034 3.320000 3.972603 4.250000 4.484848 5.055000

4.225806 4.738889 5.271357 5.765000 5.855000 6.180000

0

1.75

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5.25

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20 40 80 160 320 640

GSSSG

SSS

Number of Monitors

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20 40 80 160 320 640

MDGIP

MDG

IP

Number of Monitors

Rumor (NumSources=1)Rumor (NumSources=10)NonRumor (NumSources=100)NonRumor (NumSources=1000)

Figure 8. GSSS and MDGIP (Monitor Selection: Random)

Random Figure 8 shows the results from Random monitor section. Overall, Figure 8 looks similar to Figure 7,but the difference of GSSS and MDGIP values with different number of sources is smaller.

NI Figure 9 shows the results from NI monitor selection. Contrary to the previous two monitor selectionmethods, it shows that GSSS does not change over different number of monitors or different number of sources.In the experiments, GSSS is alway one, which means that only one candidate source can cover all positivemonitors. It also shows that MDGIP and the number of sources do not have strictly consistent relation. Overall,GSSS and MDGIP for the NI monitor selection algorithm do not give much information for rumor identification.

GSSS (Greedy Source Set Size)

Rumor (NumSources=1)Rumor (NumSources=10)NonRumor (NumSources=100)NonRumor (NumSources=1000)MDGIP (Maximal Distance of Greedy Information Propagation)

Rumor (NumSources=1)Rumor (NumSources=10)NonRumor (NumSources=100)NonRumor (NumSources=1000)

ms=20 ms=40 ms=80 ms=160 ms=320 ms=6401.000000 1.000000 1.000000 1.000000 1.000000 1.000000

1.000000 1.000000 1.000000 1.000000 1.000000 1.000000

1.000000 1.000000 1.000000 1.000000 1.000000 1.000000

1.000000 1.000000 1.000000 1.000000 1.000000 1.000000

ms=20 ms=40 ms=80 ms=160 ms=320 ms=6403.150754 3.675000 3.870000 3.665000 4.080000 4.475000

2.863636 3.585000 3.700000 3.660000 4.030000 4.310000

3.251256 3.400000 3.610000 3.625000 3.990000 4.300000

3.475000 3.780000 3.835000 3.975000 4.235000 4.345000

0

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20 40 80 160 320 640

GSSS

GSS

S

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20 40 80 160 320 640

MDGIP

MDG

IP

Number of Monitors

Rumor (NumSources=1)Rumor (NumSources=10)NonRumor (NumSources=100)NonRumor (NumSources=1000)

Figure 9. GSSS and MDGIP (Monitor Selection: NI)

NI+Dist Figure 10 shows the results from NI+Dist monitor selection. It shows the overall tendency thatGSSS and MDGIP increases with the number of sources.

BC Figure 11 shows the results from BC monitor selection. Similar to NI, GSSS does not change and MDGIPshows inconsistent values with different number of sources.

BC+Dist Figure 12 shows the results from BC+Dist monitor selection. Similar to Dist, Random and NI+Dist,it shows the overall tendency that GSSS and MDGIP increase with the number of sources.

3.3.1 Classification

Previously, we have shown that GSSS and MDGIP can be used to classify a piece of information as rumor ornon-rumor. Figure 13 visualizes GSSS/MDGIP and rumor classification in more detail. Four figures compare

GSSS (Greedy Source Set Size)

Rumor (NumSources=1)Rumor (NumSources=10)NonRumor (NumSources=100)NonRumor (NumSources=1000)MDGIP (Maximal Distance of Greedy Information Propagation)

Rumor (NumSources=1)Rumor (NumSources=10)NonRumor (NumSources=100)NonRumor (NumSources=1000)

ms=20 ms=40 ms=80 ms=160 ms=320 ms=6401.000000 1.000000 1.000000 1.000000 1.000000 1.000000

1.000000 1.000000 1.000000 1.000000 1.000000 1.030928

1.000000 1.000000 1.000000 1.005348 1.095477 1.465000

1.000000 1.025253 1.065000 1.485000 3.580000 9.375000

ms=20 ms=40 ms=80 ms=160 ms=320 ms=6403.677852 4.060606 4.441989 4.505263 4.900000 5.051546

3.537879 4.109677 4.403409 4.839779 5.069519 5.500000

3.909774 4.253333 4.652941 4.812834 5.613065 6.325000

4.360406 4.787879 5.585000 6.825000 7.365000 7.570000

0

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SSS

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MDG

IP

Number of Monitors

Rumor (NumSources=1)Rumor (NumSources=10)NonRumor (NumSources=100)NonRumor (NumSources=1000)

Figure 10. GSSS and MDGIP (Monitor Selection: NI+Dist)

GSSS (Greedy Source Set Size)

Rumor (NumSources=1)Rumor (NumSources=10)NonRumor (NumSources=100)NonRumor (NumSources=1000)MDGIP (Maximal Distance of Greedy Information Propagation)

Rumor (NumSources=1)Rumor (NumSources=10)NonRumor (NumSources=100)NonRumor (NumSources=1000)

ms=20 ms=40 ms=80 ms=160 ms=320 ms=6401.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000

1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.005000 1.010000 1.170000

1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.025000 1.055000 3.515000

1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 2.105000 3.070000 23.410000

ms=20 ms=40 ms=80 ms=160 ms=320 ms=6403.659574 3.628141 3.875000 4.195000 4.805000 5.015000 5.040000 5.645000 4.145000

3.379888 3.568528 3.894472 4.370000 4.655000 4.800000 5.420000 5.620000 4.565000

3.525714 3.558974 3.909091 4.280000 4.645000 4.905000 5.720000 6.350000 6.255000

3.495000 3.865000 4.240000 4.820000 5.755000 6.310000 7.530000 8.035000 7.785000

0

0.25

0.5

0.75

1

20 40 80 160 320 640

GSSS

GSS

S

Number of Monitors

0

1.75

3.5

5.25

7

20 40 80 160 320 640

MDGIP

MDG

IP

Number of Monitors

Rumor (NumSources=1)Rumor (NumSources=10)NonRumor (NumSources=100)NonRumor (NumSources=1000)

Figure 11. GSSS and MDGIP (Monitor Selection: BC)

the cases in which rumors have 1 or 10 sources and non-rumors have 100 or 1000 sources when Dist monitorselection algorithm is used and the number of monitors is 640. When there is a large difference in the numberof sources of rumors and non-rumors (two right figures), it is shown that rumors and non-rumors are clearlyseparated. However, when the difference is smaller (two left figures), rumors and non-rumors overlap in somecases which causes inaccuracy in classification.

Using the experimental data, we evaluated how accurately logistic regression can classify rumor and non-rumors. We used the first half of experimental data as training set and the second half as test set. Table 1summarizes the results when the number of monitors is 640. The first column of Table 1 shows the monitorselection algorithm. The second and third columns show the number of sources of a rumor and a non-rumor.Next three columns (4–6) show the classification results of 100 rumors. They are classified as rumors (TruePositive, Column 4) or non-rumors (False Negative, Column 5). If no monitor hears the rumor, our classificationalgorithm cannot work, so it cannot be classified (Column 6). Similarly, last three columns (7–9) show theclassification results of 100 non-rumors. They are classified as non-rumors (True Negative, Column 7) or rumors(False Positive, Column 8). If no monitor hears anything, it cannot be classified (Column 9).

From the table, we can observe that, if rumors and non-rumors have very large difference in the number ofsources, rumor classification can be done with very high accuracy. As the difference in the number of sources ofrumors and non-rumors decreases, it gets harder to classify rumors and non-rumors accurately.

