A model of social networks based on social distance attachment
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| Top panel: Examples of typical networks generated for an average degree k=10, N=250, and different values of the homophily exponent. Bottom panel: Binary trees representing the community structure of the corresponding networks (see text). Solid (green) circles are the original vertices of the network whereas hollow circles stand for the communities generated by the Girvan-Newman algorithm. |
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Main
plot: Clustering coefficient for as a function of the homophily
exponent and fixed average degree. The solid line corresponds to the
theoretical value and symbols are simulation results. Inset: Average
clustering coefficient as a function of the degree k for different
values of the homophily exponent (from bottom to top,1.5, 2.5, and
3.5). In all cases, the size of the network is N=100.000. |
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Average nearest neighbors degree for as a function of k, for different values of the homnophily exponent. In all cases, the size of the network is N=100.000. |
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Cumulative size distribution obtained using the GN algorithm for different values of a. As the homophily exponent grows the network becomes a perfectly hierarchical network characterized by a power law community size distribution. In all the cases the size of the network is N=1000. |
Albert Díaz-Guilera