相关论文: Topological phase transition in complex networks

In this paper we provide numerical evidence of the richer behavior of the connectivity degrees in heterogeneous preferential attachment networks in comparison to their homogeneous counterparts. We analyze the degree distribution in the…

The linear preferential attachment hypothesis has been shown to be quite successful to explain the existence of networks with power-law degree distributions. It is then quite important to determine if this mechanism is the consequence of a…

In this contribution we introduce local attachment as an universal network-joining protocol for peer-to-peer networks, social networks, or other kinds of networks. Based on this protocol nodes in a finite-size network dynamically create…

We characterize the tail behavior of the distribution of the PageRank of a uniformly chosen vertex in a directed preferential attachment graph and show that it decays as a power law with an explicit exponent that is described in terms of…

The network topology can be described by the number of nodes and the interconnections among them. The degree of a node in a network is the number of connections it has to other nodes and the degree distribution is the probability…

We consider a general model in which there is a coupled dynamics of node states and links states in a network. This coupled dynamics coevolves with dynamical changes of the topology of the network caused by a link rewiring mechanism. Such…

Many real-world complex networks arise as a result of a competition between growth and rewiring processes. Usually the initial part of the evolution is dominated by growth while the later one rather by rewiring. The initial growth allows…

I start by reviewing some basic properties of random graphs. I then consider the role of random walks in complex networks and show how they may be used to explain why so many long tailed distributions are found in real data sets. The key…

In the field of complex networks, hypergraph models have so far received significantly less attention than graphs. However, many real-life networks feature multiary relations (co-authorship, protein reactions) may therefore be modeled way…

The Watts-Strogatz algorithm of transferring the square lattice to a small world network is modified by introducing preferential rewiring constrained by connectivity demand. The evolution of the network is two-step: sequential preferential…

The exponential family of random graphs is one of the most promising class of network models. Dependence between the random edges is defined through certain finite subgraphs, analogous to the use of potential energy to provide dependence…

In principle, the rules of links formation of a network model can be considered as a kind of link prediction algorithm. By revisiting the preferential attachment mechanism for generating a scale-free network, here we propose a class of…

This paper presents an analysis of a temporal network that describes the social connections of a large-scale (~ 30,000) sample of online social network users, inhabitants of a fixed city. We tested how the main network formation…

Many networks exhibit scale free behavior where their degree distribution obeys a power law for large vertex degrees. Models constructed to explain this phenomena have relied on preferential attachment where the networks grow by the…

We analyze Axelrod's model of social interactions on coevolving complex networks. We introduce four extensions with different mechanisms of edge rewiring. The models are intended to catch two kinds of interactions - preferential attachment,…

We propose a model of network growth in which the network is co-evolving together with the dynamics of a quantum mechanical system, namely a quantum walk taking place over the network. The model naturally generalizes the Barab\'{a}si-Albert…

We consider the evolution of scale-free networks according to preferential attachment schemes and show the conditions for which the exponent characterizing the degree distribution is bounded by upper and lower values. Our framework is an…

We investigate the higher-order connectivity of scale-free networks using algebraic topology. We model scale-free networks as preferential attachment graphs, and we study the algebraic-topological properties of their clique complexes. We…

The classical preferential attachment model is sensitive to the choice of the initial configuration of the network. As the number of initial nodes and their degree grow, so does the time needed for an equilibrium degree distribution to be…

We introduce a new model of competition on growing networks. This extends the preferential attachment model, with the key property that node choices evolve simultaneously with the network. When a new node joins the network, it chooses…