Another observation from the table is that the algorithms which show good results in rumor source identifi-cation (BC and BC+Dist) do not always work well in rumor classification. This is because the two tasks havedifferent conditions for best performance. In rumor source identification, it is best to have monitors near therumor source, so that they receive the rumor and estimate the rumor source based on their locations. In rumorclassification, it is best to have monitors in various places in the rumor propagation trees so that GSSS andMDGIP can be estimated accurately. We leave finding a monitor selection algorithm that is good for both tasksas future work.

GSSS (Greedy Source Set Size)

Rumor (NumSources=1)Rumor (NumSources=10)NonRumor (NumSources=100)NonRumor (NumSources=1000)MDGIP (Maximal Distance of Greedy Information Propagation)

Rumor (NumSources=1)Rumor (NumSources=10)NonRumor (NumSources=100)NonRumor (NumSources=1000)

ms=20 ms=40 ms=80 ms=160 ms=320 ms=6401.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000

1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.015000 1.170000 1.440000

1.000000 1.000000 1.000000 1.000000 1.015000 1.015000 1.255000 3.170000 6.285000

1.000000 1.000000 1.000000 1.000000 1.370000 1.545000 5.310000 21.220000 41.075000

ms=20 ms=40 ms=80 ms=160 ms=320 ms=6403.551136 3.809524 3.984848 4.351759 4.517588 5.225000 4.815000 3.985000 3.995000

3.486631 3.702564 3.954082 4.295000 4.750000 5.405000 5.020000 4.240000 4.635000

3.305195 3.688525 4.037037 4.250000 5.175000 5.870000 5.890000 5.925000 6.235000

3.538071 4.185000 5.440000 5.710000 7.025000 8.060000 7.025000 7.355000 7.830000

0

0.4

0.8

1.2

1.6

20 40 80 160 320 640

GSSSG

SSS

Number of Monitors

0

2.25

4.5

6.75

9

20 40 80 160 320 640

MDGIP

MDG

IP

Number of Monitors

Rumor (NumSources=1)Rumor (NumSources=10)NonRumor (NumSources=100)NonRumor (NumSources=1000)

Figure 12. GSSS and MDGIP (Monitor Selection: BC+Dist)

Rumor (NumSources

=10)

Num of monitors =

640

NonRumor (NumSources

=100)

Num of monitors =

6401 6.000000 3 7.0000001 3.000000 1 6.0000001 4.000000 2 9.0000001 4.000000 2 2.0000001 4.000000 3 5.0000001 4.000000 1 4.0000001 7.000000 2 4.0000001 5.000000 2 6.0000001 0.000000 2 8.0000001 9.000000 1 0.0000001 10.000000 4 7.0000001 1.000000 2 9.0000001 9.000000 3 8.0000001 3.000000 6 1.0000001 0.000000 2 1.0000001 0.000000 4 6.0000001 1.000000 2 8.0000001 8.000000 1 5.0000001 3.000000 2 8.0000001 4.000000 2 6.0000001 2.000000 2 5.0000001 1.000000 3 7.0000001 2.000000 2 7.0000001 3.000000 1 0.0000001 0.000000 3 1.0000001 6.000000 2 8.0000001 3.000000 2 4.0000001 5.000000 3 5.0000001 5.000000 3 8.0000001 3.000000 2 9.0000001 3.000000 1 9.0000001 6.000000 2 8.0000002 8.000000 1 8.0000001 0.000000 3 4.0000001 8.000000 4 9.0000001 4.000000 1 7.0000001 4.000000 1 0.0000001 6.000000 1 9.0000001 5.000000 4 6.0000001 4.000000 3 1.0000001 4.000000 2 10.0000001 1.000000 1 0.0000002 6.000000 1 9.0000001 7.000000 3 0.0000001 2.000000 6 3.0000001 3.000000 3 6.0000002 4.000000 3 4.0000001 5.000000 1 0.0000001 3.000000 4 7.0000001 0.000000 2 7.0000001 3.000000 3 5.0000001 9.000000 1 4.0000001 0.000000 2 1.0000001 7.000000 3 5.0000001 0.000000 1 6.0000001 1.000000 1 6.0000001 3.000000 2 8.0000002 7.000000 2 5.0000001 4.000000 3 6.0000001 4.000000 3 5.0000001 8.000000 5 2.0000001 7.000000 2 9.0000001 0.000000 2 8.0000001 5.000000 1 6.0000001 8.000000 1 8.0000001 8.000000 3 1.0000001 1.000000 2 1.0000002 1.000000 1 7.0000001 7.000000 2 7.0000001 7.000000 1 0.0000001 0.000000 1 7.0000001 0.000000 1 9.0000001 3.000000 3 5.0000002 6.000000 3 6.0000001 4.000000 2 7.0000001 5.000000 1 10.0000002 1.000000 2 1.0000001 3.000000 2 4.0000001 4.000000 1 9.0000001 1.000000 2 7.0000001 6.000000 3 5.0000001 5.000000 3 4.0000001 4.000000 1 7.0000001 1.000000 2 0.0000001 4.000000 1 0.0000002 2.000000 1 8.0000001 6.000000 1 7.0000001 7.000000 2 9.0000002 2.000000 1 8.0000001 6.000000 3 4.0000002 0.000000 4 10.0000001 0.000000 1 7.0000001 5.000000 2 8.0000002 1.000000 1 9.0000001 3.000000 3 7.0000001 4.000000 2 4.0000001 0.000000 2 8.0000001 7.000000 2 7.0000001 10.000000 1 7.0000001 8.000000 1 2.0000001 4.000000 5 8.0000001 0.000000 3 1.0000001 4.000000 2 7.0000001 8.000000 3 10.0000001 6.000000 1 7.0000001 3.000000 1 5.0000001 3.000000 3 5.0000001 0.000000 1 0.0000001 7.000000 4 6.0000001 5.000000 3 7.0000001 3.000000 1 9.0000001 7.000000 2 6.0000001 5.000000 1 3.0000001 0.000000 2 7.0000001 4.000000 4 6.0000001 2.000000 3 6.0000001 0.000000 1 8.0000001 0.000000 2 5.0000001 8.000000 2 3.0000001 5.000000 1 6.0000002 5.000000 6 7.0000001 3.000000 2 9.0000001 1.000000 2 4.0000002 4.000000 2 2.0000001 1.000000 1 1.0000001 4.000000 2 6.0000001 3.000000 2 0.0000001 7.000000 3 7.0000001 5.000000 1 7.0000001 6.000000 3 1.0000001 0.000000 1 0.0000001 5.000000 2 7.0000001 10.000000 2 5.0000001 5.000000 3 6.0000001 8.000000 2 5.0000001 4.000000 4 8.0000001 5.000000 2 5.0000001 4.000000 1 7.0000001 5.000000 2 6.0000001 4.000000 4 6.0000001 4.000000 2 1.0000001 4.000000 1 7.0000001 5.000000 1 5.0000001 0.000000 1 5.0000002 5.000000 5 6.0000001 5.000000 1 7.0000001 3.000000 2 6.0000001 4.000000 3 1.0000002 6.000000 2 6.0000001 2.000000 2 5.0000001 4.000000 3 7.0000001 3.000000 2 6.0000001 0.000000 2 8.0000001 4.000000 3 1.0000001 5.000000 2 1.0000001 5.000000 4 6.000000

2 5.0000002 1.0000004 4.0000002 8.0000003 0.0000003 6.0000003 7.0000005 7.0000001 9.0000001 3.0000002 8.0000002 4.0000001 0.0000002 4.0000002 0.0000001 1.0000002 5.0000002 10.0000004 5.0000002 4.0000002 2.0000004 4.0000002 9.0000004 5.0000003 6.0000004 8.0000001 5.0000003 7.0000001 5.0000002 8.0000002 7.0000001 4.0000001 7.0000005 5.0000001 1.0000004 4.0000005 1.0000002 7.0000003 6.0000003 5.0000001 12.000000

