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There is increasing evidence that dense networks occur in on-line social networks, recommendation networks and in the brain. In addition to being dense, these networks are often also scale-free, i.e. their degree distributions follow…
We investigate the consensus dynamics of the voter model on large random graphs with heterogeneous and directed features, focusing in particular on networks with power-law degree distributions. By extending recent results on sparse directed…
Network growth is currently explained through mechanisms that rely on node prestige measures, such as degree or fitness. In many real networks those who create and connect nodes do not know the prestige values of existing nodes, but only…
The Japanese shareholding network at the end of March 2002 is studied. To understand the characteristics of this network intuitively, we visualize it as a directed graph and an adjacency matrix. Especially detailed features of networks…
The analysis in this paper helps to explain the formation of growing networks with degree distributions that follow extended exponential or power-law tails. We present a generic model in which edge dynamics are driven by a continuous…
A model for directed networks is proposed and power laws for their in-degree and/or out-degree distributions are derived from the model. It is based on the Barabasi-Albert model and contains two parameters. The parameters serve as…
Regarding the analysis of Web communication, social and complex networks the fast finding of most influential nodes in a network graph constitutes an important research problem. We use two indices of the influence of those nodes, namely,…
Many complex networks are described by directed links; in such networks, a link represents, for example, the control of one node over the other node or unidirectional information flows. Some centrality measures are used to determine the…
Although the spectral properties of random graphs have been a long-standing focus of network theory, the properties of right eigenvectors of directed graphs have so far eluded an exact analytic treatment. We present a general theory for the…
Despite several advances in recent years, learning causal structures represented by directed acyclic graphs (DAGs) remains a challenging task in high dimensional settings when the graphs to be learned are not sparse. In this paper, we…
Consensus about the universality of the power law feature in complex networks is experiencing profound challenges. To shine fresh light on this controversy, we propose a generic theoretical framework in order to examine the power law…
We provide a local probabilistic description of the limiting statistics of large preferential attachment trees in terms of the ordinary degree (number of neighbors) but augmented with information on leafdegree (number of neighbors that are…
What distribution of graphical degree sequence is invariant under ``scaling''? Are these graphs always power-law graphs? We show the answer is a surprising ``yes'' for sparse graphs if we ignore isolated vertices, or more generally, the…
Let $d$ be a fixed large integer. For any $n$ larger than $d$, let $A_n$ be the adjacency matrix of the random directed $d$-regular graph on $n$ vertices, with the uniform distribution. We show that $A_n$ has rank at least $n-1$ with…
In many real world networks, the number of links increases nonlinearly with the number of nodes. Models of such accelerated growth have been considered earlier with deterministic and stochastic number of links. Here we consider stochastic…
Preferential attachment graphs are random graphs designed to mimic properties of typical real world networks. They are constructed by a random process that iteratively adds vertices and attaches them preferentially to vertices that already…
Many weighted scale-free networks are known to have a power-law correlation between strength and degree of nodes, which, however, has not been well explicated. We investigate the dynamic behaviors of resource/traffic flow on scale-free…
Recently several authors have proposed stochastic models of the growth of the Web graph that give rise to power-law distributions. These models are based on the notion of preferential attachment leading to the ``rich get richer''…
In this paper the web is analyzed as a graph aggregated by host and pay-level domain (PLD). The web graph datasets, publicly available, have been released by the Common Crawl Foundation and are based on a web crawl performed during the…
We study the organization and dynamics of growing directed networks. These networks are built by adding nodes successively in such a way that each new node has $K$ directed links to the existing ones. The organization of a growing directed…