Related papers: Phase transition in evolving networks that combine…
The degree distribution is a key statistical indicator in network theory, often used to understand how information spreads across connected nodes. In this paper, we focus on non-growing networks formed through a rewiring algorithm and…
Network growth processes can be understood as generative models of the structure and history of complex networks. This point of view naturally leads to the problem of network archaeology: reconstructing all the past states of a network from…
From the proliferative mechanisms generating neurons from progenitor cells to neuron migration and synaptic connection formation, several vicissitudes culminate in the mature brain. Both component loss and gain remain ubiquitous during…
We derive a analytic evolution equation for overlap parameters including the effect of degree distribution on the transient dynamics of sequence processing neural networks. In the special case of globally coupled networks, the precisely…
In the context of network dynamics, the complexity of systems increases possible evolutionary paths that often are not deterministic. Occasionally, some map routs form over the course of time which guide systems towards some particular…
Modeling complex networks has been the focus of much research for over a decade. Preferential attachment (PA) is considered a common explanation to the self organization of evolving networks, suggesting that new nodes prefer to attach to…
There has been considerable recent interest in the properties of networks, such as citation networks and the worldwide web, that grow by the addition of vertices, and a number of simple solvable models of network growth have been studied.…
We present a general framework for the study of coevolution in dynamical systems. This phenomenon consists of the coexistence of two dynamical processes on networks of interacting elements: node state change and rewiring of links between…
A first-order percolation transition, called explosive percolation, was recently discovered in evolution networks with random edge selection under a certain restriction. However, the network percolation with more realistic evolution…
We consider the preferential attachment model. This is a growing random graph such that at each step a new vertex is added and forms $m$ connections. The neighbors of the new vertex are chosen at random with probability proportional to…
Evolving networks are more widely existed in real world than static networks, and studying their statistical characteristics is vital to recognize and explore them further. But for the networks with nodes preferential deletion, there are…
Random walks constitute a fundamental mechanism for a large set of dynamics taking place on networks. In this article, we study random walks on weighted networks with an arbitrary degree distribution, where the weight of an edge between two…
Many networks generated by nature have two generic properties: they are formed in the process of {preferential attachment} and they are scale-free. Considering these features, by interfering with mechanism of the {preferential attachment},…
We investigate various aspects of the statistics of leaders in growing network models defined by stochastic attachment rules. The leader is the node with highest degree at a given time (or the node which reached that degree first if there…
In many real-world networks, the rates of node and link addition are time dependent. This observation motivates the definition of accelerating networks. There has been relatively little investigation of accelerating networks and previous…
We study the evolution of the graph distance and weighted distance between two fixed vertices in dynamically growing random graph models. More precisely, we consider preferential attachment models with power-law exponent $\tau\in(2,3)$,…
We derive distributional approximations for the number of triangles in the linear preferential attachment model $\mathrm{PAM}(m,\delta)$, where $m\ge 2$ and $\delta>-m$, with explicit rates of convergence. The limiting distribution…
In this paper, a baseline model termed as random birth-and-death network model (RBDN) is considered, in which at each time step, a new node is added into the network with probability p (0<p <1) connect it with m old nodes uniformly, or an…
We consider a generalised d-dimensional model for asymptotically-scale-free geographical networks. Central to many networks of this kind, when considering their growth in time, is the attachment rule, i.e. the probability that a new node is…
In the coevolution of network structures and opinion formation, we investigate the effects of a mixed population with distinctive relinking preferences on both the convergence time and the network structures. It has been found that a…