0

3.75

7.5

11.25

15

0 1 2 3 4 5 6

MDG

IP

GSSSRumor (NumSources=10)NonRumor (NumSources=100)

Rumor (NumSources

=1)

Num of monitors =

640

NonRumor (NumSources

=1000)

Num of monitors =

6401 5.000000 21 8.0000001 5.000000 18 7.0000001 4.000000 15 9.0000001 5.000000 14 7.0000001 3.000000 19 8.0000001 6.000000 10 7.0000001 5.000000 13 8.0000001 4.000000 24 9.0000001 4.000000 14 8.0000001 4.000000 26 8.0000001 3.000000 17 9.0000001 1.000000 15 5.0000001 11.000000 22 7.0000001 4.000000 16 10.0000001 8.000000 22 9.0000001 6.000000 22 9.0000001 1.000000 25 6.0000001 2.000000 19 10.0000001 9.000000 24 8.0000001 3.000000 22 9.0000001 5.000000 11 10.0000001 5.000000 18 8.0000001 3.000000 16 6.0000001 8.000000 22 7.0000001 1.000000 16 5.0000001 3.000000 21 11.0000001 7.000000 19 8.0000001 1.000000 11 9.0000001 5.000000 19 8.0000001 3.000000 22 9.0000001 7.000000 18 8.0000001 6.000000 18 8.0000001 5.000000 20 9.0000001 0.000000 22 7.0000001 5.000000 23 7.0000001 6.000000 17 8.0000001 8.000000 16 8.0000001 3.000000 16 8.0000001 2.000000 13 6.0000001 3.000000 22 8.0000001 1.000000 22 7.0000001 3.000000 15 6.0000001 6.000000 17 8.0000001 0.000000 11 7.0000001 5.000000 20 8.0000001 0.000000 21 6.0000001 3.000000 16 6.0000001 8.000000 17 9.0000001 1.000000 16 10.0000001 1.000000 15 9.0000001 4.000000 20 9.0000001 3.000000 19 7.0000001 3.000000 17 6.0000001 1.000000 14 8.0000001 4.000000 22 6.0000001 4.000000 15 12.0000001 5.000000 22 6.0000001 2.000000 13 9.0000001 0.000000 20 7.0000001 5.000000 11 6.0000001 5.000000 19 10.0000001 5.000000 18 8.0000001 4.000000 27 13.0000001 0.000000 16 7.0000001 5.000000 18 7.0000001 3.000000 13 7.0000001 5.000000 13 9.0000001 7.000000 13 8.0000001 0.000000 15 8.0000001 3.000000 19 9.0000001 4.000000 16 8.0000001 4.000000 21 6.0000001 6.000000 22 6.0000001 4.000000 10 9.0000001 7.000000 25 6.0000001 3.000000 11 8.0000001 3.000000 24 5.0000001 3.000000 18 8.0000001 4.000000 26 10.0000001 0.000000 23 8.0000001 6.000000 25 7.0000001 3.000000 17 7.0000001 3.000000 18 7.0000001 1.000000 18 5.0000001 4.000000 16 6.0000001 1.000000 21 8.0000001 3.000000 21 8.0000001 4.000000 20 7.0000001 0.000000 24 10.0000001 5.000000 14 7.0000001 5.000000 17 7.0000001 7.000000 14 9.0000001 7.000000 8 8.0000001 3.000000 12 6.0000001 5.000000 22 9.0000001 5.000000 11 8.0000001 1.000000 19 10.0000001 3.000000 23 6.0000001 5.000000 19 7.0000001 0.000000 19 7.0000001 3.000000 26 7.0000001 2.000000 15 7.0000001 5.000000 20 11.0000001 6.000000 23 11.0000001 5.000000 14 5.0000001 4.000000 18 7.0000001 2.000000 23 11.0000001 5.000000 16 6.0000001 4.000000 16 8.0000001 3.000000 17 6.0000001 0.000000 12 8.0000001 3.000000 16 8.0000001 0.000000 19 10.0000001 5.000000 8 6.0000001 5.000000 18 6.0000001 5.000000 13 7.0000001 0.000000 22 5.0000001 4.000000 14 7.0000001 6.000000 12 9.0000001 0.000000 24 9.0000001 1.000000 12 7.0000001 7.000000 23 9.0000001 1.000000 12 8.0000001 5.000000 14 8.0000001 3.000000 15 7.0000001 8.000000 15 7.0000001 0.000000 22 10.0000001 1.000000 20 6.0000001 2.000000 12 9.0000001 2.000000 17 9.0000001 6.000000 12 11.0000001 4.000000 17 6.0000001 6.000000 19 6.0000001 4.000000 19 8.0000001 6.000000 25 5.0000001 3.000000 24 11.0000001 7.000000 16 9.0000001 1.000000 17 9.0000001 8.000000 18 9.0000001 8.000000 17 7.000000

23 8.00000011 8.00000015 8.00000018 6.00000013 8.00000014 7.00000023 7.00000024 7.00000021 10.00000015 6.00000014 9.00000015 9.00000015 7.00000019 7.00000018 9.00000019 14.00000018 11.00000015 8.00000019 8.00000016 8.00000021 9.00000015 9.00000010 7.00000025 7.00000026 10.00000020 12.00000015 9.00000017 7.00000014 7.00000024 9.00000021 6.00000018 7.00000018 9.00000021 6.00000016 10.00000016 6.00000017 7.00000017 8.00000025 7.00000016 9.00000020 6.00000014 9.00000016 9.00000018 6.00000020 10.00000011 9.00000021 7.00000020 7.00000022 9.00000016 6.00000013 9.00000017 10.00000013 8.00000011 11.00000013 5.00000016 9.00000013 7.00000015 11.00000015 8.00000019 6.000000

0

3.75

7.5

11.25

15

0 7.5 15 22.5 30

MDG

IP

GSSSRumor (NumSources=1)NonRumor (NumSources=1000)

Rumor (NumSources

=1)

Num of monitors =

640

NonRumor (NumSources

=100)

