Most real-world networks exhibit a high clustering coefficient—the probability that two neighbors of a node are also neighbors of each other. We propose two algorithms, Conf and Throw, that take triangle and single edge degree sequences as input and generate a random graph with a target...

We consider the coherent exciton transport, modeled by continuous-time quantum walks, on Erdös–Rény graphs in the presence of a random distribution of traps. The role of trap concentration and of the substrate dilution is deepened showing that, at long times and for intermediate degree of...

We analyze dynamic local interaction in population games where the local interaction structure (modeled as a graph) can change over time: A stochastic process generates a random sequence of graphs. This contrasts with models where the initial interaction structure (represented by a deterministic...

A preferential attachment model for a growing network incorporating the deletion of edges is studied and the expected asymptotic degree distribution is analyzed. At each time step t=1,2,…, with probability π10 a new vertex with one edge attached to it is added to the network and the edge is...

We investigate the finite size corrections to the equilibrium magnetization of an Ising model on a random graph with N nodes and Nγ edges, with 1γ≤2. By conveniently rescaling the coupling constant, the free energy is made extensive. As expected, the system displays a phase transition of the...

We present a complete analytical solution of a system of Potts spins on a random k-regular graph in both the canonical and microcanonical ensembles, using the Large Deviation Cavity Method (LDCM). The solution is shown to be composed of three different branches, resulting in a non-concave...

We discuss various ensembles of homogeneous complex networks and a Monte-Carlo method of generating graphs from these ensembles. The method is quite general and can be applied to simulate micro-canonical, canonical or grand-canonical ensembles for systems with various statistical weights. It can...

A foam is a space-filling cellular pattern, that can be decomposed into successive layers or strata. Each layer contains all cells at the same topological distance to an origin (cell, cluster of cells, or basal layer). The disorder of the underlying structure imposes a characteristic roughening...