network - skyeome.netskyeome.net/text/skyebudapestnotes.pdf · network data representation:...

17
Network Analysis Lab Budapest Complex Systems Summer School Skye Bender-deMoll [email protected] http://student.bennington.edu/~skyebend direction of talk: hopefully a bit more of a seminar than a lecture let me know if I leave anything out anything important, please interject examples or how relevant to your own work. cover some very basic network concepts (review for many people) provide references to more in-depth material for later research demo network analysis and visualization software (but mostly to give examples of capabilities, if it something you’d like to use, we can do a more in-depth tutorial later) visualization of networks brief examples of agent-based network models in REPAST network: (some of this is lifted from scott and some from the rehannen paper, definite SN bent) basic idea of relational dataset one or more sets with explicit relations between their members nodes, actors, people connected, tied, linked to each other by edges, arcs, ties close relation to graph theory important to distingusih what kinds of ties are allowed in specific network binary / vs. asymmetric relation is either present or absent, no directionality binary vs. valued/weighted ties have a “weight”, “cost” or “distance” associated with them symmetric vs. asymmetric edges are symmetric, no directionality, A <–> B arcs have directionality, but can exist both ways, A –> B and/or A <– B negative “distrust” , “avoidance” multiple relations possible to have multiple sets of relations for the same actors coding different kinds of data (friendship, trust, exchange) or the "same" network at different points in time self loops in some nets nodes are permitted to link to themselves - measurement algorithms and stats ma be ill-defined for some classes of nets

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Page 1: network - skyeome.netskyeome.net/text/skyeBudapestNotes.pdf · network data representation: matrices - ¡not necessarily square! elegant concept closely related to graph theory (but

Netw

ork Analysis Lab

Budapest C

omplex S

ystems S

umm

er School

Skye B

ender-deMoll

[email protected]

http://student.bennington.edu/~skyebend

direction of talk:

hopefully a bit more of a sem

inar than a lecture

let me know

if I leave anything out anything important,

please interject examples or how

relevant to your own w

ork.

cover some very basic netw

ork concepts (review for m

any people)

provide references to more in-depth m

aterial for later research

demo netw

ork analysis and visualization software (but m

ostly to give examples of

capabilities, if it something you’d like to use, w

e can do a more in-depth tutorial later)

visualization of networks

brief examples of agent-based netw

ork models in R

EP

AS

T

network:

(some of this is lifted from

scott and some from

the rehannen paper, definite SN

bent)

basic idea of relational datasetone or m

ore sets with explicit relations betw

een their mem

bers

no

de

s, acto

rs, pe

op

le co

nn

ecte

d, tie

d, lin

ked

to e

ach

oth

er b

y ed

ge

s, arcs, tie

s

close relation to graph theory

important to distingusih w

hat kinds of ties are allowed in specific netw

ork

binary /vs. asym

metric

relation is either present or absent, no directionality

binary vs. valued/weighted

ties h

ave

a “w

eig

ht”, “co

st” or “d

istan

ce” a

ssocia

ted

with

the

m

symm

etric vs. asymm

etricedges are sym

metric, no directionality, A

<–>

Barcs have directionality, but can exist both w

ays, A –>

B and/or A

<– B

negative“d

istrust” , “a

void

an

ce”

multiple relations

possible to have multiple sets of relations for the sam

e actorscoding different kinds of data (friendship, trust, exchange)or the "sam

e" network at different points in tim

e

self loopsin som

e nets nodes are permitted to link to them

selves

- measurem

ent algorithms and stats m

a be ill-defined for some classes of nets

Page 2: network - skyeome.netskyeome.net/text/skyeBudapestNotes.pdf · network data representation: matrices - ¡not necessarily square! elegant concept closely related to graph theory (but

network data representation:

matrices - ¡not necessarily square!