Num of monitors =

6401 5.000000 3 7.0000001 5.000000 1 6.0000001 4.000000 2 9.0000001 5.000000 2 2.0000001 3.000000 3 5.0000001 6.000000 1 4.0000001 5.000000 2 4.0000001 4.000000 2 6.0000001 4.000000 2 8.0000001 4.000000 1 0.0000001 3.000000 4 7.0000001 1.000000 2 9.0000001 11.000000 3 8.0000001 4.000000 6 1.0000001 8.000000 2 1.0000001 6.000000 4 6.0000001 1.000000 2 8.0000001 2.000000 1 5.0000001 9.000000 2 8.0000001 3.000000 2 6.0000001 5.000000 2 5.0000001 5.000000 3 7.0000001 3.000000 2 7.0000001 8.000000 1 0.0000001 1.000000 3 1.0000001 3.000000 2 8.0000001 7.000000 2 4.0000001 1.000000 3 5.0000001 5.000000 3 8.0000001 3.000000 2 9.0000001 7.000000 1 9.0000001 6.000000 2 8.0000001 5.000000 1 8.0000001 0.000000 3 4.0000001 5.000000 4 9.0000001 6.000000 1 7.0000001 8.000000 1 0.0000001 3.000000 1 9.0000001 2.000000 4 6.0000001 3.000000 3 1.0000001 1.000000 2 10.0000001 3.000000 1 0.0000001 6.000000 1 9.0000001 0.000000 3 0.0000001 5.000000 6 3.0000001 0.000000 3 6.0000001 3.000000 3 4.0000001 8.000000 1 0.0000001 1.000000 4 7.0000001 1.000000 2 7.0000001 4.000000 3 5.0000001 3.000000 1 4.0000001 3.000000 2 1.0000001 1.000000 3 5.0000001 4.000000 1 6.0000001 4.000000 1 6.0000001 5.000000 2 8.0000001 2.000000 2 5.0000001 0.000000 3 6.0000001 5.000000 3 5.0000001 5.000000 5 2.0000001 5.000000 2 9.0000001 4.000000 2 8.0000001 0.000000 1 6.0000001 5.000000 1 8.0000001 3.000000 3 1.0000001 5.000000 2 1.0000001 7.000000 1 7.0000001 0.000000 2 7.0000001 3.000000 1 0.0000001 4.000000 1 7.0000001 4.000000 1 9.0000001 6.000000 3 5.0000001 4.000000 3 6.0000001 7.000000 2 7.0000001 3.000000 1 10.0000001 3.000000 2 1.0000001 3.000000 2 4.0000001 4.000000 1 9.0000001 0.000000 2 7.0000001 6.000000 3 5.0000001 3.000000 3 4.0000001 3.000000 1 7.0000001 1.000000 2 0.0000001 4.000000 1 0.0000001 1.000000 1 8.0000001 3.000000 1 7.0000001 4.000000 2 9.0000001 0.000000 1 8.0000001 5.000000 3 4.0000001 5.000000 4 10.0000001 7.000000 1 7.0000001 7.000000 2 8.0000001 3.000000 1 9.0000001 5.000000 3 7.0000001 5.000000 2 4.0000001 1.000000 2 8.0000001 3.000000 2 7.0000001 5.000000 1 7.0000001 0.000000 1 2.0000001 3.000000 5 8.0000001 2.000000 3 1.0000001 5.000000 2 7.0000001 6.000000 3 10.0000001 5.000000 1 7.0000001 4.000000 1 5.0000001 2.000000 3 5.0000001 5.000000 1 0.0000001 4.000000 4 6.0000001 3.000000 3 7.0000001 0.000000 1 9.0000001 3.000000 2 6.0000001 0.000000 1 3.0000001 5.000000 2 7.0000001 5.000000 4 6.0000001 5.000000 3 6.0000001 0.000000 1 8.0000001 4.000000 2 5.0000001 6.000000 2 3.0000001 0.000000 1 6.0000001 1.000000 6 7.0000001 7.000000 2 9.0000001 1.000000 2 4.0000001 5.000000 2 2.0000001 3.000000 1 1.0000001 8.000000 2 6.0000001 0.000000 2 0.0000001 1.000000 3 7.0000001 2.000000 1 7.0000001 2.000000 3 1.0000001 6.000000 1 0.0000001 4.000000 2 7.0000001 6.000000 2 5.0000001 4.000000 3 6.0000001 6.000000 2 5.0000001 3.000000 4 8.0000001 7.000000 2 5.0000001 1.000000 1 7.0000001 8.000000 2 6.0000001 8.000000 4 6.000000

2 1.0000001 7.0000001 5.0000001 5.0000005 6.0000001 7.0000002 6.0000003 1.0000002 6.0000002 5.0000003 7.0000002 6.0000002 8.0000003 1.0000002 1.0000004 6.0000002 5.0000002 1.0000004 4.0000002 8.0000003 0.0000003 6.0000003 7.0000005 7.0000001 9.0000001 3.0000002 8.0000002 4.0000001 0.0000002 4.0000002 0.0000001 1.0000002 5.0000002 10.0000004 5.0000002 4.0000002 2.0000004 4.0000002 9.0000004 5.0000003 6.0000004 8.0000001 5.0000003 7.0000001 5.0000002 8.0000002 7.0000001 4.0000001 7.0000005 5.0000001 1.0000004 4.0000005 1.0000002 7.0000003 6.0000003 5.0000001 12.000000

0

3.75

7.5

11.25

15

0 1.5 3 4.5 6

MDG

IP

GSSSRumor (NumSources=1)NonRumor (NumSources=100)

Rumor (NumSources

=10)

Num of monitors =

640

NonRumor (NumSources

=1000)

Num of monitors =

6401 6.000000 21 8.0000001 3.000000 18 7.0000001 4.000000 15 9.0000001 4.000000 14 7.0000001 4.000000 19 8.0000001 4.000000 10 7.0000001 7.000000 13 8.0000001 5.000000 24 9.0000001 0.000000 14 8.0000001 9.000000 26 8.0000001 10.000000 17 9.0000001 1.000000 15 5.0000001 9.000000 22 7.0000001 3.000000 16 10.0000001 0.000000 22 9.0000001 0.000000 22 9.0000001 1.000000 25 6.0000001 8.000000 19 10.0000001 3.000000 24 8.0000001 4.000000 22 9.0000001 2.000000 11 10.0000001 1.000000 18 8.0000001 2.000000 16 6.0000001 3.000000 22 7.0000001 0.000000 16 5.0000001 6.000000 21 11.0000001 3.000000 19 8.0000001 5.000000 11 9.0000001 5.000000 19 8.0000001 3.000000 22 9.0000001 3.000000 18 8.0000001 6.000000 18 8.0000002 8.000000 20 9.0000001 0.000000 22 7.0000001 8.000000 23 7.0000001 4.000000 17 8.0000001 4.000000 16 8.0000001 6.000000 16 8.0000001 5.000000 13 6.0000001 4.000000 22 8.0000001 4.000000 22 7.0000001 1.000000 15 6.0000002 6.000000 17 8.0000001 7.000000 11 7.0000001 2.000000 20 8.0000001 3.000000 21 6.0000002 4.000000 16 6.0000001 5.000000 17 9.0000001 3.000000 16 10.0000001 0.000000 15 9.0000001 3.000000 20 9.0000001 9.000000 19 7.0000001 0.000000 17 6.0000001 7.000000 14 8.0000001 0.000000 22 6.0000001 1.000000 15 12.0000001 3.000000 22 6.0000002 7.000000 13 9.0000001 4.000000 20 7.0000001 4.000000 11 6.0000001 8.000000 19 10.0000001 7.000000 18 8.0000001 0.000000 27 13.0000001 5.000000 16 7.0000001 8.000000 18 7.0000001 8.000000 13 7.0000001 1.000000 13 9.0000002 1.000000 13 8.0000001 7.000000 15 8.0000001 7.000000 19 9.0000001 0.000000 16 8.0000001 0.000000 21 6.0000001 3.000000 22 6.0000002 6.000000 10 9.0000001 4.000000 25 6.0000001 5.000000 11 8.0000002 1.000000 24 5.0000001 3.000000 18 8.0000001 4.000000 26 10.0000001 1.000000 23 8.0000001 6.000000 25 7.0000001 5.000000 17 7.0000001 4.000000 18 7.0000001 1.000000 18 5.0000001 4.000000 16 6.0000002 2.000000 21 8.0000001 6.000000 21 8.0000001 7.000000 20 7.0000002 2.000000 24 10.0000001 6.000000 14 7.0000002 0.000000 17 7.0000001 0.000000 14 9.0000001 5.000000 8 8.0000002 1.000000 12 6.0000001 3.000000 22 9.0000001 4.000000 11 8.0000001 0.000000 19 10.0000001 7.000000 23 6.0000001 10.000000 19 7.0000001 8.000000 19 7.0000001 4.000000 26 7.0000001 0.000000 15 7.0000001 4.000000 20 11.0000001 8.000000 23 11.0000001 6.000000 14 5.0000001 3.000000 18 7.0000001 3.000000 23 11.0000001 0.000000 16 6.0000001 7.000000 16 8.0000001 5.000000 17 6.0000001 3.000000 12 8.0000001 7.000000 16 8.0000001 5.000000 19 10.0000001 0.000000 8 6.0000001 4.000000 18 6.0000001 2.000000 13 7.0000001 0.000000 22 5.0000001 0.000000 14 7.0000001 8.000000 12 9.0000001 5.000000 24 9.0000002 5.000000 12 7.0000001 3.000000 23 9.0000001 1.000000 12 8.0000002 4.000000 14 8.0000001 1.000000 15 7.0000001 4.000000 15 7.0000001 3.000000 22 10.0000001 7.000000 20 6.0000001 5.000000 12 9.0000001 6.000000 17 9.0000001 0.000000 12 11.0000001 5.000000 17 6.0000001 10.000000 19 6.0000001 5.000000 19 8.0000001 8.000000 25 5.0000001 4.000000 24 11.0000001 5.000000 16 9.0000001 4.000000 17 9.0000001 5.000000 18 9.0000001 4.000000 17 7.0000001 4.000000 23 8.0000001 4.000000 11 8.0000001 5.000000 15 8.0000001 0.000000 18 6.0000002 5.000000 13 8.0000001 5.000000 14 7.0000001 3.000000 23 7.0000001 4.000000 24 7.0000002 6.000000 21 10.0000001 2.000000 15 6.0000001 4.000000 14 9.0000001 3.000000 15 9.0000001 0.000000 15 7.0000001 4.000000 19 7.0000001 5.000000 18 9.0000001 5.000000 19 14.000000

