Social Networks

Including material from Dr. Giorgos Cheliotis

(gcheliotis@nus.edu.sg)Communications and New Media, National University of Singapore

What are social networks?

• The set of (exchange) relationships between people or other social units.

• A directed graph, with people, groups, or organizations as the nodes and the entities exchanged as the link

• Vary in size, density, clumpiness

• Some types of networks

• Communication

• Advice/information

• Friendship

• Trust/social support

• Tangible exchange/Material support

• Similarity

• Structure matters

•Clique•Isolates•Stars•Boundary spanners

Types of Relationships Among People

Distinguish between attribute & network dataStudent Female CMU

Bob 0 0 1Sara 0 1 1Irina 1 1 1Katie 1 1 1Fleming 1 0 1David 1 0 1Kim 1 1 1J onathon 0 0 0Brian 0 0 0Bonka 0 1 0Lisa 0 1 0Xiaoqing 1 1 0

Bob Sara Irina Katie Fleming David Kim J onathon Brian Bonka Lisa XiaoqingBob 0 7 5 4 2 3 5 5 6 6 4 4Sara 7 0 5 5 0 0 0 6 2 5 0 0Irina 5 5 0 5 2 4 0 4 0 3 0 0Katie 4 5 5 0 1 0 0 1 0 3 0 0Fleming 2 0 2 1 0 0 0 0 0 0 0 0David 3 0 4 0 0 0 5 0 3 0 4 3Kim 5 0 0 0 0 5 0 0 3 0 4 5J onathon 5 6 4 1 0 0 0 0 0 3 0 0Brian 6 2 0 0 0 3 3 0 0 0 3 7Bonka 6 5 3 3 0 0 0 3 0 0 0 0Lisa 4 0 0 0 0 4 4 0 3 0 0 3Xiaoqing 4 0 0 0 0 3 5 0 7 0 3 0

Attribute data-Features of nodes

Network-Relationships between nodes(how closely does X work with Y?)

Why are they important?• Actors who are connected, influence each other• “Goods” (e.g., info, opportunities, power) flow through networks

• Actors’ position in the network influence their success• Good managers cultivate extensive networks, inside & outside the organization at all levels

Social Capital

• Capital– A resource that can be accumulated– Availability allows people to create more value for self

or others

• Physical capital (vs. labor)– E.g., Factories, tools, computers

• Human capital– E.g., Training, education

• Social capital– E.g., Friendships, trust, common identity

Social Capital

• The extra resources that people get by being connected to others– Analogous to physical capital (e.g., factory

automation)– Human capital (e.g., college education)

• Social capital benefits– Individual – increased health & happiness– Communities – reduced corruption

Effects of Social Capital

• Social capital is correlated with positive individual and collective outcome– Better health– Lower crime– Better educational outcomes– Good government

• Age-adjusted relative risk of dying among those lacking social contact during a 9-year period (Berkman, 1983)

• Sources of social support• Being married  • Frequent contact with family

and close friends • Active member of a church • Active participation in a club

or other social group

Social Support Health & Happiness

Strength of ties

• Strong ties (Krackhard)– Intimacy, self-disclosure, provide support– Feel close w/frequent contact– Spouse, relatives, close friends

• Weak ties (Granovetter)– Diverse resources, broader base– Feel distance w/infrequent contact– Acquaintances, colleagues from elsewhere

• Strong tie = “close relationship/friend”• Social relationship with high frequency, emotional

commitment, multiplicity (overlap), and reciprocity• Strong ties tend to know same things & people• Strong ties tend to fill in the gaps (e.g., friends of

friends become friends; friends tend to share taste)

• Strong ties useful for– Money– Advice– Arduous help– Friendship

Nature of the Social Tie Matters

• Weak tie = “weak relationship/causal acquaintance” • Social relationships with low frequency, intensity, breadth, and

reciprocity (Granovetter: Strength of Weak Ties)

• Hypothesis: Weak ties lead to more extensive and diverse social networks, and are more likely to overcome gaps of class, race, and other sources of division

• Data: Job changers get their jobs through weak ties: e.g.. only 16% from contacts they see weekly and 28% they see less than yearly