elegant concept

closely related to graph theory (but read the other way)

useful for direct computation (m

atrix algebra)(ex. pow

ers of matrix gives distances on graph)

not very efficient for large sparse networks

adjacency matrix (square)

node X node , individual X

individual

affiliation matrix

individual X non-surveyed individuals

may be possible to extract square subset

individual X event

can use to construct square co-incidence matrix

1 1 1 1 1

1 2 3 4 5 6 7 8 9 0 1 2 3 4

E E E E E E E E E E E E E E

- - - - - - - - - - - - - -

1 EVELYN 1 1 1 1 1 1 0 1 1 0 0 0 0 0

2 LAURA 1 1 1 0 1 1 1 1 0 0 0 0 0 0

3 THERESA 0 1 1 1 1 1 1 1 1 0 0 0 0 0

4 BRENDA 1 0 1 1 1 1 1 1 0 0 0 0 0 0

5 CHARLOTTE 0 0 1 1 1 0 1 0 0 0 0 0 0 0

6 FRANCES 0 0 1 0 1 1 0 1 0 0 0 0 0 0

7 ELEANOR 0 0 0 0 1 1 1 1 0 0 0 0 0 0

8 PEARL 0 0 0 0 0 1 0 1 1 0 0 0 0 0

9 RUTH 0 0 0 0 1 0 1 1 1 0 0 0 0 0

10 VERNE 0 0 0 0 0 0 1 1 1 0 0 1 0 0

11 MYRNA 0 0 0 0 0 0 0 1 1 1 0 1 0 0

12 KATHERINE 0 0 0 0 0 0 0 1 1 1 0 1 1 1

13 SYLVIA 0 0 0 0 0 0 1 1 1 1 0 1 1 1

14 NORA 0 0 0 0 0 1 1 0 1 1 1 1 1 1

15 HELEN 0 0 0 0 0 0 1 1 0 1 1 1 1 1

16 DOROTHY 0 0 0 0 0 0 0 1 1 1 0 1 0 0

17 OLIVIA 0 0 0 0 0 0 0 0 1 0 1 0 0 0

18 FLORA 0 0 0 0 0 0 0 0 1 0 1 0 0 0

linked list

generally a list of nodes denoting their attributes

followed by a list of ties (nodeA

-> nodeB

, strength, etc)

less standardized

can store additional info

generally less efficient for some algorithm

s

more efficient storage for large sparse graphs

kinds of networks

treesno cycles

planar vs. hi-dimesional

bi-partite

Page 3: network - skyeome.netskyeome.net/text/skyeBudapestNotes.pdf · network data representation: matrices - ¡not necessarily square! elegant concept closely related to graph theory (but

where does netw

ork data come from

, and how is it collected?

sampling m

ethods

full network

requires entire population is known and can be bounded

query each individual about connections

snowball

when population is not know

nchoose starting set of individuals (random

ly, or from som

e other criteria) starting set is a very sm

all subset of the population of interestquery each individual for their connectionsrepeat for all new

individuals listed¡w

ill not locate isolates!starting point chosen m

ay influence findings

ego-centric sampling

pick random sam

ple of nodesask each to nam

e alterscheck for overlaps

observation"unobtrusive" observer records interactions or exchanges of interestrestricted dom

ain

previously recorded "incidental" data phone recordsbank bookshistorical docum

entsem

ail forwards

perscription records

random w

alk / link trace

choose individualrandom

ly choose outgoing connection to locate next individualrandom

ly choose outgoing connection from new

individualrepeat, w

atch for overlaps

Klovdahl, A

lden S. (1989) "U

rban Social N

etworks: S

ome M

ethodological Problem

s and P

ossibilities" in Kochren, M

anfred ed. T

he S

mall W

orld A

blex, Norw

ood NJ

200 residents in dense central core of Canaberra urban netw

ork

Page 4: network - skyeome.netskyeome.net/text/skyeBudapestNotes.pdf · network data representation: matrices - ¡not necessarily square! elegant concept closely related to graph theory (but