18 11.00000015 8.00000019 8.00000016 8.00000021 9.00000015 9.00000010 7.00000025 7.00000026 10.00000020 12.00000015 9.00000017 7.00000014 7.00000024 9.00000021 6.00000018 7.00000018 9.00000021 6.00000016 10.00000016 6.00000017 7.00000017 8.00000025 7.00000016 9.00000020 6.00000014 9.00000016 9.00000018 6.00000020 10.00000011 9.00000021 7.00000020 7.00000022 9.00000016 6.00000013 9.00000017 10.00000013 8.00000011 11.00000013 5.00000016 9.00000013 7.00000015 11.00000015 8.00000019 6.000000

0

3.75

7.5

11.25

15

0 7.5 15 22.5 30

MDG

IP

GSSSRumor (NumSources=10)NonRumor (NumSources=1000)

Rumor (NumSources

=10)

Num of monitors =

640

NonRumor (NumSources

=100)

Num of monitors =

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0

3.75

7.5

11.25

15

0 1 2 3 4 5 6

MDG

IP

GSSSRumor (NumSources=10)NonRumor (NumSources=100)

Rumor (NumSources

=1)

Num of monitors =

640

NonRumor (NumSources

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Num of monitors =

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0

3.75

7.5

11.25

15

0 7.5 15 22.5 30

MDG

IP

GSSSRumor (NumSources=1)NonRumor (NumSources=1000)

Rumor (NumSources

=1)

Num of monitors =

640

NonRumor (NumSources

=100)

Num of monitors =

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0

3.75

7.5

11.25

15

0 1.5 3 4.5 6

MDG

IP

GSSSRumor (NumSources=1)NonRumor (NumSources=100)

Rumor (NumSources

=10)

Num of monitors =

640

NonRumor (NumSources

=1000)

Num of monitors =

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0

3.75

7.5

11.25

15

0 7.5 15 22.5 30

MDG

IP

GSSSRumor (NumSources=10)NonRumor (NumSources=1000)

Rumor (NumSources

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Num of monitors =

640

NonRumor (NumSources

=100)

Num of monitors =

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0

3.75

7.5

11.25

15

0 1 2 3 4 5 6

MDG

IP

GSSSRumor (NumSources=10)NonRumor (NumSources=100)

Rumor (NumSources

=1)

Num of monitors =

640

NonRumor (NumSources

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Num of monitors =

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0

3.75

7.5

11.25

15

0 7.5 15 22.5 30

MDG

IP

GSSSRumor (NumSources=1)NonRumor (NumSources=1000)

Rumor (NumSources

=1)

Num of monitors =

640

NonRumor (NumSources

=100)

Num of monitors =

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0

3.75

7.5

11.25

15

0 1.5 3 4.5 6

MDG

IP

GSSSRumor (NumSources=1)NonRumor (NumSources=100)

Rumor (NumSources

=10)

Num of monitors =

640

NonRumor (NumSources

=1000)

Num of monitors =

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0

3.75

7.5

11.25

15

0 7.5 15 22.5 30

MDG

IP

GSSSRumor (NumSources=10)NonRumor (NumSources=1000)

Rumor (NumSources

=10)

Num of monitors =

640

NonRumor (NumSources

=100)

Num of monitors =

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0

3.75

7.5

11.25

15

0 1 2 3 4 5 6

MDG

IP

GSSSRumor (NumSources=10)NonRumor (NumSources=100)

Rumor (NumSources

=1)

Num of monitors =

640

NonRumor (NumSources

=1000)

Num of monitors =

6401 5.000000 21 8.0000001 5.000000 18 7.0000001 4.000000 15 9.0000001 5.000000 14 7.0000001 3.000000 19 8.0000001 6.000000 10 7.0000001 5.000000 13 8.0000001 4.000000 24 9.0000001 4.000000 14 8.0000001 4.000000 26 8.0000001 3.000000 17 9.0000001 1.000000 15 5.0000001 11.000000 22 7.0000001 4.000000 16 10.0000001 8.000000 22 9.0000001 6.000000 22 9.0000001 1.000000 25 6.0000001 2.000000 19 10.0000001 9.000000 24 8.0000001 3.000000 22 9.0000001 5.000000 11 10.0000001 5.000000 18 8.0000001 3.000000 16 6.0000001 8.000000 22 7.0000001 1.000000 16 5.0000001 3.000000 21 11.0000001 7.000000 19 8.0000001 1.000000 11 9.0000001 5.000000 19 8.0000001 3.000000 22 9.0000001 7.000000 18 8.0000001 6.000000 18 8.0000001 5.000000 20 9.0000001 0.000000 22 7.0000001 5.000000 23 7.0000001 6.000000 17 8.0000001 8.000000 16 8.0000001 3.000000 16 8.0000001 2.000000 13 6.0000001 3.000000 22 8.0000001 1.000000 22 7.0000001 3.000000 15 6.0000001 6.000000 17 8.0000001 0.000000 11 7.0000001 5.000000 20 8.0000001 0.000000 21 6.0000001 3.000000 16 6.0000001 8.000000 17 9.0000001 1.000000 16 10.0000001 1.000000 15 9.0000001 4.000000 20 9.0000001 3.000000 19 7.0000001 3.000000 17 6.0000001 1.000000 14 8.0000001 4.000000 22 6.0000001 4.000000 15 12.0000001 5.000000 22 6.0000001 2.000000 13 9.0000001 0.000000 20 7.0000001 5.000000 11 6.0000001 5.000000 19 10.0000001 5.000000 18 8.0000001 4.000000 27 13.0000001 0.000000 16 7.0000001 5.000000 18 7.0000001 3.000000 13 7.0000001 5.000000 13 9.0000001 7.000000 13 8.0000001 0.000000 15 8.0000001 3.000000 19 9.0000001 4.000000 16 8.0000001 4.000000 21 6.0000001 6.000000 22 6.0000001 4.000000 10 9.0000001 7.000000 25 6.0000001 3.000000 11 8.0000001 3.000000 24 5.0000001 3.000000 18 8.0000001 4.000000 26 10.0000001 0.000000 23 8.0000001 6.000000 25 7.0000001 3.000000 17 7.0000001 3.000000 18 7.0000001 1.000000 18 5.0000001 4.000000 16 6.0000001 1.000000 21 8.0000001 3.000000 21 8.0000001 4.000000 20 7.0000001 0.000000 24 10.0000001 5.000000 14 7.0000001 5.000000 17 7.0000001 7.000000 14 9.0000001 7.000000 8 8.0000001 3.000000 12 6.0000001 5.000000 22 9.0000001 5.000000 11 8.0000001 1.000000 19 10.0000001 3.000000 23 6.0000001 5.000000 19 7.0000001 0.000000 19 7.0000001 3.000000 26 7.0000001 2.000000 15 7.0000001 5.000000 20 11.0000001 6.000000 23 11.0000001 5.000000 14 5.0000001 4.000000 18 7.0000001 2.000000 23 11.0000001 5.000000 16 6.0000001 4.000000 16 8.0000001 3.000000 17 6.0000001 0.000000 12 8.0000001 3.000000 16 8.0000001 0.000000 19 10.0000001 5.000000 8 6.0000001 5.000000 18 6.0000001 5.000000 13 7.0000001 0.000000 22 5.0000001 4.000000 14 7.0000001 6.000000 12 9.0000001 0.000000 24 9.0000001 1.000000 12 7.0000001 7.000000 23 9.0000001 1.000000 12 8.0000001 5.000000 14 8.0000001 3.000000 15 7.0000001 8.000000 15 7.0000001 0.000000 22 10.0000001 1.000000 20 6.0000001 2.000000 12 9.0000001 2.000000 17 9.0000001 6.000000 12 11.0000001 4.000000 17 6.0000001 6.000000 19 6.0000001 4.000000 19 8.0000001 6.000000 25 5.0000001 3.000000 24 11.0000001 7.000000 16 9.0000001 1.000000 17 9.0000001 8.000000 18 9.0000001 8.000000 17 7.000000

