Social Network Generation: Difference between revisions

From InfoVis:Wiki
Jump to navigation Jump to search
Line 60: Line 60:
* Matrices are shown both with the initial order (middle image) and reordered with the TSP-Based algorithm (right image) described by Henry and Fekete [Infovis 2006].
* Matrices are shown both with the initial order (middle image) and reordered with the TSP-Based algorithm (right image) described by Henry and Fekete [Infovis 2006].


W1 [http://insitu.lri.fr/~nhenry/socnets/SmallWorld_47_0.1_6.xml SmallWorld_47_0.1_6.xml]
W1 [http://insitu.lri.fr/~nhenry/socnets/wsmallworld/wSmallWorld_47_0.1_6.xml SmallWorld_47_0.1_6.xml]


[[image:wSmallWorld_47_0.1_6.JPG|150px]]
[[image:wSmallWorld_47_0.1_6.JPG|150px]]
Line 67: Line 67:




W2 SmallWorld_47_0.3_6
W2 [http://insitu.lri.fr/~nhenry/socnets/wsmallworld/wSmallWorld_47_0.3_6.xml SmallWorld_47_0.3_6.xml]


[[image:wSmallWorld_47_0.3_6.JPG|150px]]
[[image:wSmallWorld_47_0.3_6.JPG|150px]]
Line 74: Line 74:




W3 SmallWorld_47_0.5_6
W3 [http://insitu.lri.fr/~nhenry/socnets/wsmallworld/wSmallWorld_47_0.5_6.xml SmallWorld_47_0.5_6.xml]


[[image:wSmallWorld_47_0.5_6.JPG|150px]]
[[image:wSmallWorld_47_0.5_6.JPG|150px]]
Line 80: Line 80:
[[image:wSmallWorldM_47_0.5_6.PNG|165px]]
[[image:wSmallWorldM_47_0.5_6.PNG|165px]]


W4 SmallWorld_47_0.7_6
W4 [http://insitu.lri.fr/~nhenry/socnets/wsmallworld/wSmallWorld_47_0.7_6.xml SmallWorld_47_0.7_6.xml]


[[image:wSmallWorld_47_0.7_6.JPG|150px]]
[[image:wSmallWorld_47_0.7_6.JPG|150px]]
Line 86: Line 86:
[[image:wSmallWorldM_47_0.7_6.PNG|165px]]
[[image:wSmallWorldM_47_0.7_6.PNG|165px]]


W5 SmallWorld_47_0.9_6
W5 [http://insitu.lri.fr/~nhenry/socnets/wsmallworld/wSmallWorld_47_0.9_6.xml SmallWorld_47_0.9_6.xml]
 


[[image:wSmallWorld_47_0.9_6.JPG|150px]]
[[image:wSmallWorld_47_0.9_6.JPG|150px]]
Line 92: Line 93:
[[image:WSmallWorldM_47_0.9_6.PNG|165px]]
[[image:WSmallWorldM_47_0.9_6.PNG|165px]]


W6 SmallWorld_47_0.3_2
W6 [http://insitu.lri.fr/~nhenry/socnets/wsmallworld/wSmallWorld_47_0.3_2.xml SmallWorld_47_0.3_2.xml]


[[image:wSmallWorld_47_0.3_2.JPG|150px]]
[[image:wSmallWorld_47_0.3_2.JPG|150px]]
Line 98: Line 99:
[[image:WSmallWorldM_47_0.3_2.PNG|165px]]
[[image:WSmallWorldM_47_0.3_2.PNG|165px]]


W7 SmallWorld_47_0.3_4
W7 [http://insitu.lri.fr/~nhenry/socnets/wsmallworld/wSmallWorld_47_0.3_4.xml SmallWorld_47_0.3_4.xml]
 


[[image:wSmallWorld_47_0.3_4.JPG|150px]]
[[image:wSmallWorld_47_0.3_4.JPG|150px]]
Line 104: Line 106:
[[image:WSmallWorldM_47_0.3_4.PNG|165px]]
[[image:WSmallWorldM_47_0.3_4.PNG|165px]]


W8 SmallWorld_47_0.3_8
W8 [http://insitu.lri.fr/~nhenry/socnets/wsmallworld/wSmallWorld_47_0.3_8.xml SmallWorld_47_0.3_8.xml]
 


[[image:wSmallWorld_47_0.3_8.JPG|150px]]
[[image:wSmallWorld_47_0.3_8.JPG|150px]]
Line 111: Line 114:




W9 SmallWorld_47_0.3_10
W9 [http://insitu.lri.fr/~nhenry/socnets/wsmallworld/wSmallWorld_47_0.3_10.xml SmallWorld_47_0.3_10.xml]


