Social Network Generation
samsung ringtones viagra online motorola ringtones viagra online order phentermine ultram online cheap diazepam cheap rivotril cheap ativan clonazepam online cheap tramadol buy carisoprodol meridia online cheap valium cheap zoloft cyclobenzaprine online sonyericsson ringtones cheap flexeril xanax online free nokia ringtones cheap valium cheap wellbutrin sildenafil online zoloft online cheap valium midi ringtones cialis online free qwest ringtones free real ringtones free real ringtones polyphonic ringtones free tracfone ringtones cheap ultracet cheap norco polyphonic ringtones buy levitra cheap ambien cheap sildenafil cheap prozac xanax online ortho online free funny ringtones vicodin online phentermine online cheap norco buy lortab cheap hydrocodone cheap ativan buy paxil free mono ringtones valium cheap tramadol cheap zoloft hydrocodone cheap viagra cheap albuterol cheap rivotril verizon ringtones lorazepam online viagra online order didrex order phentermine free cingular ringtones free ericsson ringtones sony ericsson ringtones motorola ringtones buy zanaflex flexeril online samsung ringtones nokia ringtones cheap diazepam free sonyericsson ringtones buy lorazepam free real ringtones but rivotril ambien online albuterol online cialis online ambien online sagem ringtones cheap norco meridia online nexium online free mono ringtones cheap hgh cheap ultram ativan online buy wellbutrin free free ringtones order diazepam free sprint ringtones lortab online buy carisoprodol free verizon ringtones buy clomid xenical online cheap xanax free ringtones cheap wellbutrin carisoprodol online tracfone ringtones free sharp ringtones buy ativan buy norco free sony ericsson ringtones tracfone ringtones free sonyericsson ringtones soma online cheap meridia zyban online clonazepam free music ringtones cheap cyclobenzaprine ativan online cheap paxil ativan online cheap nexium mp3 ringtones cheap hgh propecia online free samsung ringtones online ortho zyban free punk ringtones order lipitor free mtv ringtones cheap vigrx lorazepam online buy fioricet order lorazepam free cool ringtones free qwest ringtones cheap diazepam cheap tenuate cheap clonazepam buy fioricet ativan online buy clonazepam cheap propecia mp3 ringtones hydrocodone online carisoprodol online cheap didrex levitra free nextel ringtones zyban online mp3 ringtones levitra buy celexa tracfone ringtones cheap adipex free ringtones free music ringtones nextel ringtones nokia ringtones cheap levitra free ringtones propecia online cheap nexium cialis online soma online free mp3 ringtones tramadol online phentermine online funny ringtones cheap nexium buy wellbutrin cheap adipex cialis online cheap ultram free alltel ringtones free funny ringtones funny ringtones celexa online real ringtones free free ringtones free samsung ringtones viagra online cheap diazepam cheap ultram vicodin online alprazolam online propecia online diazepam online mp3 ringtones cheap meridia cheap meridia free nokia ringtones adipex online cheap xenical online hydrocodone cingular ringtones free sagem ringtones buy xanax lisinopril online funny ringtones cheap valium tracfone ringtones samsung ringtones ativan online alprazolam online free samsung ringtones cheap viagra free motorola ringtones cheap viagra cheap phentermine ultram online cheap diazepam cheap rivotril cheap ativan clonazepam online tramadol online buy carisoprodol meridia online cheap valium cheap zoloft cyclobenzaprine online sonyericsson ringtones flexeril online xanax free nokia ringtones valium online wellbutrin online online sildenafil order zoloft valium online midi ringtones cheap cialis qwest ringtones real ringtones real ringtones polyphonic ringtones tracfone ringtones ultracet online cheap norco free polyphonic ringtones levitra online cheap ambien cheap sildenafil prozac online online xanax ortho online free funny ringtones vicodin online phentermine online cheap norco lortab online cheap hydrocodone ativan online buy paxil free mono ringtones online valium cheap tramadol cheap zoloft hydrocodone viagra online but albuterol cheap rivotril free verizon ringtones lorazepam viagra online cheap didrex order phentermine free cingular ringtones free ericsson ringtones sony ericsson ringtones motorola ringtones buy zanaflex cheap flexeril free samsung