Watts-Strogatz Tutorial


  1. Go to the Cytoscape menu and select: Plugins → Random Network Plugin → Generate Random Network


  2. Select Watts-Strogatz Model check box and select the "Next" button.



  3. The variables are explained below:



    • Number of Nodes:  The number of nodes in the random network.  The number here has to be a natural number greater than 0.
    • β (Linear Interpolation):  The probability of shuffling edges in the regular lattice.  As this value approaches 1.0, the resulting network becomes an erdos-renyi network. This value has to be a real number between [0,1].
    • Node Degree:   This value specificies how many neighbors each node has.  The node will be connected to Node Degree nodes on its left and on its right in the intermediary regular lattice.  This value has to be an integer greater than 0.
    • Undirected: If this checkbox is selected then the resulting Cytoscape network may only have a single edge between any two nodes.  As of Cytoscape 2.6.0 only directed edge may actually exist, however, this should change as of v.3.0.
    • Allow Self Edges:  If this checkbox is selected then there may exist edges with the same source and target.  If this checkbox is not selected then self-looping edge will not occur.

  4. Below is the resulting network from the values given above.

    The resulting network has 50 nodes and 100 edges.


  5. Below displays the resulting network with the same values except that the Beta value was set to 0.  The below network is an undirected regular circular-lattice where each node is connected to four nodes.

        The resulting network has 50 nodes and 100 edges.



  6.                                          

Images












N = 1000
Degree = 2
E = 2000
Beta = 0
undirected

Resulting Clustering Coefficient = 0.5



















N = 1000
Degree = 2
E = 2000
Beta = 0.05
undirected

Resulting Clustering Coefficient = 0.428

























N = 1000
Degree = 2
E = 2000
Beta = 0.1
undirected

Resulting Clustering Coefficient = 0.372























N = 1000
Degree = 2
E = 2000
Beta = 0.3
undirected

Resulting Clustering Coefficient = 0.195













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