Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2009-05-26
Physics
Condensed Matter
Disordered Systems and Neural Networks
28 pages, 6 figures
Scientific paper
We introduce a statistical mechanics formalism for the study of constrained graph evolution as a Markovian stochastic process, in analogy with that available for spin systems, deriving its basic properties and highlighting the role of the `mobility' (the number of allowed moves for any given graph). As an application of the general theory we analyze the properties of degree-preserving Markov chains based on elementary edge switchings. We give an exact yet simple formula for the mobility in terms of the graph's adjacency matrix and its spectrum. This formula allows us to define acceptance probabilities for edge switchings, such that the Markov chains become controlled Glauber-type detailed balance processes, designed to evolve to any required invariant measure (representing the asymptotic frequencies with which the allowed graphs are visited during the process). As a corollary we also derive a condition in terms of simple degree statistics, sufficient to guarantee that, in the limit where the number of nodes diverges, even for state-independent acceptance probabilities of proposed moves the invariant measure of the process will be uniform. We test our theory on synthetic graphs and on realistic larger graphs as studied in cellular biology.
Annibale Alessia
Coolen Anthony C. C.
Martino Alessandro de
No associations
LandOfFree
Constrained Markovian dynamics of random graphs does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Constrained Markovian dynamics of random graphs, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Constrained Markovian dynamics of random graphs will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-646673