ringtones nokia ringtones diazepam online free sonyericsson ringtones lorazepam online free real ringtones but rivotril ambien online cheap albuterol buy cialis ambien online sagem ringtones cheap norco order meridia cheap nexium free mono ringtones hgh online ultram online ativan online buy wellbutrin free free ringtones order diazepam sprint ringtones buy lortab buy carisoprodol verizon ringtones clomid online cheap xenical xanax online free ringtones cheap wellbutrin carisoprodol online free tracfone ringtones sharp ringtones buy ativan norco online free sony ericsson ringtones tracfone ringtones sonyericsson ringtones soma online cheap meridia buy zyban online clonazepam free music ringtones cyclobenzaprine online cheap ativan cheap paxil cheap ativan nexium mp3 ringtones cheap hgh buy propecia free samsung ringtones ortho zyban punk ringtones lipitor online mtv ringtones cheap vigrx lorazepam online fioricet online lorazepam online cool ringtones qwest ringtones cheap diazepam cheap tenuate clonazepam online fioricet online ativan online buy clonazepam cheap propecia mp3 ringtones buy hydrocodone cheap carisoprodol didrex online online levitra nextel ringtones zyban online mp3 ringtones levitra celexa online tracfone ringtones adipex online free free ringtones music ringtones nextel ringtones nokia ringtones levitra online free free ringtones cheap propecia cheap nexium cialis buy soma mp3 ringtones tramadol online cheap phentermine free funny ringtones nexium online buy wellbutrin cheap adipex cheap cialis cheap ultram alltel ringtones free funny ringtones free funny ringtones cheap celexa real ringtones free free ringtones free samsung ringtones viagra online diazepam online ultram online cheap vicodin buy alprazolam cheap propecia diazepam online free mp3 ringtones cheap meridia cheap meridia nokia ringtones adipex online xenical online online hydrocodone cingular ringtones free sagem ringtones xanax online lisinopril online funny ringtones order valium free tracfone ringtones samsung ringtones This wiki page is under construction...
Research work and images have been realised by Nathalie Henry and Jean-Daniel Fekete, using MatrixExplorer, built with the Infovis Toolkit.
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.
About datasets and representations
- All datasets are downloadable in GraphMl format.
- 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].
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 |
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 |
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 |
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) | Infovis component 1 | Infovis component 2 | Infovis component 3 | Infovis component 4 |
| Source | Collected | Contest | Contest | Contest | Contest | |
| numNodes | 146 | 135 | 48 | 47 | 32 | |
| numEdges | 540 | 321 | 91 | 114 | 109 | |
| components | 1 | 1 | 1 | 1 | 1 | |
| density | 0.16 | 0.13 | 0.2 | 0.23 | 0.33 | |
| clusteringCoefficient | 0.91 | 0.82 | 0.79 | 0.83 | 0.81 | |
| diameter | 4 | 11 | 7 | 10 | 6 | |
| averageShortestDistance | 2.65 | 4.4 | 3.71 | 3.84 | 2.6 | |
| minDegree | 1 | 1 | 1 | 1 | 1 | |
| maxDegree | 57 | 22 | 11 | 15 | 15 |
TeamCollaborationExternal TeamCollaborationExternal.xml
Infovis Component 1 ivComp1.xml
Infovis Component 2 ivComp2.xml
Infovis Component 3 ivComp3.xml
Infovis Component 4 ivComp4.xml
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 GondolaGen.xml
MSTTransmission 1 Mst1.xml
MSTTransmission 2 Mst2.xml
HIV Transmission Hiv.xml
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 emailDay.xml
Email exchange per person during a week emailWeek.xml
Email exchange per person during a month emailMonth.xml
Email exchange per person during a year emailYear.xml
Email exchange per research group during a day emailGDay.xml
Number of email coded with link width in the nodelink, edge color in the matrix
Email exchange per research group during a week emailGWeek.xml
Number of email coded with link width in the nodelink, edge color in the matrix
Email exchange per research group during a month emailGMonth.xml
Number of email coded with link width in the nodelink, edge color in the matrix
Email exchange per research group during a year emailGYear.xml
Number of email coded with link width in the nodelink, edge color in the matrix
