Related papers: Rewiring driven evolution of quenched frustrated s…
The effects of link rewiring are considered for the class of directed networks where each node has the same fixed out-degree. We model a network generated by three mechanisms that are present in various networked systems; growth, global…
We consider the rewiring of a bipartite graph using a mixture of random and preferential attachment. The full mean field equations for the degree distribution and its generating function are given. The exact solution of these equations for…
Evolving networks with a constant number of edges may be modelled using a rewiring process. These models are used to describe many real-world processes including the evolution of cultural artifacts such as family names, the evolution of…
Signed networks with positive and negative interaction are widely observed in the real systems. The negative links would induce frustration, then affect global properties of the system. Based on previous studies, frustration of signed…
We investigate the susceptible-infected-susceptible dynamics on configuration model networks. In an effort for the unification of current approaches, we consider a network whose edges are constantly being rearranged, with a tunable rewiring…
We look at the evolution through rewiring of the degree distribution of a network so the number edges is constant. This is exactly equivalent to the evolution of probability distributions in models of cultural transmission with drift and…
In this paper we investigate networks whose evolution is governed by the interaction of a random assembly process and an optimization process. In the first process, new nodes are added one at a time and form connections to randomly selected…
We define a dynamic model of random networks, where new vertices are connected to old ones with a probability proportional to a sublinear function of their degree. We first give a strong limit law for the empirical degree distribution, and…
We investigate structural transitions in adaptive networks where node states remain fixed and only the connections evolve via state-dependent rewiring. Using a general framework characterized by probabilistic rules for disconnection and…
In many real-world networks, the rates of node and link addition are time dependent. This observation motivates the definition of accelerating networks. There has been relatively little investigation of accelerating networks and previous…
We numerically investigate jamming transitions in complex heterogeneous networks. Inspired by Internet routing protocols, we study a general model that incorporates local traffic information through a tunable parameter. The results show…
Recently we showed that a simple model of network rewiring could be solved exactly for any time and any parameter value. We also showed that this model can be recast in terms of several well known models of statistical physics such as Urn…
We investigate two competing contact processes on a set of Watts--Strogatz networks with the clustering coefficient tuned by rewiring. The base for network construction is one-dimensional chain of $N$ sites, where each site $i$ is directly…
The frustration index is a key measure for analysing signed networks, which has been underused due to its computational complexity. We use an exact optimisation-based method to analyse frustration as a global structural property of signed…
Epidemics on complex networks is a widely investigated topic in the last few years, mainly due to the last pandemic events. Usually, real contact networks are dynamic, hence much effort has been invested in studying epidemics on evolving…
An exactly solvable model for the rewiring dynamics of weighted, directed networks is introduced. Simulations indicate that the model exhibits two types of condensation: (i) a phase in which, for each node, a finite fraction of its total…
A dynamic model for a random network evolving in continuous time is defined where new vertices are born and existing vertices may die. The fitness of a vertex is defined as the accumulated in-degree of the vertex and a new vertex is…
We investigate equilibrium properties of small world networks, in which both connectivity and spin variables are dynamic, using replicated transfer matrices within the replica symmetric approximation. Population dynamics techniques allow us…
Recent studies from social, biological, and engineering network systems have drawn attention to the dynamics over signed networks, where each link is associated with a positive/negative sign indicating trustful/mistrustful,…
We analyze Axelrod's model of social interactions on coevolving complex networks. We introduce four extensions with different mechanisms of edge rewiring. The models are intended to catch two kinds of interactions - preferential attachment,…