A Annibale et al 2009 J. Phys. A: Math. Theor. 42 485001 doi:10.1088/1751-8113/42/48/485001
Tailored graph ensembles as proxies or null models for real networks I: tools for quantifying structure
A Annibale1, A C C Coolen1,2, L P Fernandes2, F Fraternali2 and J Kleinjung3
Show affiliationsWe study the tailoring of structured random graph ensembles to real networks, with the objective of generating precise and practical mathematical tools for quantifying and comparing network topologies macroscopically, beyond the level of degree statistics. Our family of ensembles can produce graphs with any prescribed degree distribution and any degree–degree correlation function; its control parameters can be calculated fully analytically, and as a result we can calculate (asymptotically) formulae for entropies and complexities and for information-theoretic distances between networks, expressed directly and explicitly in terms of their measured degree distribution and degree correlations.
- PACS
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89.75.Hc Networks and genealogical trees
02.50.Ng Distribution theory and Monte Carlo studies
02.10.Ox Combinatorics; graph theory
- MSC
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05C75 Structural characterization of types of graphs
- Subjects
- Dates
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Issue 48 (4 December 2009)
Received 14 August 2009, in final form 6 October 2009
Published 11 November 2009
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Tailored graph ensembles as proxies or null models for real networks I: tools for quantifying structure
A Annibale et al 2009 J. Phys. A: Math. Theor. 42 485001
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