Related papers: Analytic solution of the two-star model with corre…

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…

A model of correlated random networks is examined, i.e. networks with correlations between the degrees of neighboring nodes. These nodes do not necessarily have to be direct neighbors, the maximum range of the correlations can be…

Spreading of either information or matter can often be treated as a network problem. It can be of great importance to be able to estimate the likelihood that spreading through a network reaches essentially the entire network while still not…

We generalize the degree-organizational view of real-world networks with broad degree-distributions in a landscape analogue with mountains (high-degree nodes) and valleys (low-degree nodes). For example, correlated degrees between adjacent…

The use of degree-degree correlations to model realistic networks which are characterized by their Pearson's coefficient, has become widespread. However the effect on how different correlation algorithms produce different results on…

Random Threshold Networks with sparse, asymmetric connections show complex dynamical behavior similar to Random Boolean Networks, with a transition from ordered to chaotic dynamics at a critical average connectivity $K_c$. In this type of…

Classes of graphs with bounded expansion are a generalization of both proper minor closed classes and degree bounded classes. Such classes are based on a new invariant, the greatest reduced average density (grad) of G with rank r,…

We study the growth of bipartite networks in which the number of nodes in one of the partitions is kept fixed while the other partition is allowed to grow. We study random and preferential attachment as well as combination of both. We…

We study the metastable behaviour of a stochastic system of particles with hard-core interactions in a high-density regime. Particles sit on the vertices of a bipartite graph. New particles appear subject to a neighbourhood exclusion…

Competing inhomogeneous orders are a central feature of correlated electron materials including the high-temperature superconductors. The two- dimensional Hubbard model serves as the canonical microscopic physical model for such systems.…

We study an asymptotical behavior of the maximal degree in the degree distribution in an evolving tree model combining the local choice and the Mori's preferential attachment. In the considered model, the random graph is constructed in the…

We study random graphs with arbitrary distributions of expected degree and derive expressions for the spectra of their adjacency and modularity matrices. We give a complete prescription for calculating the spectra that is exact in the limit…

We present an analytic formalism describing structural properties of random uncorrelated networks with arbitrary degree distributions. The formalism allows to calculate the main network characteristics like: the position of the phase…

Generative graph models struggle to scale due to the need to predict the existence or type of edges between all node pairs. To address the resulting quadratic complexity, existing scalable models often impose restrictive assumptions such as…

Random networks are intensively used as null models to investigate properties of complex networks. We describe an efficient and accurate algorithm to generate arbitrarily two-point correlated undirected random networks without self- or…

We discuss three related models of scale-free networks with the same degree distribution but different correlation properties. Starting from the Barabasi-Albert construction based on growth and preferential attachment we discuss two other…

We study a class models of correlated random networks in which vertices are characterized by \textit{hidden variables} controlling the establishment of edges between pairs of vertices. We find analytical expressions for the main topological…

Disease and information spread over social and information networks. Understanding the spread phenomena in networks requires paying attention not only to the degree distribution but also to the degree correlation. However, it is considered…

In this paper we describe the emergence of scale-free degree distributions from statistical mechanics principles. We define an energy associated to a degree sequence as the logarithm of the number of indistinguishable simple networks it is…

In this study, we investigate bond percolation in networks that have the Poisson degree distribution and a nearest-neighbor degree-degree correlation. Previous numerical studies on percolation critical behaviors of degree-correlated…