Menzel, H

erbert, and Katz, E

lihu (1955) "Social R

elations and Innovations in the Medical

Profession: T

he Epidem

iology of a New

Drug"

Pu

blic O

pin

ion

Qu

arte

rly 19:337-352 [C

lassic study tracking the diffusion of instances of a drug prescription among a

ne

two

rk of d

octo

rs]

artificially constructed studies of comm

unication, interaction, etc.

in lab setting or constrained environment w

here recording is possible

MIT

conference badges, email com

unication studies

computer sim

ulation data

networks can be generated using specific distribution or algorithm

makes possible the investigation of a class of netw

orks

- Skvoretz, John (1990) "B

iased Net T

heory: Approxim

ations, Sim

ulations and O

bservations" Socia

l Ne

two

rks 12:217-238

but it is surprisingly difficult to generate "realistic" social networks

often necessary to make assum

ptions about an underlying social process

- Jin, Em

ily., New

man, M

ark (2000) "From

Friendship to C

omm

unity: Modeling S

ocial N

etworks" S

anta Fe Institute R

EU

paperform

al analytical

random (E

rdos-Rényi, other distributions)

lattices (various geometries)

grid

ring

connection radius

“sma

ll wo

rld”

combination fraction of random

connections on regular substrate

W

atts-Strogatz circular substrate w

ith random rew

iring

Page 5: network - skyeome.netskyeome.net/text/skyeBudapestNotes.pdf · network data representation: matrices - ¡not necessarily square! elegant concept closely related to graph theory (but

other types of real world data archives:

gene linkagesflorence tax-roll datacom

piler graphsbiblom

etric citation networks

biological neuron networks

com

pu

ter n

etw

orks

company interlocks

genealogical data (family trees)

social science data archivesindustry/international trade dataS

TD

/AID

S sexual netw

orksA

IDS

needle sharingecological food w

ebsgeographic dataelectrical pow

er gridsm

ovie co-stars

some difficulties w

ith network data

bounding problems

if individuals can be linked by many-step connections, w

here does a network end?

respondent reliability problems

- F

erligoj, Anuska and H

lebec, Valentina., (1999) "E

valuation of social network

measurem

ent instruments

" So

cial N

etw

orks 21:111-130 [C

omparison of various social

support network questions and generators in S

lovinian high school]

computational storage problem

s

matrices go up as the

squ

are of the num

ber of nodes

most com

putations scale much w

orse

a few inks to data sets:

INS

NA

(International Netw

ork for Social N

etwork A

nalysis) data pagehttp://w

ww

.sfu.ca/~insna/IN

SN

A/data_inf.htm

l

Chicago Law

yers (ICP

SR

)http://w

ww

.icpsr.umich.edu:8080/A

BS

TR

AC

TS

/08218.xml?form

at=IC

PS

R

Police com

munication (IC

PS

R)

http://ww

w.icpsr.um

ich.edu:8080/AB

ST

RA

CT

S/02480.xm

l?format=

ICP

SR

Com

munity political sytem

s (ICP

SR

)http://w

ww

.icpsr.umich.edu:8080/A

BS

TR

AC

TS

/07092.xml?form

at=IC

PS

R

1992 Dom

estic Terrorism

Prepardness (IC

PS

R)

http://ww

w.icpsr.um

ich.edu:8080/AB

ST

RA

CT

S/06566.xm

l?format=

ICP

S

several example data sets are included w

ith UC

INE

T

- Marsden, P

eter V. (1990) "N

etwork D

ata and Measurem

ent" Annual R

eview

of Sociology 16:435-498 [D

iscussion of measurem

ent techniques, some general results

an

d b

iase

s]

basic network stats / concepts

degreein-degree -> num

ber of connections coming in, or "pointing tow

ards" a node

out-dgree -> num

ber of "outgoing connections"

both are the same in non-directed graphs

degree distribution of graph/network

poisson

po

we

r law

Page 6: network - skyeome.netskyeome.net/text/skyeBudapestNotes.pdf · network data representation: matrices - ¡not necessarily square! elegant concept closely related to graph theory (but

distance

(graph theoretic) min. num

ber of "steps" or links it take to traverse a path

can take into account weights of edges/arcs, sum

to a "cost function"

similarity/dissim

ilarity

important to be clear about w

hat weights of edges are m

easuring

"how close" - sim

ilarity (lager value means closer together)

