Related papers: Analytic solution of a static scale-free network m…

We study fully synchronized states in scale-free networks of chaotic logistic maps as a function of both dynamical and topological parameters. Three different network topologies are considered: (i) random scale-free topology, (ii)…

A thorough discussion of the statistical ensemble of scale-free connected random tree graphs is presented. Methods borrowed from field theory are used to define the ensemble and to study analytically its properties. The ensemble is…

A semi-parametric, non-linear regression model in the presence of latent variables is applied towards learning network graph structure. These latent variables can correspond to unmodeled phenomena or unmeasured agents in a complex system of…

In this paper, we present a simple model of scale-free networks that incorporates both preferential & random attachment and anti-preferential & random deletion at each time step. We derive the degree distribution analytically and show that…

The rate equations are used to study the scale-free behavior of the weight distribution in evolving networks whose topology is determined only by degrees of preexisting vertices. An analysis of these equations shows that the degree…

Using a steady state process of node duplication and deletion we produce networks with 1/k scale-free degree distributions in the limit of vanishing connectance. This occurs even though there is no growth involved and inherent preferential…

In the past few years, several studies have explored the topology of interactions in different complex systems. Areas of investigation span from biology to engineering, physics and the social sciences. Although having different microscopic…

Methods connecting dynamical systems and graph theory have attracted increasing interest in the past few years, with applications ranging from a detailed comparison of different kinds of dynamics to the characterisation of empirical data.…

We introduce a general formulation for an implicit equation-free method in the setting of slow-fast systems. First, we give a rigorous convergence result for equation-free analysis showing that the implicitly defined coarse-level time…

The structure of complex networks in previous research has been widely described as scale-free networks generated by the preferential attachment model. However, the preferential attachment model does not take into account the detailed…

We analyze about two hundred naturally occurring networks with distinct dynamical origins to formally test whether the commonly assumed hypothesis of an underlying scale-free structure is generally viable. This has recently been questioned…

Recently, a novel model to describe ordering in systems comprising agents which, although matching in their binarity (i.e., maintaining the iconic Ising features of ``+'' or ``-'', ``up'' or ``down'', ``yes'' or ``no''), still differing in…

Co-evolution exhibited by a network system, involving the intricate interplay between the dynamics of the network itself and the subsystems connected by it, is a key concept for understanding the self-organized, flexible nature of…

There are many networks in real life which exist as form of Scale-free networks such as World Wide Web, protein-protein interaction network, semantic networks, airline networks, interbank payment networks, etc. If we want to analyze these…

Real-world networks may exhibit detachment phenomenon determined by the cancelling of previously existing connections. We discuss a tractable extension of Yule model to account for this feature. Analytical results are derived and discussed…

In many networks such as transportation or communication networks, distance is certainly a relevant parameter. In addition, real-world examples suggest that when long-range links are existing, they usually connect to hubs-the well connected…

We investigate by numerical simulations and analytical calculations the Bak-Sneppen model for biological evolution in scale-free networks. By using large scale numerical simulations, we study the avalanche size distribution and the activity…

In this article, we investigate an artificial traffic model on scale-free networks. Instead of using the routing strategy of the shortest path, a generalized routing algorithm is introduced to improve the transportation throughput, which is…

Identifiability of parameters is an essential property for a statistical model to be useful in most settings. However, establishing parameter identifiability for Bayesian networks with hidden variables remains challenging. In the context of…

We propose a geometric growth model for weighted scale-free networks, which is controlled by two tunable parameters. We derive exactly the main characteristics of the networks, which are partially determined by the parameters. Analytical…