Intrinsic limitations of inverse inference in the pairwise Ising spin glass

We analyze the limits inherent to the inverse reconstruction of a pairwise Ising spin glass based on susceptibility propagation. We establish the conditions under which the susceptibility propagation algorithm is able to reconstruct the characteristics of the network given first- and second-order local observables, evaluate eventual errors due to various types of noise in the originally observed data, and discuss the scaling of the problem with the number of degrees of freedom

Ranking by Loops: a new approach to categorization

We introduce Loop Ranking, a new ranking measure based on the detection of closed paths, which can be computed in an efficient way. We analyze it with respect to several ranking measures which have been proposed in the past, and are widely used to capture the relative importance of the vertices in complex networks. We argue that Loop Ranking is a very appropriate measure to quantify the role of both vertices and edges in the network traffic.Comment: 4 pages, 2 figures, 1 table, corrected misprin

Finding long cycles in graphs

We analyze the problem of discovering long cycles inside a graph. We propose and test two algorithms for this task. The first one is based on recent advances in statistical mechanics and relies on a message passing procedure. The second follows a more standard Monte Carlo Markov Chain strategy. Special attention is devoted to Hamiltonian cycles of (non-regular) random graphs of minimal connectivity equal to three

Ageing, dynamical heterogeneities and crystallization in the Biroli-Mezard model.

Disponibile in rete su ArXiV.org come cond-mat/051024

Ranking Vertices or Edges of a Network by Loops: A New Approach

preprint arXiv:0804.143