Related papers: Critical phenomena on heterogeneous small-world ne…
Many real-world complex networks contain a significant amount of structural redundancy, in which multiple vertices play identical topological roles. Such redundancy arises naturally from the simple growth processes which form and shape many…
We live in a modern world supported by large, complex networks. Examples range from financial markets to communication and transportation systems. In many realistic situations the flow of physical quantities in the network, as characterized…
We consider the influence of a power-law deviation from the critical coupling such that the system is critical at its surface. We develop a scaling theory showing that such a perturbation introduces a new length scale which governs the…
The hierarchical small-world network is a real-world network. It models well the benefit transmission web of the pyramid selling in China and many other countries. In this paper, by applying the spectral graph theory, we study three…
Many-body systems when continuous phase transition occurs are mainly built in the interrelationship between particles, implemented through many-body correlations. Some of them may exhibit so-called topological order hardly measured by…
Complex networks have been studied extensively due to their relevance to many real systems as diverse as the World-Wide-Web (WWW), the Internet, energy landscapes, biological and social networks…
We show how one can trace in a systematic way the coarse-grained solutions of individual-based stochastic epidemic models evolving on heterogeneous complex networks with respect to their topological characteristics. In particular, we have…
Collective dynamics on small-world networks emerge in a broad range of systems with their spectra characterizing fundamental asymptotic features. Here we derive analytic mean field predictions for the spectra of small-world models that…
We present an analysis of the classical contact process on scale-free networks. A mean-field study, both for finite and infinite network sizes, yields an absorbing-state phase transition at a finite critical value of the control parameter,…
A detailed analysis of three species-rich ecosystem food webs has shown that they display scale-free distributions of connections. Such graphs of interaction are in fact shared by a number of biological and technological networks, which…
Many real-world networks exhibit scale-free feature, have a small diameter and a high clustering tendency. We have studied the properties of a growing network, which has all these features, in which an incoming node is connected to its…
The rapidly developing theory of complex networks indicates that real networks are not random, but have a highly robust large-scale architecture, governed by strict organizational principles. Here, we focus on the properties of biological…
Small-world networks are ubiquitous in real-life systems. Most previous models of small-world networks are stochastic. The randomness makes it more difficult to gain a visual understanding on how do different nodes of networks interact with…
We present a family of scale-free network model consisting of cliques, which is established by a simple recursive algorithm. We investigate the networks both analytically and numerically. The obtained analytical solutions show that the…
Previous studies on the invulnerability of scale-free networks under edge attacks supported the conclusion that scale-free networks would be fragile under selective attacks. However, these studies are based on qualitative methods with…
Criticality has been proposed as a key principle underlying complex behavior in biological and artificial systems; however, how criticality translates from individual dynamics to collective behavior remains unclear. We study this question…
We quantify the dynamical implications of the small-world phenomenon. We consider the generic synchronization of oscillator networks of arbitrary topology, and link the linear stability of the synchronous state to an algebraic condition of…
We show that subsets of interacting oscillators may synchronize in different ways within a single network. This diversity of synchronization patterns is promoted by increasing the heterogeneous distribution of coupling weights and/or…
This review explains in a self-contained way the properties of random Boolean networks and their attractors, with a special focus on critical networks. Using small example networks, analytical calculations, phenomenological arguments, and…
The talk presented at ICMP 97 focused on the scaling limits of critical percolation models, and some other systems whose salient features can be described by collections of random lines. In the scaling limit we keep track of features seen…