[[image:wSmallWorld_47_0.3_10.JPG|150px]]
[[image:wSmallWorld_47_0.3_10.JPG|150px]]
Line 118: Line 121:




W10 SmallWorld_47_0.7_4
W10 [http://insitu.lri.fr/~nhenry/socnets/wsmallworld/wSmallWorld_47_0.7_4.xml SmallWorld_47_0.7_4.xml]


[[image:wSmallWorld_47_0.7_4.JPG|150px]]
[[image:wSmallWorld_47_0.7_4.JPG|150px]]
Line 124: Line 127:
[[image:wSmallWorldM_47_0.7_4.PNG|165px]]
[[image:wSmallWorldM_47_0.7_4.PNG|165px]]


W11 SmallWorld_47_0.1_8
W11 [http://insitu.lri.fr/~nhenry/socnets/wsmallworld/wSmallWorld_47_0.1_8.xml SmallWorld_47_0.1_8.xml]


[[image:wSmallWorld_47_0.1_8.JPG|150px]]
[[image:wSmallWorld_47_0.1_8.JPG|150px]]
Line 130: Line 133:
[[image:wSmallWorldM_47_0.1_8.PNG|165px]]
[[image:wSmallWorldM_47_0.1_8.PNG|165px]]


W12 SmallWorld_94_0.1_8
W12 [http://insitu.lri.fr/~nhenry/socnets/wsmallworld/wSmallWorld_94_0.1_8.xml SmallWorld_94_0.1_8.xml]


[[image:wSmallWorld_94_0.1_8.JPG|150px]]
[[image:wSmallWorld_94_0.1_8.JPG|150px]]

Revision as of 09:01, 4 December 2006

This wiki page is under construction...

Social Network Characterization

Social networks involve persons or groups called actors and relationship between them, with a lot of variety in the kind of actors and relationships. As described in Wasserman and Faust, actors can be people, subgroups, organizations or collectivities; relations may be friendship (relationships), interactions, communications, transactions, movement or kinship. However, the nature of actors and relations does not really matter: we focus on their structure. We can classify the social networks studied in the literature in three categories:

  • Tree-like are trees with additional links forming cycles with a specified probability. This category includes genealogy data and very sparse graphs such as Sexually-Transmitted Disease (STD) transmission patterns. We call them “almost trees” because they have are mostly acyclic and nodes have very few parents.
  • Almost complete graphs are complete graphs with missing relations. For example, data about trade between countries, cities or companies are almost complete graphs. They are interesting to study as valued graphs; since they usually carry values on their edges.
  • Small-world networks (also scale-free or power-law degree-distribution networks) have been studied intensely since they were first described in Watts and Strogatz. They defined them as graphs with three properties: power-law degree distribution, high clustering coefficient and small average shortest path. They are locally dense (sparse with dense sub-graphs).


Three methods exist to select datasets for assessing the quality of analysis systems in the context of social networks: selecting one or two real datasets hoping they are representative, selecting several datasets or generating random datasets with well-known characteristics shared by social networks. With this last method, one should generate datasets with a controlled set of properties and evaluate the systems knowing the properties in advance. It should then eliminate biases linked to a particular dataset and eases the replication of experiments. Unfortunately, while generating tree-like and almost-complete graphs is relatively straightforward, generating graphs with a small-world network structure is still a research topic for computer scientists and physicists. This page shows the results of popular and available network generators. In light of the real social networks we present in the #Real Social Networks, we consider them unsuitable for evaluations since users can easily notice their artifical nature.


Issues on Social Network Generation for Evaluating Visualizations

Watts and Strogatz first described in (Watts, D. J. and S. H. Strogatz (1998). "Collective dynamics of 'small-world' networks." Nature 393: 440 - 442) the concept of small-world networks. They formalized these networks as graphs with three properties: power-law degree distribution, high clustering coefficient and small average shortest path. In the same paper they propose a basic model fitting these properties consisting in a grid (fixed local neighborhood) with additional links simulating some unexpected relations support to the six degrees of separation discovered by Milgram (Milgram, S. (1967). "The small world problem." Psychology Today: 60-67). Barabási and Albert proposed an incremental model to improve it (Barabási, A.-L. and R. Albert (1999). "Emergence of Scaling in Random Networks." Science 286(5439): 509 - 512. ). Since Watts and Strogatz’ model, several have been proposed each generating networks with one or two of the described properties (power-law) but none combine the three of them.

Here are some results of available generators present in the JUNG package. Let's note that for each network generated we only keep the biggest component. Generators present in Pajek[1] and Geomi[2] are incremental scale-free networks generators such as the Barabasi and Albert model.