"how far" - dissim

ilarity (larger value means farther apart)

diameter of graph

longest shortest path between all pairs of nodes

densitycom

plete graph / components / isolates

density of graph is number of edges as a fraction of m

ax. possible number

__

__L_

__

_

__

_L_

__

_

density = n(n-1)/2 for directed graph =

n(n-1)

clustering coeff (personal network density)

fraction of potential ties among neighbors w

hich are realizedordegree to w

hich acquaintances are acquainted with each other

__ number of edges in ngh. of v ___

clustering coeff = total num

ber of possible edges in ngh. of v

averaged over all vertices in graph

clustering coeff equal to density if graph is not very “neighbor-hoody”

value of 1 implies netw

ork disconnected but complete sub graphs

value of 0 implies that no neighbors know

each other

node-independent paths

number of unique (sam

e node is not used in more than one path) paths betw

een nodesused in algorithm

s for finding bridges and clusters in graphs

cores, cliques

clique is a fully-connected subgraph <exam

ple>

not so useful alone, usually the patter of clique overlaps is examined

often with a hierarchical clustering m

ethod

SINGLE-LINK HIERARCHICAL CLUSTERING (of TARO data)

1 1 1 1 1 1 1 1 2 2 1 1 2Level 8 9 0 3 2 4 5 6 9 5 6 4 7 1 1 0 1 3 2 7 8 2----- - - - - - - - - - - - - - - - - - - - - - - 2 . . . . XXX . . . . XXX . . XXX . . XXX . . 1 XXXXX XXXXXXX . . XXXXXXXXXXXXX XXXXXXXXXXX 0 XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX

level indicates number of shared cliques, and X

Xs (crude dendogram

) indicate who w

ith

Page 7: network - skyeome.netskyeome.net/text/skyeBudapestNotes.pdf · network data representation: matrices - ¡not necessarily square! elegant concept closely related to graph theory (but

These data represent the relation of gift-giving (taro exchange) am

ong 22 households in a P

apuan village. Hage &

Harary (1983) used them

to illustrate a graph hamiltonian cycle.

Schw

imm

er points out how these ties function to define the appropriate persons to

mediate the act of asking for or receiving assistance am

ong group mem

bers.

reciprocity and transitivity

reciprocityfraction of A

-> B

ties for which there is a B

-> A

tie

transitivity (balance theory)triadsfraction of B

-> C

ties present when A

-> B

and A ->

C are present

<diagram

here>

status/control measures/centrality

locally central if it has lots of links to nodes in imm

ediate environment

globally central if it has position of strategic significance to network

degree centrality (local)“sta

r-ne

ss” of n

od

e norm

alized degree centrality is the degree divided by the maxim

um

possible degree expressed as a percentage

betweenness centrality (global)how

much a point lies betw

een other points on graphproportion of paths betw

een X and Z

that use Yevaluated over entire netw

ork - proportion of geodesics on graph that use Y

structural equivalence, role equivalence

find actors (nodes) that have similar roles in netw

ork

similar pattern of connections to other nodes, social positions

block models / im

age matrix

use cluster-analysis techniques to partition nodes into “equivalent” sets

possible examine pattern of set-relations as if it is a new

network

Page 8: network - skyeome.netskyeome.net/text/skyeBudapestNotes.pdf · network data representation: matrices - ¡not necessarily square! elegant concept closely related to graph theory (but