• Weak ties useful for – New information– Finding jobs

Nature of the Social Tie Matters

Role of strong versus weak ties in organizations

• How does information flow in a large company?• Benefits

– Weak times wide scope, may lead to easier discovery of relevant knowledge– Strong times other people will take the time to guide you through the use of

their knowledge (e.g., undocumented software)

– Needed most when transferred product is undocumented or dependent on other hardware/software components

• Research setting– The transfer of hardware or software between divisions in a large, multinational

electronics company– Data from surveys of R&D and project managers

• Controls: Time period, Size, Budget, Reuse of existing components, Product type, Patents

• IV: Codification of ware; Stand-alone nature of ware; Avg. frequency & closeness of division to other divisions + interactions

• DV: Speed of project completion

Hansen, M. T. (1999). The search-transfer problem: The role of weak ties in sharing knowledge across organization subunits. Administrative Science Quarterly, 44(1), 82-111.

Trade-offs btw tie strength & codification of knowledge

Knowledge Tie Strength

Weak Strong

Codified &Documented

Search benefitsFew transfer problems

Low search benefitsFew transfer problems

Uncodified Search benefitsSevere transfer problems

Low search benefitsFew transfer problems

Hansen Results

• Weak ties most useful for codified & stand-alone “ware”

• Strong ties most useful to uncodified & dependent/embedded “ware”

• Multiplier effect of (between projects ) ties strength on completion time, for components of different codification and stand-aloneness• Note: Multipliers > 1, implies weak ties speed completion

Codified, stand-alone projects

Uncodified, dependent projects

Kraut’s Facebook Network

http://www.wolframalpha.com/input/?i=facebook+report

Why are they important?

• Examining social networks can help diagnose organizational problems– find informational bottlenecks/distribution channels– select successful team leaders and managers

• Good managers understand that there are both formal and

informal networks in an organization

Examples: Interdisciplinary collaboration

Stunning Density ComparisonArchitecture BHA/BSA:

Race & school friendships

Moody, Jame (2002) Race, School Integration, and Friendship Segregation in America. The American journal of sociology [0002-9602] Moody yr:2002 vol:107 iss:3 pg:679

Familiarity in a CMU Project Class

79% non-Asian

83% Asian

Examples: World of Warcraft (Guild 1)

• Links = Frequency of playing together

• Guild as a whole plays togetherfrequently

• Some pairs especially close

Examples: WoW Guild 2

• Links = Frequency of playing together

• Cliques

Bloggers X Party

Some Stylized Facts

• Size of personal networks– Weak ties: ~280 persons known– Strong ties: 6-30

• Networks generally sparse– Most of one’s ties don’t know each

other

• Ties are specialized– Exchange different resources with

different ties (e.g., friendship & work)

– Only weak correlations among exchanges within a tie (e.g., correlations between communication frequency across modalities=~.3 to. 4)

• Strong ties useful for– Money– Advice– Arduous help– Friendship

• Weak ties useful for – New information

Basic Concepts

• Networks

• Tie Strength

• Key Players

• Cohesion

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How to represent various social networks

How to identify strong/weak ties in the network

How to identify key/central nodes in network

Measures of overall network structure

Representing relations as networks

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1 2 3 4

Graph

AnneAnne JimJimMaryMary

JohnJohn

Vertex (node) Edge (link)

Can we study their interactions as a

network?

Communication

Anne: Jim, tell the Murrays they’re invited

Jim: Mary, you and your dad should come for dinner!

Jim: Mr. Murray, you should both come for dinner

Anne: Mary, did Jim tell you about the dinner? You must come.

John: Mary, are you hungry?

…

Entering data on a directed graph

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Graph (directed)

Edge list

Adjacency matrix

Representing an undirected graph

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Edge list remains the same

Adjacency matrix becomes symmetric

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Directed

Undirected(who knows whom)

(who contacts whom)But interpretation is different now

Basic Concepts

Networks Tie Strength

Key Players

Cohesion

CNM Social Media Module – Giorgos Cheliotis (gcheliotis@nus.edu.sg)

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How to represent various social networks

How to identify strong/weak ties in the network

How to identify key/central nodes in network

Measures of overall network structure

Adding weights to edges (directed or undirected)

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Edge list: add column of weights

Adjacency matrix: add weights instead of 1Weights could be:•Frequency of interaction in period of observation•Number of items exchanged in period•Individual perceptions of strength of relationship•Costs in communication or exchange, e.g. distance•Combinations of these

