Weighted hypersoft configuration model
Journal
Physical Review Research
Date Issued
December 2020
DOI
10.1103/PhysRevResearch.2.043157
Abstract
Maximum entropy null models of networks come in different flavors that depend
on the type of constraints under which entropy is maximized. If the constraints
are on degree sequences or distributions, we are dealing with configuration
models. If the degree sequence is constrained exactly, the corresponding
microcanonical ensemble of random graphs with a given degree sequence is the
configuration model per se. If the degree sequence is constrained only on
average, the corresponding grand-canonical ensemble of random graphs with a
given expected degree sequence is the soft configuration model. If the degree
sequence is not fixed at all but randomly drawn from a fixed distribution, the
corresponding hypercanonical ensemble of random graphs with a given degree
distribution is the hypersoft configuration model, a more adequate description
of dynamic real-world networks in which degree sequences are never fixed but
degree distributions often stay stable. Here, we introduce the hypersoft
configuration model of weighted networks. The main contribution is a particular
version of the model with power-law degree and strength distributions, and
superlinear scaling of strengths with degrees, mimicking the properties of some
real-world networks. As a byproduct, we generalize the notions of sparse
graphons and their entropy to weighted networks.
on the type of constraints under which entropy is maximized. If the constraints
are on degree sequences or distributions, we are dealing with configuration
models. If the degree sequence is constrained exactly, the corresponding
microcanonical ensemble of random graphs with a given degree sequence is the
configuration model per se. If the degree sequence is constrained only on
average, the corresponding grand-canonical ensemble of random graphs with a
given expected degree sequence is the soft configuration model. If the degree
sequence is not fixed at all but randomly drawn from a fixed distribution, the
corresponding hypercanonical ensemble of random graphs with a given degree
distribution is the hypersoft configuration model, a more adequate description
of dynamic real-world networks in which degree sequences are never fixed but
degree distributions often stay stable. Here, we introduce the hypersoft
configuration model of weighted networks. The main contribution is a particular
version of the model with power-law degree and strength distributions, and
superlinear scaling of strengths with degrees, mimicking the properties of some
real-world networks. As a byproduct, we generalize the notions of sparse
graphons and their entropy to weighted networks.
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