useful references-

Scott, John (1991) So

cial N

etw

ork A

na

lysis: A H

an

db

oo

k (2nd ed.) London, S

AG

E

Publications

sections of Scott's book are online (probably illegal) at

http://ww

w.analytictech.com

/mb119/tableof.htm

Boissevain, Jerem

y, Mitchell, C

lyde J. (1973) N

etw

ork a

nalysis: stu

die

s in h

um

an

inte

ractio

n The H

ague, Mouton

Marsden, P

eter V. (1990) "N

etwork D

ata and Measurem

ent" Annual R

eview of

Sociology

16:435-498 [Discussion of m

easurement techniques, som

e general results and biases]

analytic tech's (UC

INE

T's publisher) online netw

ork tutorial http://w

ww

.analytictech.com/netw

orks/topics.htm

Introduction to Social N

etwork M

ethods (online text and pdf) http://w

izard.ucr.edu/~rhannem

a/networks/text/textindex.htm

l

useful network softw

are

UC

INE

T - B

orgatti, Everett, and F

reeman

http://ww

w.analytictech.com

/

PA

JEK

- Vladim

ir Batagelj, A

ndrej Mrvar U

niversity of Ljubljana, Slovenia

http://vlado.fmf.uni-lj.si/pub/netw

orks/pajek/

PajekC

onverter http://student.bennington.edu/~

skyebend/pajekConvert.htm

GraphV

iz (N

eato/Dotty) - A

T&

T inform

ation visualization lab http://w

ww

.research.att.com/sw

/tools/graphviz/

trick for all of these is to figure out an effecient path to get from the data at hand to

desired results

usually more than one w

ay, just getting an easy sequence of operations and keeping track of w

here you are is sometim

es difficult.

UC

INE

T - http://w

ww

.analytictech.com/

Borgatti, E

verett, and Freem

an

P

C/w

ind

ow

sfree 30 day trial, then ~

$30US

for studentssort of the standard in the social netw

orks world

interface is a bit clunky (used to be cmd line)

matrix based

DL file form

at

UC

INE

T’s m

ain functions

matrix algebra

add, subtract, multiply, pow

ers, boolean operations on matrices

utility/data managem

ent functions sym

etrize, binarize, truncate, partitionQ

AP

regression / correlationestim

ate relationships between m

atrices by rearranging matrices

MD

S (M

ulti Dim

ensional Scaling) m

ethods (metric/non m

etric)represent as vectors, find low

dimensional em

bedding to represent them

with m

inimal distortion

useful as means of assessing "sim

ilarity" or visual layout with distances

dissimilarity m

atrixhierarchical clusteringdendogram

sblock m

odelingm

ost net stat and descriptive statscorrespondence analysisfactor analysis,cluster analysism

ultiple regressioncliques and com

ponentsread/w

rite to PA

JEK

format

library of demo data sets

kinmage

Page 9: network - skyeome.netskyeome.net/text/skyeBudapestNotes.pdf · network data representation: matrices - ¡not necessarily square! elegant concept closely related to graph theory (but

UC

INE

T operating m

etaphor

asks for input filename and param

eters

performs operations on m

atrix files

saves out new m

atrix files

reports results in log window

-----------

input p

ara

mete

rs ---> | | --->

outp

ut te

xt | P

RO

CE

DU

RE

| in

put d

ata

sets --->

| | ---> o

utp

ut d

ata

sets

-----------

important to be very careful about nam

ing,

during an analysis all of the output files will get confusing

online help files give explanation of procedures during use

P

AJE

K - http://vlado.fm

f.uni-lj.si/pub/networks/pajek/

Vladim

ir Batagelj and A

ndrej Mrvar U

niversity of Ljubljana, Slovenia

Pajek's U

ser interface

Pa

jek's D

raw

win

do

w[Davis’s Southern W

omen (B

i-partite) Data using 2-D

Fruchterm

an-Reingold A

lgorithm, D

efining Shapes and Colors of V

ertices with Input

File]

