Related papers: Generation of arbitrarily two-point correlated ran…
Let $F$ be a probability distribution with support on the non-negative integers. Two algorithms are described for generating a stationary random graph, with vertex set $\mathbb{Z}$, so that the degrees of the vertices are i.i.d.\ random…
We apply a Bethe-Peierls approach to statistical-mechanics models defined on random networks of arbitrary degree distribution and arbitrary correlations between the degrees of neighboring vertices. Using the NP-hard optimization problem of…
The poster presents an analytic formalism describing metric properties of undirected random graphs with arbitrary degree distributions and statistically uncorrelated (i.e. randomly connected) vertices. The formalism allows to calculate the…
Designing algorithms that generate networks with a given degree sequence while varying both subgraph composition and distribution of subgraphs around nodes is an important but challenging research problem. Current algorithms lack control of…
A determinant property of the structure of a biological network is the distribution of local connectivity patterns, i.e., network motifs. In this work, a method for creating directed, unweighted networks while promoting a certain…
In the sufficiently sparse case, we find the probability that a uniformly random bipartite graph with given degree sequence contains no edge from a specified set of edges. This enables us to enumerate loop-free digraphs and oriented graphs…
We propose a general approach to the description of spectra of complex networks. For the spectra of networks with uncorrelated vertices (and a local tree-like structure), exact equations are derived. These equations are generalized to the…
We define a dynamic model of random networks, where new vertices are connected to old ones with a probability proportional to a sublinear function of their degree. We first give a strong limit law for the empirical degree distribution, and…
Social networks are organized into communities with dense internal connections, giving rise to high values of the clustering coefficient. In addition, these networks have been observed to be assortative, i.e. highly connected vertices tend…
Large real-life complex networks are often modeled by various random graph constructions and hundreds of further references therein. In many cases it is not at all clear how the modeling strength of differently generated random graph model…
We propose and study a hierarchical algorithm to generate graphs having a predetermined distribution of cliques, the fully connected subgraphs. The construction mechanism may be either random or incorporate preferential attachment. We…
Complex network theory crucially depends on the assumptions made about the degree distribution, while fitting degree distributions to network data is challenging, in particular for scale-free networks with power-law degrees. We present a…
In the field of complex networks and graph theory, new results are typically tested on graphs generated by a variety of algorithms such as the Erd\H{o}s-R\'{e}nyi model or the Barab\'{a}si-Albert model. Unfortunately, most graph generating…
We investigate the joint distribution of the vertex degrees in three models of random bipartite graphs. Namely, we can choose each edge with a specified probability, choose a specified number of edges, or specify the vertex degrees in one…
We study the properties of the giant connected component in random graphs with arbitrary degree distribution. We concentrate on the degree-degree correlations. We show that the adjoining nodes in the giant connected component are correlated…
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 have analysed some structural properties of scale-free networks with the same degree distribution. Departing from a degree distribution obtained from the Barab\'asi-Albert (BA) algorithm, networks were generated using four additional…
We develop random graph models where graphs are generated by connecting not only pairs of vertices by edges but also larger subsets of vertices by copies of small atomic subgraphs of arbitrary topology. This allows the for the generation of…
We study the tailoring of structured random graph ensembles to real networks, with the objective of generating precise and practical mathematical tools for quantifying and comparing network topologies macroscopically, beyond the level of…
Anomaly detection algorithms are a valuable tool in network science for identifying unusual patterns in a network. These algorithms have numerous practical applications, including detecting fraud, identifying network security threats, and…