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0

3.75

7.5

11.25

15

0 7.5 15 22.5 30

MDG

IP

GSSSRumor (NumSources=1)NonRumor (NumSources=1000)

Rumor (NumSources

=1)

Num of monitors =

640

NonRumor (NumSources

=100)

Num of monitors =

6401 5.000000 3 7.0000001 5.000000 1 6.0000001 4.000000 2 9.0000001 5.000000 2 2.0000001 3.000000 3 5.0000001 6.000000 1 4.0000001 5.000000 2 4.0000001 4.000000 2 6.0000001 4.000000 2 8.0000001 4.000000 1 0.0000001 3.000000 4 7.0000001 1.000000 2 9.0000001 11.000000 3 8.0000001 4.000000 6 1.0000001 8.000000 2 1.0000001 6.000000 4 6.0000001 1.000000 2 8.0000001 2.000000 1 5.0000001 9.000000 2 8.0000001 3.000000 2 6.0000001 5.000000 2 5.0000001 5.000000 3 7.0000001 3.000000 2 7.0000001 8.000000 1 0.0000001 1.000000 3 1.0000001 3.000000 2 8.0000001 7.000000 2 4.0000001 1.000000 3 5.0000001 5.000000 3 8.0000001 3.000000 2 9.0000001 7.000000 1 9.0000001 6.000000 2 8.0000001 5.000000 1 8.0000001 0.000000 3 4.0000001 5.000000 4 9.0000001 6.000000 1 7.0000001 8.000000 1 0.0000001 3.000000 1 9.0000001 2.000000 4 6.0000001 3.000000 3 1.0000001 1.000000 2 10.0000001 3.000000 1 0.0000001 6.000000 1 9.0000001 0.000000 3 0.0000001 5.000000 6 3.0000001 0.000000 3 6.0000001 3.000000 3 4.0000001 8.000000 1 0.0000001 1.000000 4 7.0000001 1.000000 2 7.0000001 4.000000 3 5.0000001 3.000000 1 4.0000001 3.000000 2 1.0000001 1.000000 3 5.0000001 4.000000 1 6.0000001 4.000000 1 6.0000001 5.000000 2 8.0000001 2.000000 2 5.0000001 0.000000 3 6.0000001 5.000000 3 5.0000001 5.000000 5 2.0000001 5.000000 2 9.0000001 4.000000 2 8.0000001 0.000000 1 6.0000001 5.000000 1 8.0000001 3.000000 3 1.0000001 5.000000 2 1.0000001 7.000000 1 7.0000001 0.000000 2 7.0000001 3.000000 1 0.0000001 4.000000 1 7.0000001 4.000000 1 9.0000001 6.000000 3 5.0000001 4.000000 3 6.0000001 7.000000 2 7.0000001 3.000000 1 10.0000001 3.000000 2 1.0000001 3.000000 2 4.0000001 4.000000 1 9.0000001 0.000000 2 7.0000001 6.000000 3 5.0000001 3.000000 3 4.0000001 3.000000 1 7.0000001 1.000000 2 0.0000001 4.000000 1 0.0000001 1.000000 1 8.0000001 3.000000 1 7.0000001 4.000000 2 9.0000001 0.000000 1 8.0000001 5.000000 3 4.0000001 5.000000 4 10.0000001 7.000000 1 7.0000001 7.000000 2 8.0000001 3.000000 1 9.0000001 5.000000 3 7.0000001 5.000000 2 4.0000001 1.000000 2 8.0000001 3.000000 2 7.0000001 5.000000 1 7.0000001 0.000000 1 2.0000001 3.000000 5 8.0000001 2.000000 3 1.0000001 5.000000 2 7.0000001 6.000000 3 10.0000001 5.000000 1 7.0000001 4.000000 1 5.0000001 2.000000 3 5.0000001 5.000000 1 0.0000001 4.000000 4 6.0000001 3.000000 3 7.0000001 0.000000 1 9.0000001 3.000000 2 6.0000001 0.000000 1 3.0000001 5.000000 2 7.0000001 5.000000 4 6.0000001 5.000000 3 6.0000001 0.000000 1 8.0000001 4.000000 2 5.0000001 6.000000 2 3.0000001 0.000000 1 6.0000001 1.000000 6 7.0000001 7.000000 2 9.0000001 1.000000 2 4.0000001 5.000000 2 2.0000001 3.000000 1 1.0000001 8.000000 2 6.0000001 0.000000 2 0.0000001 1.000000 3 7.0000001 2.000000 1 7.0000001 2.000000 3 1.0000001 6.000000 1 0.0000001 4.000000 2 7.0000001 6.000000 2 5.0000001 4.000000 3 6.0000001 6.000000 2 5.0000001 3.000000 4 8.0000001 7.000000 2 5.0000001 1.000000 1 7.0000001 8.000000 2 6.0000001 8.000000 4 6.000000

2 1.0000001 7.0000001 5.0000001 5.0000005 6.0000001 7.0000002 6.0000003 1.0000002 6.0000002 5.0000003 7.0000002 6.0000002 8.0000003 1.0000002 1.0000004 6.0000002 5.0000002 1.0000004 4.0000002 8.0000003 0.0000003 6.0000003 7.0000005 7.0000001 9.0000001 3.0000002 8.0000002 4.0000001 0.0000002 4.0000002 0.0000001 1.0000002 5.0000002 10.0000004 5.0000002 4.0000002 2.0000004 4.0000002 9.0000004 5.0000003 6.0000004 8.0000001 5.0000003 7.0000001 5.0000002 8.0000002 7.0000001 4.0000001 7.0000005 5.0000001 1.0000004 4.0000005 1.0000002 7.0000003 6.0000003 5.0000001 12.000000