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Edge weights as relationship strength

• Edges can represent interactions, flows of information or goods, similarities/affiliations, or social relations

• Specifically for social relations, a ‘proxy’ for the strength of a tie can be:

(a) the frequency of interaction (communication) or the amount of flow (exchange)

(b) reciprocity in interaction or flow(c) the type of interaction or flow between the two

parties (e.g., intimate or not)(d) other attributes of the nodes or ties (e.g., kin

relationships)(e) The structure of the nodes’ neighborhood (e.g.

many mutual ‘friends’)

• Surveys and interviews allows us to establish the existence of mutual or one-sided strength/affection with greater certainty, but proxies above are also useful

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Basic Concepts

Networks

Tie Strength Key Players

Cohesion

CNM Social Media Module – Giorgos Cheliotis (gcheliotis@nus.edu.sg)

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How to represent various social networks

How to identify strong/weak ties in the network

How to identify key/central nodes in network

Measures of overall network structure

Measures of Centrality

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Degree

Betweenness

Closeness

Eigenvector

How many people can this person reach directly?

How likely is this person to be the most direct route between two people in the network?

How fast can this person reach everyone in the network?

How well is this person connected to other well-connected people?

Centrality measure Interpretation in social networks

Degree centrality• A node’s (in-) or (out-)degree is the

number of links that lead into or out of the node

• In an undirected graph they are of course identical

• Often used as measure of a node’s degree of connectedness and hence also influence and/or popularity

• Useful in assessing which nodes are central with respect to spreading information and influencing others in their immediate ‘neighborhood’

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Nodes 3 and 5 have the highest degree (4)

Nodes 3 and 5 have the highest degree (4)

Hypothetical graph

Betweenness centrality For a given node v, calculate the number

of shortest paths between nodes i and j that pass through v, and divide by all shortest paths between nodes i and j

Sum the above values for all node pairs i,j

Sometimes normalized such that the highest value is 1or that the sum of all betweenness centralities in the network is 1

Shows which nodes are more likely to be in communication paths between other nodes

Also useful in determining points where the network would break apart (think who would be cut off if nodes 3 or 5 would disappear)

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1.5

6.5

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Node 5 has higher betweenness centrality than 3

Node 5 has higher betweenness centrality than 3

Closeness centrality• Calculate the mean length of all

shortest paths from a node to all other nodes in the network (i.e. how many hops on average it takes to reach every other node)

• Take the reciprocal of the above value so that higher values are ‘better’ (indicate higher closeness) like in other measures of centrality

• It is a measure of reach, i.e. the speed with which information can reach other nodes from a given starting node

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0.5

0.67

0.75

0.460.75

0.460.46

Nodes 3 and 5 have the highest (i.e. best) closeness, while node 2 fares almost as wellNodes 3 and 5 have the highest (i.e. best)

closeness, while node 2 fares almost as well Note: Sometimes closeness is calculated without taking the reciprocal of the mean shortest path length. Then lower values are ‘better’.

Eigenvector centrality

• A node’s eigenvector centrality is proportional to the sum of the eigenvector centralities of all nodes directly connected to it

• In other words, a node with a high eigenvector centrality is connected to other nodes with high eigenvector centrality

• This is similar to how Google ranks web pages: links from highly linked-to pages count more

• Useful in determining who is connected to the most connected nodes

CNM Social Media Module – Giorgos Cheliotis (gcheliotis@nus.edu.sg)

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0.36

0.49

0.54

0.190.49

0.170.17

Node 3 has the highest eigenvector centrality, closely followed by 2 and 5

Node 3 has the highest eigenvector centrality, closely followed by 2 and 5 Note: The term ‘eigenvector’ comes from mathematics (matrix

algebra), but it is not necessary for understanding how to interpret this measure

Values computed with the sna package in the R programming environment. Definitions of centrality measures may vary slightly in other software.