Small-World Generators

WattsBetaSmallWorldGenerator

Parameters: numVertices (the number of nodes in the ring lattice), beta (the probability of an edge being rewired randomly; the proportion of randomly rewired edges in a graph) and degree( the number of edges connected to each vertex; the local neighborhood size). Degree must be even.

Parameters and Resulting Graph characteristics
graphs W1 W2 W3 W4 W5 W6 W7 W8 W9 W10 W11 W12
numVertices 47 47 47 47 47 47 47 47 47 47 47 94
beta 0.1 0.3 0.5 0.7 0.9 0.3 0.3 0.3 0.3 0.7 0.1 0.1
degree 6 6 6 6 6 2 4 8 10 4 8 8
numVertices 47 47 47 47 47 47 47 47 47 47 47 94
numEdges 282 282 282 282 282 94 188 376 470 188 376 752
components 1 1 1 1 1 2 1 1 1 1 1 1
density 0.36 0.36 0.36 0.36 0.36 0.21 0.29 0.41 0.46 0.29 0.41 0.29
clusteringCoefficient 0.51 0.25 0.15 0.09 0.12 0.23 0.25 0.32 0.38 0.07 0.53 0.52
diameter 6 4 4 4 4 - 6 4 3 5 5 6
averageShortestDistance 2.97 2.4 2.32 2.3 2.29 - 3.24 2.15 1.98 2.83 2.56 3.15
minDegree 5 4 4 3 4 1 2 5 8 2 7 6
maxDegree 8 9 9 9 9 4 6 10 13 8 10 10

GraphMl files and Pictures:

  • Node-Link diagrams are ordered with the linLog algorithm of Andreas Noack [Graph Drawing 2005] (with edge-repulsion coefficient of 2.5f).
  • Matrices are shown both with the initial order (middle image) and reordered with the TSP-Based algorithm (right image) described by Henry and Fekete [Infovis 2006].

W1 SmallWorld_47_0.1_6.xml


W2 SmallWorld_47_0.3_6.xml


W3 SmallWorld_47_0.5_6.xml

W4 SmallWorld_47_0.7_6.xml

W5 SmallWorld_47_0.9_6.xml


W6 SmallWorld_47_0.3_2.xml

W7 SmallWorld_47_0.3_4.xml


W8 SmallWorld_47_0.3_8.xml



W9 SmallWorld_47_0.3_10.xml


W10 SmallWorld_47_0.7_4.xml

W11 SmallWorld_47_0.1_8.xml

W12 SmallWorld_94_0.1_8.xml


KleinbergSmallWorldGenerator

Parameters:latticeSize (the lattice size (length of row or column dimension)) and clusteringExponent (the clustering exponent parameter).

Parameters and Resulting Graph characteristics
graphs W1 W2 W3 W4 W5 W6 W7 W8 W9 W10 W11
latticeSize 7 7 7 7 7 7 7 10 10 10 10
clusteringExponent 0.1 0.5 1 2 2.5 4 8 2 4 8 12
numVertices 49 49 49 49 49 49 49 100 100 100 100
numEdges 490 490 490 490 490 490 490 1000 1000 1000 1000
components 1 1 1 1 1 1 1 1 1 1 1
density 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.32 0.32 0.32 0.32
clusteringCoefficient 0.08 0.09 0.14 0.19 0.19 0.26 0.32 0.18 0.23 0.32 0.33
diameter 4 4 4 4 4 5 5 5 6 7 7
averageShortestDistance 2.38 2.36 2.37 2.44 2.48 2.54 2.73 3.1 3.57 3.65 3.68
minDegree 9 9 9 9 9 9 9 9 9 9 9
maxDegree 14 12 13 12 12 13 12 13 13 14 12

W1 SmallWorld_49_0.1

W2 SmallWorld_49_0.5

W3 SmallWorld_49_1.0

W4 SmallWorld_49_2.0

W5 SmallWorld_49_2.5

W6 SmallWorld_49_4.0

W7 SmallWorld_49_8.0

W8 SmallWorld_100_2.0

W9 SmallWorld_100_4.0

W10 SmallWorld_100_8.0

W11 SmallWorld_100_12.0

Scale-Free Networks Generator

BarabasiAlbertGenerator

Parameters: init_vertices (number of vertices that the graph should start with), numEdgesToAttach (the number of edges that should be attached from the new vertex to pre-existing vertices at each time step) and numSteps (number of time steps). init_vertices must be superior or equal to numEdgesToAttach.