0

3.75

7.5

11.25

15

0 1.5 3 4.5 6

MDG

IP

GSSSRumor (NumSources=1)NonRumor (NumSources=100)

Rumor (NumSources

=10)

Num of monitors =

640

NonRumor (NumSources

=1000)

Num of monitors =

6401 6.000000 21 8.0000001 3.000000 18 7.0000001 4.000000 15 9.0000001 4.000000 14 7.0000001 4.000000 19 8.0000001 4.000000 10 7.0000001 7.000000 13 8.0000001 5.000000 24 9.0000001 0.000000 14 8.0000001 9.000000 26 8.0000001 10.000000 17 9.0000001 1.000000 15 5.0000001 9.000000 22 7.0000001 3.000000 16 10.0000001 0.000000 22 9.0000001 0.000000 22 9.0000001 1.000000 25 6.0000001 8.000000 19 10.0000001 3.000000 24 8.0000001 4.000000 22 9.0000001 2.000000 11 10.0000001 1.000000 18 8.0000001 2.000000 16 6.0000001 3.000000 22 7.0000001 0.000000 16 5.0000001 6.000000 21 11.0000001 3.000000 19 8.0000001 5.000000 11 9.0000001 5.000000 19 8.0000001 3.000000 22 9.0000001 3.000000 18 8.0000001 6.000000 18 8.0000002 8.000000 20 9.0000001 0.000000 22 7.0000001 8.000000 23 7.0000001 4.000000 17 8.0000001 4.000000 16 8.0000001 6.000000 16 8.0000001 5.000000 13 6.0000001 4.000000 22 8.0000001 4.000000 22 7.0000001 1.000000 15 6.0000002 6.000000 17 8.0000001 7.000000 11 7.0000001 2.000000 20 8.0000001 3.000000 21 6.0000002 4.000000 16 6.0000001 5.000000 17 9.0000001 3.000000 16 10.0000001 0.000000 15 9.0000001 3.000000 20 9.0000001 9.000000 19 7.0000001 0.000000 17 6.0000001 7.000000 14 8.0000001 0.000000 22 6.0000001 1.000000 15 12.0000001 3.000000 22 6.0000002 7.000000 13 9.0000001 4.000000 20 7.0000001 4.000000 11 6.0000001 8.000000 19 10.0000001 7.000000 18 8.0000001 0.000000 27 13.0000001 5.000000 16 7.0000001 8.000000 18 7.0000001 8.000000 13 7.0000001 1.000000 13 9.0000002 1.000000 13 8.0000001 7.000000 15 8.0000001 7.000000 19 9.0000001 0.000000 16 8.0000001 0.000000 21 6.0000001 3.000000 22 6.0000002 6.000000 10 9.0000001 4.000000 25 6.0000001 5.000000 11 8.0000002 1.000000 24 5.0000001 3.000000 18 8.0000001 4.000000 26 10.0000001 1.000000 23 8.0000001 6.000000 25 7.0000001 5.000000 17 7.0000001 4.000000 18 7.0000001 1.000000 18 5.0000001 4.000000 16 6.0000002 2.000000 21 8.0000001 6.000000 21 8.0000001 7.000000 20 7.0000002 2.000000 24 10.0000001 6.000000 14 7.0000002 0.000000 17 7.0000001 0.000000 14 9.0000001 5.000000 8 8.0000002 1.000000 12 6.0000001 3.000000 22 9.0000001 4.000000 11 8.0000001 0.000000 19 10.0000001 7.000000 23 6.0000001 10.000000 19 7.0000001 8.000000 19 7.0000001 4.000000 26 7.0000001 0.000000 15 7.0000001 4.000000 20 11.0000001 8.000000 23 11.0000001 6.000000 14 5.0000001 3.000000 18 7.0000001 3.000000 23 11.0000001 0.000000 16 6.0000001 7.000000 16 8.0000001 5.000000 17 6.0000001 3.000000 12 8.0000001 7.000000 16 8.0000001 5.000000 19 10.0000001 0.000000 8 6.0000001 4.000000 18 6.0000001 2.000000 13 7.0000001 0.000000 22 5.0000001 0.000000 14 7.0000001 8.000000 12 9.0000001 5.000000 24 9.0000002 5.000000 12 7.0000001 3.000000 23 9.0000001 1.000000 12 8.0000002 4.000000 14 8.0000001 1.000000 15 7.0000001 4.000000 15 7.0000001 3.000000 22 10.0000001 7.000000 20 6.0000001 5.000000 12 9.0000001 6.000000 17 9.0000001 0.000000 12 11.0000001 5.000000 17 6.0000001 10.000000 19 6.0000001 5.000000 19 8.0000001 8.000000 25 5.0000001 4.000000 24 11.0000001 5.000000 16 9.0000001 4.000000 17 9.0000001 5.000000 18 9.0000001 4.000000 17 7.0000001 4.000000 23 8.0000001 4.000000 11 8.0000001 5.000000 15 8.0000001 0.000000 18 6.0000002 5.000000 13 8.0000001 5.000000 14 7.0000001 3.000000 23 7.0000001 4.000000 24 7.0000002 6.000000 21 10.0000001 2.000000 15 6.0000001 4.000000 14 9.0000001 3.000000 15 9.0000001 0.000000 15 7.0000001 4.000000 19 7.0000001 5.000000 18 9.0000001 5.000000 19 14.000000

18 11.00000015 8.00000019 8.00000016 8.00000021 9.00000015 9.00000010 7.00000025 7.00000026 10.00000020 12.00000015 9.00000017 7.00000014 7.00000024 9.00000021 6.00000018 7.00000018 9.00000021 6.00000016 10.00000016 6.00000017 7.00000017 8.00000025 7.00000016 9.00000020 6.00000014 9.00000016 9.00000018 6.00000020 10.00000011 9.00000021 7.00000020 7.00000022 9.00000016 6.00000013 9.00000017 10.00000013 8.00000011 11.00000013 5.00000016 9.00000013 7.00000015 11.00000015 8.00000019 6.000000

0

3.75

7.5

11.25

15

0 7.5 15 22.5 30

MDG

IP

GSSSRumor (NumSources=10)NonRumor (NumSources=1000)

Figure 13. Scatterplot of GSSS and MDGIP (Monitor Selection: Dist, Number of Monitors: 640)

4. RELATED WORK

Online social networks have emerged as a new medium for information sharing.1,5 Contrary to the traditionalmedia, anyone can share information and it can be delivered to a large number of people in a very short time.2

Unfortunately, it also carries undesirable information such as rumors.6

Shah and Zaman addressed the problem of finding rumor sources.7 They model rumor spreading with avariant of an SIR model8 and define rumor centrality as an ML estimator to find the rumor source. Theiralgorithm makes use of all nodes that hear the rumor. In contrast, our algorithm is based on a small set ofmonitors which are pre-selected by various methods.

A way to avoid rumors is to subscribe only trustworthy information sources. Adler and Alfaro proposed acontent-driven reputation system for Wikipedia authors.9 For each preserved edit or rollback of a user’s edit,reputation is adjusted. Zhao et al. also proposed SocialWiki in which social context including each user’s interest

Table 1. Classification of rumors and non-rumors (Number of Monitors: 640).