Pa

jek P

C/w

indows F

RE

EW

AR

E

network analysis and visualization

, now does m

ost stats as well

2d and 3d visualization

fast, comm

itment to sub quadratic algorithm

s

good spring-embedder visualization techniques (K

amada-K

awi, F

ruch-Riengold)

tree visualization

list based

can associate coordinates, colors, shapes with nodes and arcs.

time

ba

sed

ne

two

rks

most netw

ork descriptive stats

export BM

P, P

S, V

RM

L, SV

G,

Page 10: network - skyeome.netskyeome.net/text/skyeBudapestNotes.pdf · network data representation: matrices - ¡not necessarily square! elegant concept closely related to graph theory (but

Pajek operating m

etaphor

¡LOT

S of hierarchical m

enus!

data is maintained in list form

at files, which are loaded into m

emory

operations can performed on and using:

nets - collections of nodes and arcs/edges

partitions - segregate nodes into separate classes

clusters

permutations - reordering of nodes in net w

orks

hierarchies - trees relating nodes

vectors - numerical node attribute data

menus are arranged according to w

hat kind of data they take as input

results of one operation are used as input for the next

PajekC

onverter

- http://student.bennington.edu/~skyebend/pajekC

onvert.htm

PajekC

onverter is a basic utility (written in Java) for converting tab-delineated

text files into a format readable by the netw

ork analysis and visualization software P

ajek.

PajekC

onverter’s intention is to make it as sim

ple as possible to go from a spreadsheet

full of data to a network im

age

tries to take advantage of Pajek’s use of attributes for operations and visualization

take over the somew

hat confusing task of formatting input files

data can be pasted in or read in from text file

helps to generate nice look postscript and SV

G files by m

apping c

columns of the input text can be assigned to control the various aspects of the im

age

categorical data –> shapes or colors of nodes

numerical data –>

line weights, line w

idth, node size, node position

can handle time code data

GraphV

iz (N

eato/Dotty) - h

ttp://w

ww

.rese

arch

.att.co

m/sw

/too

ls/gra

ph

viz/ A

T&

T inform

ation visualization lab

unix/Xw

indows F

RE

EW

AR

E

good tree layout algorithms

spring embedder layout (K

K?)

scriptable (can be piped to, etc)excellent postscript output

Page 11: network - skyeome.netskyeome.net/text/skyeBudapestNotes.pdf · network data representation: matrices - ¡not necessarily square! elegant concept closely related to graph theory (but

Code for F

inite Autom

aton graph produced from dotty, im

age belowdigraph finite_state_machine {

rankdir=LR;

size="8,5"

orientation=land;

node [shape = doublecircle]; LR_0 LR_3 LR_4 LR_8;

node [shape = circle];

LR_0 -> LR_2 [ label = "SS(B)" ];

LR_0 -> LR_1 [ label = "SS(S)" ];

LR_1 -> LR_3 [ label = "S($end)" ];

LR_2 -> LR_6 [ label = "SS(b)" ];

LR_2 -> LR_5 [ label = "SS(a)" ];

LR_2 -> LR_4 [ label = "S(A)" ];

LR_5 -> LR_7 [ label = "S(b)" ];

LR_5 -> LR_5 [ label = "S(a)" ];

LR_6 -> LR_6 [ label = "S(b)" ];

LR_6 -> LR_5 [ label = "S(a)" ];

LR_7 -> LR_8 [ label = "S(b)" ];

LR_7 -> LR_5 [ label = "S(a)" ];

LR_8 -> LR_6 [ label = "S(b)" ];

LR_8 -> LR_5 [ label = "S(a)" ];