Parameters and Resulting Graph characteristics
graphs W1 W2 W3 W4 W5 W6 W7 W8
init_vertices 4 4 4 4 2 2 2 4
numEdgesToAttach 2 2 2 1 1 1 2 4
numSteps 10 50 100 100 100 50 50 50
numVertices 14 53 104 80 76 51 52 54
numEdges 40 200 400 158 150 100 200 400
components 1 1 1 1 1 1 1 1
density 0.45 0.27 0.19 0.16 0.16 0.2 0.27 0.37
clusteringCoefficient 0.15 0.2 0.07 0.51 0.51 0.66 0.16 0.23
diameter 4 6 6 11 14 8 5 4
averageShortestDistance 2.24 2.81 3.18 5.26 5.7 3.74 2.8 2.15
minDegree 2 1 2 1 1 1 2 4
maxDegree 5 16 19 8 12 16 17 26

W1 ScaleFree_4_2_10

W2 ScaleFree_4_2_50

W3 ScaleFree_4_2_100

W4 ScaleFree_4_1_100

W5 ScaleFree_2_1_100

W6 ScaleFree_2_1_50

W7 ScaleFree_2_2_50

W8 ScaleFree_4_4_50


EppsteinPowerLawGenerator

Parameters: numVertices (the number of vertices for the generated graph), numEdges (the number of edges the generated graph will have, should be Theta(numVertices)) and r (the model parameter).

Real Social Networks

Here is a panel of undirected networks issued from scientific articles, benchmarks or contests. Social network visualization or analysis tools provide also some real datasets: Pajek [3] and UCINet [4].


Small-World

Parameters and Resulting Graph characteristics for Co-Authoring Networks
Name Team Collaboration (with external collaborators) Team Collaboration (within the team) Infovis component 1 Infovis component 2 Infovis component 3 Infovis component 4
Source Collected Collected Contest Contest Contest Contest
numNodes 146 96 135 48 47 32
numEdges 540 316 321 91 114 109
components 1 1 1 1 1 1
density 0.16 0.19 0.13 0.2 0.23 0.33
clusteringCoefficient 0.91 0.91 0.82 0.79 0.83 0.81
diameter 4 5 11 7 10 6
averageShortestDistance 2.65 2.81 4.4 3.71 3.84 2.6
minDegree 1 1 1 1 1 1
maxDegree 57 29 22 11 15 15

TeamCollaborationExternal

TeamCollaborationWithin

File:TeamCollaborationWithin.PNG File:TeamCollaborationWithinMInit.PNG File:TeamCollaborationWithinM.PNG

Infovis Component 1

Infovis Component 2

Infovis Component 3

Infovis Component 4

Tree-like

Parameters and Resulting Graph characteristics for Genealogy and Virus Transmission
Name genealogy MSTTransmission1 MSTTransmission2 HIVTransmission
Source Pajek Article [5] Article[6] Article [7]
numVertices 242 38 84 243
numEdges 510 78 182 514
components 1 1 1 1
density 0.09 0.23 0.16 0.09
clusteringCoefficient 0.66 0.53 0.52 0.65
diameter 11 10 9 23
averageShortestDistance 5.78 4.42 4.31 8.27
minDegree 1 1 1 1
maxDegree 14 7 17 20

Gondola Genealogy

MSTTransmission 1

MSTTransmission 2

HIV Transmission

Almost Complete Graphs

Parameters and Resulting Graph characteristics for Email Communication within a research lab.
Name emailDay per person emailWeek per person emailMonth per person emailYear per person emailDay per team emailWeek per team emailMonth per team emailYear per team
Source Collected Collected Collected Collected Collected Collected Collected Collected
numVertices 134 200 242 447 30 33 35 42
numEdges 442 1676 3514 11462 183 410 564 980
components 1 1 1 1 1 1 1 1
density 0.16 0.2 0.24 0.24 0.45 0.61 0.68 0.75
clusteringCoefficient 0.52 0.55 0.62 0.71 0.62 0.78 0.83 0.84
diameter 9 7 6 6 5 3 3 3
averageShortestDistance 4.29 2.92 2.52 2.42 2.17 1.71 1.57 1.45
minDegree 1 1 1 1 1 1 1 3
maxDegree 15 51 86 195 16 26 34 40

Email exchange per person during a day

Email exchange per person during a week

Email exchange per person during a month

Email exchange per person during a year

Email exchange per research group during a day (Email number is coded with link width in the nodelink, edge color in the matrix)

Email exchange per research group during a week (Email number is coded with link width in the nodelink, edge color in the matrix)

Email exchange per research group during a month (Email number is coded with link width in the nodelink, edge color in the matrix)

Email exchange per research group during a year (Email number is coded with link width in the nodelink, edge color in the matrix)