相关论文: A Random Growth Model for Power Grids and Other Sp…

We introduce a new mechanism of connectivity evolution in networks to account for the emergence of scale-free behavior. The mechanism works on a fixed set of nodes and promotes growth from a minimally connected initial topology by the…

We propose a construction procedure which generates a wide class of random evolving networks with fat-tailed degree distributions and an arbitrary clustering. This procedure applies the stochastic transformations of edges, which can be used…

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…

This article introduces a non-parametric information-theoretic approach to inference about the tail of a continuous or a discrete distribution. Leveraging a new concept named tail profile -- a set of information-theoretic quantities…

We study a class of growth algorithms for directed graphs that are candidate models for the evolution of genetic regulatory networks. The algorithms involve partial duplication of nodes and their links, together with innovation of new…

We show that not only preferential attachment but also preferential depletion leads to scale-free networks. The resulting degree distribution exponents is typically less than two (5/3) as opposed to the case of the growth models studied…

Self-organization of robust and efficient networks is important for a future design of communication or transportation systems, because both characteristics are not coexisting in many real networks. As one of the candidates for the…

We study the growth of a directed network, in which the growth is constrained by the cost of adding links to the existing nodes. We propose a new preferential-attachment scheme, in which a new node attaches to an existing node i with…

We show how scale-free degree distributions can emerge naturally from growing networks by using random walks for selecting vertices for attachment. This result holds for several variants of the walk algorithm and for a wide range of…

Kinetically grown self-avoiding walks on various types of generalized random networks have been studied. Networks with short- and long-tailed degree distributions $P(k)$ were considered ($k$, degree or connectivity), including scale-free…

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…

We introduce a model for the dynamic self-organization of the electric grid. The model is characterized by a conserved magnitude, energy, that can travel following the links of the network to satisfy nodes' load. The load fluctuates in time…

Many complex systems--from social and communication networks to biological networks and the Internet--are thought to exhibit scale-free structure. However, prevailing explanations rely on the constant addition of new nodes, an assumption…

We provide an analytic expression for the quantity described in the title. Namely, we perform a preferential attachment growth process to generate a scale-free network. At each stage we add a new node with $m$ new links. Let $k$ denote the…

One of the biggest needs in network science research is access to large realistic datasets. As data analytics methods permeate a range of diverse disciplines---e.g., computational epidemiology, sustainability, social media analytics,…

We consider the tail distribution of the edge cover time of a specific non-Markov process, $\delta$ once-reinforced random walk, on finite connected graphs, whose transition probability is proportional to weights of edges. Here the weights…

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 introduce a minimalistic model based on dynamic node deletion and node duplication with heterodimerisation. The model is intended to capture the essential features of the evolution of protein interaction networks. We derive an exact…

A version of ``preferential attachment'' random graphs, corresponding to linear ``weights'' with random ``edge additions,'' which generalizes some previously considered models, is studied. This graph model is embedded in a continuous-time…

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…