}

Finite A

utomaton graph produced from

dotty,

R S

tatistical Com

puting Environm

ent -http

://ww

w.r-p

roje

ct.org

/

SN

A R

outines for R - http://legba.hss.cmu.edu/R

.stuff/U

nix based FR

EE

WA

RE

with som

e network analysis tools

additional resources

INS

NA

links to social networks softw

arehttp://w

ww

2.heinz.cmu.edu/project/IN

SN

A/soft_inf.htm

-Sean E

verton's latest manual for using U

cinet, MS

Access, M

S E

xcel, Mage, and P

ajek for social netw

ork analysis: http://w

ww

.stanford.edu/group/esrg/siliconvalley/documents/netw

orkmem

o.doc

Visualization

no

n 'g

rap

h' m

eth

od

s

stats

blockmodel

degree distributions

adjacency matrix

Page 12: network - skyeome.netskyeome.net/text/skyeBudapestNotes.pdf · network data representation: matrices - ¡not necessarily square! elegant concept closely related to graph theory (but

de

nd

og

ram

s [from

Com

munity stru

cture

in so

cial a

nd b

iolo

gica

l netw

ork

s Girvan&

New

man 2001] F

IG. 4: (a) T

he friendship netw

ork from Z

achary's karate club study [25], as described in the text. Nodes associated w

ith the club adm

inistrator's faction are drawn as circles, w

hile those associated with the instructor's faction are draw

n as square

(b) The hierarchical tree show

ing the complete com

munity structure for the netw

ork. The initial split of the netw

ork into tw

o groups is in agreement w

ith the actual factions observed by Zachary, w

ith the exception that node 3 is m

isclassified.

fitting to (appropriate) arbitrary shape

shape reflects substrate or construction methods

circularlattice

shape reflects hierarchy (trees)

shape reflects spatial aspect of data (geographic)

reported comunication and nam

e recognition data for 22 bennington respondents arranged by residence

Page 13: network - skyeome.netskyeome.net/text/skyeBudapestNotes.pdf · network data representation: matrices - ¡not necessarily square! elegant concept closely related to graph theory (but

C

aida's skitter: The graph reflects 1,224,733 IP addresses and 2,093,194 IP links, (im

mediately adjacent

addresses in a traceroute-like path) of skitter data from 16 m

onitors probing approximately 932,000 destinations

spread across over 75,000 (70%) of globally routable netw

ork prefixes. Arranged radially according to

geographic coordinates

http://ww

w.caida.org/analysis/topology/as_core_netw

ork/about.xml

Multi D

imensional S

caling / Principal C

omponent A

nalysis

MD

S attem

pts to find a low-dim

ensional (2D or 3D

) representation of a high dim

ensional dataset with the m

inimum

of distortion

MD

S techniques

for most data sets there is no low

exact low dim

ensional embedding

idea is to find one with relatively low

stress

dim

ensions of MD

S are arbitrary

be careful about the kinds of inferences drawn

but if proprietary steps are correct, similar nodes should be grouped

Page 14: network - skyeome.netskyeome.net/text/skyeBudapestNotes.pdf · network data representation: matrices - ¡not necessarily square! elegant concept closely related to graph theory (but

optimization / spring em

bedder

rep

rese

nt n

etw

ork a

s a syste

m o

f we

igh

ts (no

de

s)

connected by springs (edges)

use some optim

ization technique to locate a low energy state for the system

Kam

ada-Kaw

ai

compute local m

inima for energy function and m

ove towards it

continue until low energy state is reached

Fruchterm

an-Riengold

uses modified force-field eqn

calculates individual displacement vectors

cooling function

GE

Maddition of local temperature, other m

odifications

SF

I colaboration network, from

C

om

mu

nity stru

cture

in so

cial a

nd

bio

log

ical n

etw

ork

s G

irvan

& N

ew

ma

n 2

00

1H

omless w

oman’s netw

ork, circular version

Page 15: network - skyeome.netskyeome.net/text/skyeBudapestNotes.pdf · network data representation: matrices - ¡not necessarily square! elegant concept closely related to graph theory (but

