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Keywords
(6)
Adjacency Matrix
Biological Network
Classical Statistical Mechanics
Evolutionary Design
Partition Function
Random Networks
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Correlated Random Networks
Correlated Random Networks,10.1103/PhysRevLett.89.228701,Physical Review Letters,Johannes Berg,Michael Lässig
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Correlated Random Networks
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Citations: 29
)
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Johannes Berg
,
Michael Lässig
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 wellknown ErdösRényi 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
DOI:
10.1103/PhysRevLett.89.228701
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Citation Context
(9)
...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 (PastorSatorras et al. 2001;
Berg and Lassing 2002
), (4) the clustering coefficient (Watts and Strogatz 1998; Ravasz et al. 2002), (5) the kcore structure (Carmi et al. 2007; AlvarezHamelin et al. 2005) and (6) the community ...
Andrea De Montis
,
et al.
Time evolution of complex networks: commuting systems in insular Italy
...To explore the optimal diversitymultiplexing 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 Bai
,
et al.
DiversityMultiplexing 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
], degreebased structure entropies[6, 7]. Studies of many significant properties of networks, such as heterogeneity[1], assortative mixing[8, 9] and selfsimilarity [10, 11], are based on these statistics...
YangHua Xiao
,
et al.
Symmetrybased 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 degreedegree 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 Silva
,
et 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 degreedegree distribution [
4
] will be a natural quantity)...
Michael P. H. Stumpf
,
et al.
Multimodel inference of network properties from incomplete data
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Citations
(29)
Statistical Inference for ValuedEdge Networks: The Generalized Exponential Random Graph Model
Bruce A. Desmarais
,
Skyler J. Cranmer
Journal:
PLOS One
, vol. 7, no. 1, 2012
Time evolution of complex networks: commuting systems in insular Italy
(
Citations: 2
)
Andrea De Montis
,
Simone Caschili
,
Alessandro Chessa
Journal:
Journal of Geographical Systems
, vol. 13, no. 1, pp. 4965, 2011
Impact of random failures and attacks on Poisson and powerlaw random networks
Clémence Magnien
,
Matthieu Latapy
,
JeanLoup Guillaume
Journal:
ACM Computing Surveys  CSUR
, vol. 43, no. 3, pp. 131, 2011
Efficient and exact sampling of simple graphs with given arbitrary degree sequence
(
Citations: 3
)
Charo I. Del Genio
,
Hyunju Kim
,
Zoltán Toroczkai
,
Kevin E. Bassler
Journal:
PLOS One
, vol. abs/1002.2, no. 4, 2010
Improved Inference for RespondentDriven Sampling Data with Application to HIV Prevalence Estimation
(
Citations: 2
)
Krista J. Gile
Published in 2010.