Related papers: Scale free networks from a Hamiltonian dynamics
We present a general model for the growth of weighted networks in which the structural growth is coupled with the edges' weight dynamical evolution. The model is based on a simple weight-driven dynamics and a weights' reinforcement…
The vast majority of real-world networks are scale-free, loopy, and sparse, with a power-law degree distribution and a constant average degree. In this paper, we study first-order consensus dynamics in binary scale-free networks, where…
Complex networks in different areas exhibit degree distributions with heavy upper tail. A preferential attachment mechanism in a growth process produces a graph with this feature. We herein investigate a variant of the simple preferential…
We propose a natural model of evolving weighted networks in which new links are not necessarily connected to new nodes. The model allows a newly added link to connect directly two nodes already present in the network. This is plausible in…
In this work we present a general mechanism by which simple dynamics running on networks become self-organized critical for scale free topologies. We illustrate this mechanism with a simple arithmetic model of division between integers, the…
We introduce a dynamical network model which unifies a number of network families which are individually known to exhibit $q$-exponential degree distributions. The present model dynamics incorporates static (non-growing) self-organizing…
In spite of its relevance to the origin of complex networks, the interplay between form and function and its role during network formation remains largely unexplored. While recent studies introduce dynamics by considering rewiring processes…
Complex networks have abundant and extensive applications in real life. Recently, researchers have proposed a number of complex networks, in which some are deterministic and others are random. Compared with deterministic networks, random…
The Erdos-Renyi classical random graph is characterized by a fixed linking probability for all pairs of vertices. Here, this concept is generalized by drawing the linking probability from a certain distribution. Such a procedure is found to…
We generalize the scale-free network model of Barab\`asi and Albert [Science 286, 509 (1999)] by proposing a class of stochastic models for scale-free interdependent networks in which interdependent nodes are not randomly connected but…
The recent discovery of universal principles underlying many complex networks occurring across a wide range of length scales in the biological world has spurred physicists in trying to understand such features using techniques from…
In this paper we theoretically and empirically study the degree and connectivity of the Internet's scale-free topology at the autonomous system (AS) level. The basic features of the scale-free network have influence on the normalization…
The local minima (inherent structures) of a system and their associated transition links give rise to a network. Here we consider the topological and distance properties of such a network in the context of spin glasses. We use steepest…
Recently, motivated by the pioneer works in revealing the small-world effect and scale-free property of various real-life networks, many scientists devote themselves to studying complex networks. In this paper, we give a brief review on the…
Systems with lattice geometry can be renormalized exploiting their coordinates in metric space, which naturally define the coarse-grained nodes. By contrast, complex networks defy the usual techniques, due to their small-world character and…
We introduce a mechanism which models the emergence of the universal properties of complex networks, such as scale independence, modularity and self-similarity, and unifies them under a scale-free organization beyond the link. This brings a…
Hierarchical models of scale free networks are introduced where numbers of nodes in clusters of a given hierarchy are stochastic variables. Our models show periodic oscillations of degree distribution P(k) in the log-log scale. Periods and…
Research in network science has shown that many naturally occurring and technologically constructed networks are scale free, that means a power law degree distribution emerges from a growth model in which each new node attaches to the…
Empirical results show that spatial factors such as distance, population density and communication range affect our social activities, also reflected by the development of ties in social networks. This motivates the need for social network…
A family of models of growing hypergraphs with preferential rules of new linking is introduced and studied. The model hypergraphs evolve via the hyperedge-based growth as well as the node-based one, thus generalizing the…