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Correlated Random Networks

Correlated Random Networks,10.1103/PhysRevLett.89.228701,Physical Review Letters,Johannes Berg,Michael Lässig

Correlated Random Networks   (Citations: 29)
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We develop a statistical theory of networks. A network is a set of vertices and links given by its adjacency matrix c, and the relevant statistical ensembles are defined in terms of a partition function Z=∑cexp([-betaH(c)]. The simplest cases are uncorrelated random networks such as the well-known Erdös-Rényi graphs. Here we study more general interactions H(c) which lead to correlations, for example, between the connectivities of adjacent vertices. In particular, such correlations occur in optimized networks described by partition functions in the limit beta-->∞. They are argued to be a crucial signature of evolutionary design in biological networks.
Journal: Physical Review Letters - PHYS REV LETT , vol. 89, no. 22, 2002
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    • ...According to Bianconi (2007), six quantities are useful to characterize network complexity: (1) the density of the links, (2) the degree sequence (Barabasi and Albert 1999), (3) the degree–degree correlations (Pastor-Satorras et al. 2001; Berg and Lassing 2002), (4) the clustering coefficient (Watts and Strogatz 1998; Ravasz et al. 2002), (5) the k-core structure (Carmi et al. 2007; Alvarez-Hamelin et al. 2005) and (6) the community ...

    Andrea De Montiset al. Time evolution of complex networks: commuting systems in insular Italy

    • ...To explore the optimal diversity-multiplexing tradeoff, we will use the correlated random graph theory, which was studied in [10]...
    • ...Then, the subcarrier allocation problem is formulated as a random bipartite graph that every edge in a complete bipartite graph KM,NL appears with the probability measure P .T his kind of random graph is referred to as correlated random bipartite graph [10], whose probability space is denoted by G {KM,NL;P}...

    Bo Baiet al. Diversity-Multiplexing Tradeoff in OFDMA Systems with Coherence Bandwi...

    • ...Previous studies primarily focus on finding various statistical properties of real networks, especially degree based statistics, such as degree distribution[1, 2], degree correlation[3, 4, 5], degree-based structure entropies[6, 7]. Studies of many significant properties of networks, such as heterogeneity[1], assortative mixing[8, 9] and self-similarity [10, 11], are based on these statistics...

    Yang-Hua Xiaoet al. Symmetry-based structure entropy of complex networks

    • ...Sampling properties of networks Uncorrelated random networks are networks which are maximally random conditional on a given degree distribution [15,16] (thus their degree-degree correlations may be different from zero); in such a case it is possible to express expectation values of many interesting network characteristics in terms of the degree distribution Pr(k); more interestingly, the degree sequence is a sufficient (see e.g...

    Eric de Silvaet al. The effects of incomplete protein interaction data on structural and e...

    • ...For the reasons outlined there we would expect that MMI offers a potential route towards predicting properties of the overall network, N , from the properties of subnet, S. This is particularly true for uncorrelated networks[18, 10] but can also be extended to correlated networks [4]...
    • ...the degree-degree distribution [4] will be a natural quantity)...

    Michael P. H. Stumpfet al. Multi-model inference of network properties from incomplete data

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