Social Network Generation: Difference between revisions

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).  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.
).  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:
Here are some results of available generators present in the JUNG package.
 
=== Small-World Generator ===
 
WattsBetaSmallWorldGenerator
 
Parameters:
'''numNodes''' (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.
 
{| border="1"
|+ Parameters and Resulting Graph characteristics
|-
| graphs || wSmallWorld_47_0.1_6 ||wSmallWorld_47_0.3_6 || wSmallWorld_47_0.5_6
|-
|'''numNodes'''||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
|-
|numNodes||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
 
wSmallWorld_47_0.1_6
wSmallWorld_47_0.3_6
wSmallWorld_47_0.5_6

Revision as of 14:57, 6 October 2006

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.

Small-World Generator

WattsBetaSmallWorldGenerator

Parameters: numNodes (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 wSmallWorld_47_0.1_6 wSmallWorld_47_0.3_6 wSmallWorld_47_0.5_6
numNodes 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
numNodes 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

wSmallWorld_47_0.1_6 wSmallWorld_47_0.3_6 wSmallWorld_47_0.5_6