Hom

less wom

an’s network, spring version

hybridcentrality m

apped to icon size<

example in pajek>

y - axis to convey status

use attribute data as one dimesion, netw

ork data for another

time-based / dynam

ic

use animation to convey changes in social structure,

change in structure leading to positional change in layout

(change in daily conversation network of bennington social netw

ork study)http://student.bennington.edu/~

skyebend/pajekAnim

ator.htm

addition / deletion of ties

“slice” o

r “thre

ash

old

” disp

lay o

f tie stre

ng

ths

Kinm

age

Page 16: network - skyeome.netskyeome.net/text/skyeBudapestNotes.pdf · network data representation: matrices - ¡not necessarily square! elegant concept closely related to graph theory (but

Mo

ne

stary d

ata

, ea

ch p

lan

e sh

ow

s ne

two

rk at su

bse

qu

en

t time

“ph

ase

dia

gra

ms” o

r “retu

rn m

ap

s”

scores for the 250 alters in bennington study showing value at t0 against t1, and t1

against t2

¡most im

portant that technique is appropriate for data and problem!

refs:

Freem

an, Lin Visua

lizing

So

cial N

etw

orks

http://ww

w.library.cm

u.edu:7850/JoSS

/article.html

[includes many of these im

ages examples and som

e animations]

Tufte, E

. R. (1983). Th

e V

isua

l Disp

lay o

f Qu

an

titative

Info

rma

tion

. Cheshire, C

N:

Graphics P

ress.

CA

IDA

's index of network visualization tools

http://ww

w.caida.org/projects/internetatlas/viz/viztools.htm

l

The structure of

world trade of betw

een 28 OE

CD

countries in 1981 and 1992. The size of the nodes gives the volum

e of flows

in dollars (imports and exports) for each country . T

he size of the links stands for the volume of trade betw

een any tw

o countries. Colors give the regional respectively m

emberships in different trade organisations: E

C

countries (yellow), E

FTA

countries (green), USA

and Canada (blue), Japan (red), E

ast Asian C

ountries (pink), O

ceania (Australia , N

ew Z

ealand) (black).

Page 17: network - skyeome.netskyeome.net/text/skyeBudapestNotes.pdf · network data representation: matrices - ¡not necessarily square! elegant concept closely related to graph theory (but

more on agent based m

odeling and RE

PA

ST

ag

en

t ba

sed

is no

t a “cu

re a

ll”

usefull to gain a qualitative understanding of the implications of a theoretical m

odel

sometim

es conceptually easier to work w

ith and explain to outsiders

simple m

odels are the most m

eaningful

easy to get distracted into a model that is too com

plex to analyses usefully

important to rem

ember lim

itations, simplifications, and com

promises m

adediscrete vs. continuous

time &

simultaneity

interaction geometry

2¢ on good working strategy

best to get as clear as possible on details of theoretical model before coding

but also investigate capabilities of modeling fram

ework as guide to im

plementation

what are the starting conditions for the sim

ulation?

how w

ill time be im

plemented in this sim

?

what is the expected behavior, how

do we know

if it is working?

what data describe the system

, how w

ill it be collected and analyzed?

what space of param

eters will w

e want to explore?

are results general, or artifacts which are specific to this sim

implem

entation?

usefull repast capabilities to consider (I’m not trying to sell it!)

- http://repast.sourceforge.net

batch parameter files for extended sim

ulation runs

running in batch mode w

ithout the GU

I

flexible scheduling

quicktime m

ovie output

read in GIS

rasterfiles as landscapes

can

ge

t as fa

r un

de

r the

ho

od

as yo

u w

an

t, bu

t do

n’t h

ave

to

op

en

sou

rce

Netw

ork Agent-B

ased models in R

epast

repast architecture well suited to netw

ork models

networks can be used to construct arbitrary interaction relations

class co

nta

inin

g “sta

nd

ard

” ne

two

rk sub

strate

ge

ne

rato

rs

generally possible to try out multiple substrates w

ithout changing code

small library of netw

ork stats (but slow

, so extensive analysis should be done in other programs)

import and export netw

ork data files for later analysis

built-in network visualization tools for dynam

ic networks (needs w

ork)