3 research outputs found
Tailored graph ensembles as proxies or null models for real networks I: tools for quantifying structure
We 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.Comment: 25 pages, 3 figure
Bethe-Peierls approximation and the inverse Ising model
We apply the Bethe-Peierls approximation to the problem of the inverse Ising
model and show how the linear response relation leads to a simple method to
reconstruct couplings and fields of the Ising model. This reconstruction is
exact on tree graphs, yet its computational expense is comparable to other
mean-field methods. We compare the performance of this method to the
independent-pair, naive mean- field, Thouless-Anderson-Palmer approximations,
the Sessak-Monasson expansion, and susceptibility propagation in the Cayley
tree, SK-model and random graph with fixed connectivity. At low temperatures,
Bethe reconstruction outperforms all these methods, while at high temperatures
it is comparable to the best method available so far (Sessak-Monasson). The
relationship between Bethe reconstruction and other mean- field methods is
discussed