MonitorSelection

NumSources(Rumor)

NumSource(Non-rumor)

Rumors NonRumorsTruePositive

FalseNegative

Not Clas-sified

TrueNegative

as FalsePositive

Not Clas-sified

Dist 1 100 70 0 30 75 24 1Random 1 100 82 18 0 59 41 0NI+Dist 1 100 84 13 3 55 45 0NI 1 100 37 63 0 67 33 0BC 1 100 51 49 0 52 48 0BC+Dist 1 100 64 36 0 43 57 0

Dist 1 1000 70 0 30 100 0 0Random 1 1000 100 0 0 99 1 0NI+Dist 1 1000 97 0 3 100 0 0NI 1 1000 37 63 0 71 29 0BC 1 1000 67 33 0 59 41 0BC+Dist 1 1000 87 13 0 82 18 0

Dist 10 100 68 10 22 73 26 1Random 10 100 81 19 0 59 41 0NI+Dist 10 100 91 6 3 43 57 0NI 10 100 34 66 0 67 33 0BC 10 100 54 46 0 48 52 0BC+Dist 10 100 51 49 0 43 57 0

Dist 10 1000 78 0 22 100 0 0Random 10 1000 99 1 0 99 1 0NI+Dist 10 1000 97 0 3 100 0 0NI 10 1000 34 66 0 71 29 0BC 10 1000 67 33 0 59 41 0BC+Dist 10 1000 89 11 0 82 18 0

and trust is used to select trustworthy contributors10 and TrustWiki in which conflicts are resolved by matchingcompatible editors and readers.11 Canini et al. proposed a system that ranks users using topical content andsocial network structure.12 Nel et al. tackled the problem of rumor detection by monitoring publishing behaviorof information sources.3 They cluster groups of sources that have similar publishing behaviors. Our approachuses social graph topology and monitors to detect rumors and it is orthogonal to user reputation systems.

Morris et al. studied how people feel about the credibility of new tweets.13 They showed that people usevarious heuristics to assess the credibility – whether the tweet is retweeted, author’s expertise, etc. This can beused to improve the quality of Twitter search engine.

Mendoza et al. studied tweets about 2010 earthquake in Chile and found that rumors and non-rumorsare retweeted in a different way.14 That is, people question more about rumors and affirm more about non-rumors when they retweet. By making use of the comments of users in retweets, they have shown that it ispossible to classify rumors and non-rumors. Castillo et al. used a machine leaning technique that makes useof text in tweets, user characteristics and tweet propagation pattern to classify rumors and non-rumors.15 Ourmethods could enhance such leaning techniques by exploiting social network graph structure even when theinvestigator has a limited view on the rumor propagation. Ratkiewicz et all developed a tool that visualizestweet propagation and can be used to detect abusive behaviors.16 This tool assumes that full provenance aboutinformation propagation is known, which is not used by our method.

5. CONCLUSION

In this paper, we proposed an approach for (i) determining whether a piece of information is a rumor or not, and(ii) finding the source of the rumor. Our approach uses a very small amount of provenance information; namely,which of a set of monitors heard the piece of informaiton at hand. To find the rumor source, our algorithm

evaluates the likelihood of each node to be the source, calculated from node connectivity and shortest pathdistances. For rumor classification, we proposed two metrics – Greedy Source Set Size (GSSS) and MaximalDistance of Greedy Information Propagation (MDGIP) – and used logistic regression. To evaluate the proposedapproach, we performed a case study involving a real social network crawled from Twitter. The algorithm showsgood potential to help users in identifying rumors and their sources.

ACKNOWLEDGMENTS

Research reported in this paper was sponsored by the Army Research Laboratory and was accomplished un-der Cooperative Agreement Number W911NF-09-2-0053 and NSF CNS 09-05014. The views and conclusionscontained in this document are those of the authors and should not be interpreted as representing the officialpolicies, either expressed or implied, of the Army Research Laboratory or the U.S. Government. The U.S.Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding anycopyright notation here on.

REFERENCES

[1] Kwak, H., Lee, C., Park, H., and Moon, S., “What is twitter, a social network or a news media?,” in[Proceedings of the 19th international conference on World wide web ], WWW ’10, 591–600, ACM, NewYork, NY, USA (2010).

[2] Sakaki, T., Okazaki, M., and Matsuo, Y., “Earthquake shakes twitter users: real-time event detectionby social sensors,” in [Proceedings of the 19th international conference on World wide web ], WWW ’10,851–860, ACM, New York, NY, USA (2010).

[3] Nel, F., Lesot, M.-J., Capet, P., and Delavallade, T., “Rumour detection and monitoring in open sourceintelligence: understanding publishing behaviours as a prerequisite,” in [Proceedings of the Terrorism andNew Media Conference ], (2010).

[4] Newman, M. E. J., [Networks: An Introduction ], Oxford University Press (March 2010).

[5] Java, A., Song, X., Finin, T., and Tseng, B., “Why we twitter: understanding microblogging usage andcommunities,” in [Proceedings of the 9th WebKDD and 1st SNA-KDD 2007 workshop on Web mining andsocial network analysis ], WebKDD/SNA-KDD ’07, 56–65, ACM, New York, NY, USA (2007).

[6] Corcoran, M., “Death by cliff plunge, with a push from twitter,” New York Times (July 12, 2009).

[7] Shah, D. and Zaman, T., “Rumors in a network: Who’s the culprit?,” IEEE Transactions on InformationTheory 57(8), 5163–5181 (2011).

[8] Bailey, N., [The mathematical theory of infectious diseases and its applications ], Mathematics in MedicineSeries, Griffin (1975).

[9] Adler, B. T. and de Alfaro, L., “A content-driven reputation system for the wikipedia,” in [Proceedings ofthe 16th international conference on World Wide Web ], WWW ’07, 261–270, ACM, New York, NY, USA(2007).

[10] Zhao, H., Ye, S., Bhattacharyya, P., Rowe, J., Gribble, K., and Wu, S. F., “Socialwiki: bring order to wikisystems with social context,” in [Proceedings of the Second international conference on Social informatics ],SocInfo’10, 232–247, Springer-Verlag, Berlin, Heidelberg (2010).

[11] Zhao, H., Kallander, W., Gbedema, T., Johnson, H., and Wu, F., “Read what you trust: An open wikimodel enhanced by social context,” in [Proceedings of the 2011 IEEE Third International Conference onSocial Computing ], SocialCom ’11, IEEE Computer Society, Boston, MA, USA (2011).

[12] Canini, K. R., Suh, B., and Pirolli, P. L., “Finding credible information sources in social networks based oncontent and social structure,” in [Proceedings of the 2011 IEEE Second International Conference on SocialComputing ], SocialCom ’11, 1–8 (2011).

[13] Morris, M. R., Counts, S., Roseway, A., Hoff, A., and Schwarz, J., “Tweeting is believing?: understandingmicroblog credibility perceptions,” in [Proceedings of the ACM 2012 conference on Computer SupportedCooperative Work ], CSCW ’12, 441–450, ACM, New York, NY, USA (2012).

[14] Mendoza, M., Poblete, B., and Castillo, C., “Twitter under crisis: can we trust what we rt?,” in [Proceedingsof the First Workshop on Social Media Analytics ], SOMA ’10, 71–79, ACM, New York, NY, USA (2010).

[15] Castillo, C., Mendoza, M., and Poblete, B., “Information credibility on twitter,” in [Proceedings of the 20thinternational conference on World wide web ], WWW ’11, 675–684, ACM, New York, NY, USA (2011).

[16] Ratkiewicz, J., Conover, M., Meiss, M., Goncalves, B., Patil, S., Flammini, A., and Menczer, F., “Truthy:mapping the spread of astroturf in microblog streams,” in [Proceedings of the 20th international conferencecompanion on World wide web ], WWW ’11, 249–252, ACM, New York, NY, USA (2011).