Related papers: Analytic solution of a static scale-free network m…
We provide a numerical study of the macroscopic model of [3] derived from an agent-based model for a system of particles interacting through a dynamical network of links. Assuming that the network remodelling process is very fast, the…
In a recursive way and by including a parameter, we introduce a family of deterministic scale-free networks. The resulting networks exhibit small-world effects. We calculate the exact results for the degree exponent, the clustering…
We prove a central limit theorem for network formation models with strategic interactions and homophilous agents. Since data often consists of observations on a single large network, we consider an asymptotic framework in which the network…
The state of many physical, biological and socio-technical systems evolves by combining smooth local transitions and abrupt resetting events to a set of reference values. The inclusion of the resetting mechanism not only provides the…
Exact method of analytical solution of flat, non-dispersive eigenstates in a class of quasi-one dimensional structures is reported within the tight-binding framework. The states are localized over certain sublattice sites. One such finite…
We present a novel type of weighted scale-free network model, in which the weight grows independently of the attachment of new nodes. The evolution of this network is thus determined not only by the preferential attachment of new nodes to…
In this letter, we proposed an ungrowing scale-free network model, wherein the total number of nodes is fixed and the evolution of network structure is driven by a rewiring process only. In spite of the idiographic form of $G$, by using a…
Many complex systems--from social and communication networks to biological networks and the Internet--are thought to exhibit scale-free structure. However, prevailing explanations rely on the constant addition of new nodes, an assumption…
Conditions are presented for different types of identifiability of discrete variable models generated over an undirected graph in which one node represents a binary hidden variable. These models can be seen as extensions of the latent class…
Scale-free networks contain many small cliques and cycles. We model such networks as inhomogeneous random graphs with regularly varying infinite-variance weights. For these models, the number of cliques and cycles have exact integral…
An important problem in modeling networks is how to generate a randomly sampled graph with given degrees. A popular model is the configuration model, a network with assigned degrees and random connections. The erased configuration model is…
Preferential attachment is one possible way to obtain a scale-free network. We develop a self-consistent method to determine whether preferential attachment occurs during the growth of a network, and to extract the preferential attachment…
Random networks with complex topology are common in Nature, describing systems as diverse as the world wide web or social and business networks. Recently, it has been demonstrated that most large networks for which topological information…
We investigate the properties of an autoassociative network of threshold-linear units whose synaptic connectivity is spatially structured and asymmetric. Since the methods of equilibrium statistical mechanics cannot be applied to such a…
We study a class models of correlated random networks in which vertices are characterized by \textit{hidden variables} controlling the establishment of edges between pairs of vertices. We find analytical expressions for the main topological…
The topology of an instant messaging system is described. Statistical measures of the network are given and compared with the statistics of a comparable random graph. The scale-free character of the network is examined and implications are…
Non-equilibrium systems lack an explicit characterisation of their steady state like the Boltzmann distribution for equilibrium systems. This has drastic consequences for the inference of parameters of a model when its dynamics lacks…
In this paper, we propose a simple rule that generates scale-free small-world networks with tunable assortative coefficient. These networks are constructed by two-stage adding process for each new node. The model can reproduce scale-free…
We consider Markov logic networks and relational logistic regression as two fundamental representation formalisms in statistical relational artificial intelligence that use weighted formulas in their specification. However, Markov logic…
It is often desirable to assess how well a given dataset is described by a given model. In network science, for instance, one often wants to say that a given real-world network appears to come from a particular network model. In statistical…