dorsal/arxiv
View SchemaLink-Space and Network Analysis
| Authors | David M. D. Smith, Chiu Fan Lee, Neil F. Johnson, Jukka-Pekka Onnela |
|---|---|
| Categories | |
| ArXiv ID | physics/0702010 |
| URL | https://arxiv.org/abs/physics/0702010 |
Abstract
Many networks contain correlations and often conventional analysis is incapable of incorporating this often essential feature. In arXiv:0708.2176, we introduced the link-space formalism for analysing degree-degree correlations in evolving networks. In this extended version, we provide additional mathematical details and supplementary material. We explore some of the common oversights when these correlations are not taken into account, highlighting the importance of the formalism. The formalism is based on a statistical description of the fraction of links l_{i,j} connecting nodes of degrees i and j. To demonstrate its use, we apply the framework to some pedagogical network models, namely, random-attachment, Barabasi-Albert preferential attachment and the classical Erdos and Renyi random graph. For these three models the link-space matrix can be solved analytically. We apply the formalism to a simple one-parameter growing network model whose numerical solution 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 for arbitrary degree distribution.
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"abstract": "Many networks contain correlations and often conventional analysis is\nincapable of incorporating this often essential feature. In arXiv:0708.2176, we\nintroduced the link-space formalism for analysing degree-degree correlations in\nevolving networks. In this extended version, we provide additional mathematical\ndetails and supplementary material.\n We explore some of the common oversights when these correlations are not\ntaken into account, highlighting the importance of the formalism. The formalism\nis based on a statistical description of the fraction of links l_{i,j}\nconnecting nodes of degrees i and j. To demonstrate its use, we apply the\nframework to some pedagogical network models, namely, random-attachment,\nBarabasi-Albert preferential attachment and the classical Erdos and Renyi\nrandom graph. For these three models the link-space matrix can be solved\nanalytically. We apply the formalism to a simple one-parameter growing network\nmodel whose numerical solution exemplifies the effect of degree-degree\ncorrelations for the resulting degree distribution. We also employ the\nformalism to derive the degree distributions of two very simple network decay\nmodels, more specifically, that of random link deletion and random node\ndeletion. The formalism allows detailed analysis of the correlations within\nnetworks and we also employ it to derive the form of a perfectly\nnon-assortative network for arbitrary degree distribution.",
"arxiv_id": "physics/0702010",
"authors": [
"David M. D. Smith",
"Chiu Fan Lee",
"Neil F. Johnson",
"Jukka-Pekka Onnela"
],
"categories": [
"physics.soc-ph"
],
"title": "Link-Space and Network Analysis",
"url": "https://arxiv.org/abs/physics/0702010"
},
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