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We study the large-deviation properties of minimum spanning trees for two ensembles of random graphs with $N$ nodes. First, we consider complete graphs. Second, we study Erd\H{o}s-R\'{e}nyi (ER) random graphs with edge probability $p=c/N$…
Networks of the brain are composed of a very large number of neurons connected through a random graph and interacting after random delays that both depend on the anatomical distance between cells. In order to comprehend the role of these…
We propose a general class of co-evolving tree network models driven by local exploration where new vertices attach to the current network via randomly sampling a vertex and then exploring the graph for a random number of steps in the…
We provide a long-time existence and sub-convergence result for the elastic flow of a three network in $\mathbb{R}^{n}$ under some mild topological assumptions. The evolution is such that the sum of the elastic energies of the three curves…
Inspired by studies on the airports' network and the physical Internet, we propose a general model of weighted networks via an optimization principle. The topology of the optimal network turns out to be a spanning tree that minimizes a…
We study the local asymptotic behavior of divergence-like functionals of a family of $d$-dimensional Infinitely Divisible Random Fields. Specifically, we derive limit theorems of surface integrals over Lipschitz manifolds for this class of…
Threshold based models have been widely used in characterizing collective behavior on social networks. An individual's threshold indicates the minimum level of influence that must be exerted, by other members of the population engaged in…
In this paper, we analyze the effects of random sampling on adaptive diffusion networks. These networks consist in a collection of nodes that can measure and process data, and that can communicate with each other to pursue a common goal of…
We considered diffusion-driven processes on small-world networks with distance-dependent random links. The study of diffusion on such networks is motivated by transport on randomly folded polymer chains, synchronization problems in…
A large and sparse random graph with independent exponentially distributed link weights can be used to model the propagation of messages or diseases in a network with an unknown connectivity structure. In this article we study an extended…
Here we present the entropic dynamics formalism for networks. That is, a framework for the dynamics of graphs meant to represent a network derived from the principle of maximum entropy and the rate of transition is obtained taking into…
Robustness of routing policies for networks is a central problem which is gaining increased attention with a growing awareness to safeguard critical infrastructure networks against natural and man-induced disruptions. Routing under limited…
A self-contained account of the theory of structure trees for edge cuts in networks is given. Applications include a generalisation of the Max-Flow Min-Cut Theorem to infinite networks and a short proof of a conjecture of Kropholler. This…
Robustness of distributed routing policies is studied for dynamical flow networks, with respect to adversarial disturbances that reduce the link flow capacities. A dynamical flow network is modeled as a system of ordinary differential…
We present simulation results for the contact process on regular, cubic networks that are composed of a one-dimensional lattice and a set of long edges with unbounded length. Networks with different sets of long edges are considered, that…
We analyse diffusion dynamics on weakly-coupled networks (interconnected networks) by means of separation of time scales. Using an adiabatic approximation we reduced the system dynamics to a Markov chain with aggregated variables and…
We consider dry granular flow down an inclined chute with a localised contraction theoretically and numerically. The flow regimes are predicted through a novel extended one-dimensional hydraulic theory. A discrete particle method validated…
McKay proved that the limiting spectral measures of the ensembles of $d$-regular graphs with $N$ vertices converge to Kesten's measure as $N\to\infty$. In this paper we explore the case of weighted graphs. More precisely, given a large…
The quantum max-flow min-cut conjecture relates the rank of a tensor network to the minimum cut in the case that all tensors in the network are identical\cite{mfmc1}. This conjecture was shown to be false in Ref. \onlinecite{mfmc2} by an…
A multi-type branching process is defined as a random tree with labeled vertices, where each vertex produces offspring independently according to the same multivariate probability distribution. We demonstrate that in realizations of the…