Related papers: Uncorrelated Random Networks
Complex networks have been mostly characterized from the point of view of the degree distribution of their nodes and a few other motifs (or modules), with a special attention to triangles and cliques. The most exotic phenomena have been…
Several fundamental properties of real complex networks, such as the small-world effect, the scale-free degree distribution, and recently discovered topological fractal structure, have presented the possibility of a unique growth mechanism…
We consider local leaders in random uncorrelated networks, i.e. nodes whose degree is higher or equal than the degree of all of their neighbors. An analytical expression is found for the probability of a node of degree $k$ to be a local…
We propose a novel measure of degree heterogeneity, for unweighted and undirected complex networks, which requires only the degree distribution of the network for its computation. We show that the proposed measure can be applied to all…
Fractal scale-free networks are empirically known to exhibit disassortative degree mixing. It is, however, not obvious whether a negative degree correlation between nearest neighbor nodes makes a scale-free network fractal. Here we examine…
We consider the problem of estimating undirected triangle-free graphs of high dimensional distributions. Triangle-free graphs form a rich graph family which allows arbitrary loopy structures but 3-cliques. For inferential tractability, we…
We study an intermittent random walk on a random network of scale-free degree distribution. The walk is a combination of simple random walks of duration $t_w$ and random long-range jumps. While the time the walker needs to cover all the…
We present a method for the construction of ensembles of random networks that consist of a single connected component with a given degree distribution. This approach extends the construction toolbox of random networks beyond the…
Complex systems, ranging from soft materials to wireless communication, are often organised as random geometric networks in which nodes and edges evenly fill up the volume of some space. Studying such networks is difficult because they…
Node betweenness has been studied recently by a number of authors, but until now less attention has been paid to edge betweenness. In this paper, we present an exact analytic study of edge betweenness in evolving scale-free and…
As a fundamental structural transition in complex networks, core percolation is related to a wide range of important problems. Yet, previous theoretical studies of core percolation have been focusing on the classical Erd\H{o}s-R\'enyi…
Real-world graphs, such as social networks, financial transactions, and recommendation systems, often demonstrate dynamic behavior. This phenomenon, known as graph stream, involves the dynamic changes of nodes and the emergence and…
We propose a model for growing networks based on a finite memory of the nodes. The model shows stylized features of real-world networks: power law distribution of degree, linear preferential attachment of new links and a negative…
A probabilistic generative network model with $n$ nodes and $m$ overlapping layers is obtained as a superposition of $m$ mutually independent Bernoulli random graphs of varying size and strength. When $n$ and $m$ are large and of the same…
Graph signals are functions of the underlying graph. When the edge-weight between a pair of nodes is high, the corresponding signals generally have a higher correlation. As a result, the signals can be represented in terms of a graph-based…
Extensive studies have been done to understand the principles behind architectures of real networks. Recently, evidences for hierarchical organization in many real networks have also been reported. Here, we present a new hierarchical model…
Degree distributions are arguably the most important property of real world networks. The classic edge configuration model or Chung-Lu model can generate an undirected graph with any desired degree distribution. This serves as a good null…
We find that transport on scale-free random networks depends strongly on degree-correlated network topologies whereas transport on Erd$\ddot{o}$s-R$\acute{e}$nyi networks is insensitive to the degree correlation. An approach for the tuning…
Why are most empirical networks, with the prominent exception of social ones, generically degree-degree anticorrelated, i.e. disassortative? With a view to answering this long-standing question, we define a general class of degree-degree…
We identify the upper large deviation probability for the number of edges in scale-free geometric random graph models as the space volume goes to infinity. Our result covers the models of scale-free percolation, the Boolean model with…