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Link-space formalism for network analysi | | David M. D. Smith
; Chiu Fan Lee
; Neil F. Johnson
; Jukka-Pekka Onnela
; | | Date: |
16 Aug 2007 | | Abstract: | We introduce the link-space formalism for analyzing network models with
degree-degree correlations. The formalism is based on a statistical description
of the fraction of links connecting nodes of degrees i and j. To demonstrate
its use, we apply the framework to three growing network models, namely,
random-attachment, Barabasi-Albert, and a model based on a mixture of random
attachment and single step random walks. For the first two models the
link-space matrix can be solved analytically while the numerical solution for
the third exemplifies the effect of degree-degree correlations for the
resulting degree distribution. We also employ the formalism to derive the
degree distributions of two very simple network decay models, more
specifically, that of random link deletion and random node deletion. The
formalism allows detailed analysis of the correlations within networks and we
also employ it to derive the form of a perfectly non-assortative network. | | Source: | arXiv, 0708.2176 | | Services: | Forum | Review | PDF | Favorites | |
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