Related papers: Phase Transitions in an Aging Network
Scale-free networks are abundant in nature and society, describing such diverse systems as the world wide web, the web of human sexual contacts, or the chemical network of a cell. All models used to generate a scale-free topology are…
We propose a dynamical process for network evolution, aiming at explaining the emergence of the small world phenomenon, i.e., the statistical observation that any pair of individuals are linked by a short chain of acquaintances computable…
We investigate a network model based on an infinite regular square lattice embedded in the Euclidean plane where the node connection probability is given by the geometrical distance of nodes. We show that the degree distribution in the…
We propose an extended local-world evolving network model including a triad formation step. In the process of network evolution, random fluctuation in the number of new edges is involved. We derive analytical expressions for degree…
Complex gene regulatory networks often display emergent simple behavior. Sometimes this simplicity can be traced to a nearly equivalent energy landscape, but not always. Here, we show how a topological theory for stochastic and biochemical…
Many real networks have cliques as their constitutional units. Here we present a family of scale-free network model consist of cliques, which is established by a simple recursive algorithm. We investigate the networks both analytically and…
Preferential attachment is often suggested to be the underlying mechanism of the growth of a network, largely due to that many real networks are, to a certain extent, scale-free. However, such attribution is usually made under debatable…
We study the non-equilibrium phase transition in a model for epidemic spreading on scale-free networks. The model consists of two particle species $A$ and $B$, and the coupling between them is taken to be asymmetric; $A$ induces $B$ while…
Real networks can be classified into two categories: fractal networks and non-fractal networks. Here we introduce a unifying model for the two types of networks. Our model network is governed by a parameter $q$. We obtain the topological…
We propose a spreading model in multilayer networks and study the nature of nonequilibrium phase transition in the model. The model integrates the susceptible-infected-susceptible (or susceptible-infected-recovered) spreading dynamics with…
The voter model is a classical interacting particle system explaining consensus formation on a social network. Real social networks feature not only a heterogeneous degree distribution but also connections changing over time. We study the…
We study an evolving spatial network in which sequentially arriving vertices are joined to existing vertices at random according to a rule that combines preference according to degree with preference according to spatial proximity. We…
Many real-world networks display a natural bipartite structure. Investigating it based on the original structure is helpful to get deep understanding about the networks. In this paper, some real-world bipartite networks are collected and…
We present a generic threshold model for the co-evolution of the structure of a network and the state of its nodes. We focus on regular directed networks and derive equations for the evolution of the system toward its absorbing state. It is…
The $k$-core percolation is a fundamental structural transition in complex networks. Through the analysis of the size jump behaviors of $k$-core in the evolution process of networks, we confirm that $k$-core percolation is continuous phase…
Recent studies introduced biased (degree-dependent) edge percolation as a model for failures in real-life systems. In this work, such process is applied to networks consisting of two types of nodes with edges running only between nodes of…
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…
The Watts-Strogatz algorithm transferring a regular lattice to the small world network is modified by introducing preferential rewiring constrained by connectivity demand. The probability to link to/ unlink form a node is dependent on a…
In our version of Watts and Strogatz's small world model, space is a d-dimensional torus in which each individual has in addition exactly one long-range neighbor chosen at random from the grid. This modification is natural if one thinks of…
We propose a model for evolving networks by merging building blocks represented as complete graphs, reminiscent of modules in biological system or communities in sociology. The model shows power-law degree distributions, power-law…