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Clustering in Small-World Networks

Clustering can be used to quantify network robustness with respect to perturbation, and a high degree of clustering is one of the features captured by the small-world networks of Watts and Strogatz. In epidemiology, a robust network allows a disease to spread similarly even if the network is perturbed.

    
Compute the global clustering coefficient of a random graph:
Wolfram Language code: RandomGraph[WattsStrogatzGraphDistribution[40, 0.05, 5]]
Wolfram Language code: GlobalClusteringCoefficient[%]
Compute the global clustering coefficients of a set of random graphs:
Wolfram Language code: {graphs, coeffs} = Transpose[SortBy[{#, GlobalClusteringCoefficient[#]}& /@ RandomGraph[WattsStrogatzGraphDistribution[30, 0.1, 3], {10000}], Last]];
Create the heat map of selected graphs with respect to the coefficient values:
Wolfram Language code: min = Min[coeffs];max = Max[coeffs];
Wolfram Language code: nf = Nearest[coeffs -> graphs];
Wolfram Language code: values = Range[min, max, (max - min) / (4 ^ 2 - 1)];
Wolfram Language code: Grid[Partition[Map[Annotate[First[nf[#]] 1, {VertexStyle -> Directive[White, EdgeForm[White]], EdgeStyle -> White, Background -> ColorData[{"SolarColors", "Reversed"}, Rescale[#, {min, max}]], ImageSize -> {100, 100}}]&, values], 4]]