Basic Concepts

Networks

Tie Strength

Key Players Cohesion

CNM Social Media Module – Giorgos Cheliotis (gcheliotis@nus.edu.sg)

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How to represent various social networks

How to identify strong/weak ties in the network

How to identify key/central nodes in network

How to characterize a network’s structure

Density

CNM Social Media Module – Giorgos Cheliotis (gcheliotis@nus.edu.sg)

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• A network’s density is the ratio of the number of edges in the network over the total number of possible edges between all pairs of nodes (which is n(n-1)/2, where n is the number of vertices, for an undirected graph)

• In the example network to the right density=5/6=0.83 (i.e. it is a fairly dense network; opposite would be a sparse network)

• It is a common measure of how well connected a network is (in other words, how closely knit it is) – a perfectly connected network is called a clique and has density=1

• A directed graph will have half the density of its undirected equivalent, because there are twice as many possible edges, i.e. n(n-1)

• Density is useful in comparing networks against each other, or in doing the same for different regions within a single network

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density = 5/6 = 0.83

density = 5/12 = 0.42

Edge present in network

Possible but not present

Clustering

CNM Social Media Module – Giorgos Cheliotis (gcheliotis@nus.edu.sg)

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N/aN/a

• A node’s clustering coefficient is the number of closed triplets in the node’s neighborhood over the total number of triplets in the neighborhood. It is also known as transitivity.

• E.g., node 1 to the right has a value of 1 because it is only connected to 2 and 3, and these nodes are also connected to one another (i.e. the only triplet in the neighborhood of 1 is closed). We say that nodes 1,2, and 3 form a clique.

• Clustering algorithms identify clusters or ‘communities’ within networks based on network structure and specific clustering criteria (example shown to the right with two clusters is based on edge betweenness, an equivalent for edges of the betweenness centrality presented earlier for nodes)

Network clustering coefficient = 0.375 (3 nodes in each triangle x 2 triangles = 6 closed triplets divided by 16 total)

Cluster A

Cluster B

Values computed with the igraph package in the R programming environment. Definitions of centrality measures may vary slightly in other software.

Preferential Attachment

CNM Social Media Module – Giorgos Cheliotis (gcheliotis@nus.edu.sg)

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A property of some networks, where, during their evolution and growth in time, a the great majority of new edges are to nodes with an already high degree; the degree of these nodes thus increases disproportionately, compared to most other nodes in the network

The result is a network with few very highly connected nodes and many nodes with a low degree

Such networks are said to exhibit a long-tailed degree distribution

And they tend to have a small-world structure!

(so, as it turns out, transitivity and strong/weak tie characteristics are

not necessary to explain small world structures, but they are common and

can also lead to such structures)

nodes ordered in descending degree

degr

ee

short head

long tail

Example of network with preferential attachment

Sketch of long-tailed degree distribution

Social Capital

• Investment in time, energy and other resources in individual and organized social relationships

• Relationships have benefits – Knowledge, innovation, resources– Individual health and happiness– Community efficiency, safety and quality

Social Capital

Groups rely upon networks for

success• Allen: Bring technical knowledge into R&D teams

• Coleman: Rapid adoption of medical innovations among community of MDs

• Curtis: Software engineering

• Getting application domain requirements

• Keeping up with changing environment of use and development

• Ancona: New product development teams

• Convince the boss

• Get the support of "sister" departments

Dense Social Networks Are Good(Coleman, 1990)

• Density = # links/size, where size=(N*(N-1))– # actual links/#potential links

• Dense networks are useful at the organizational level

• Provide– Information & other resources– Trust thru effects of reputation

Who Helps Whom with the Rice Harvest?

Which Village Is More Likely to Survive?

Allen-Gatekeepers• Gatekeepers moderate the flow of technical

information into R&D groups– Connected both within and outside the group– Technically competent & often a supervisor

Allen-Gatekeepers• Groups rely on this network structure to bring

new knowledge into the system

Outside connections improve performance evaulations

Cross, R & Cummings, J. (2004) Tie and network correlates of individual performance in knowledge intensive work Academy of Management Journal, 47(6), 928.

Structural Holes

• Network closure – relations are embedded in a network– Enhance group identification– Foster exchange of ideas

• Structural holes – relations bridge disconnected networks– Access to unique information– Broker third parties

Structural holes – benefits• A structural hole exists when there is only a

weak connection between two dense clusters– Control benefits:

• brokers control the interaction between two network components

– Information benefits: • brokers have access to unique information, this makes them

invaluable

• Structural holes are a competitive advantage– Separate non-redundant sources of information– Information from different sources is more additive

than overlapping

Advantages of Structural Holes (Burt, 2000)

Zoom in on a cluster