Related papers: Degree distributions under general node removal: P…
We include complex connectivity structures and heterogeneity in models of multilayer networks or multilayer hypergraphs growing by preferential attachment. We consider the most generic connectivity structure, where the probability of…
Network growth as described by the Duplication-Divergence model proposes a simple general idea for the evolution dynamics of natural networks. In particular it is an alternative to the well known Barab\'asi-Albert model when applied to…
Convergence of resource allocation algorithms is well covered in the literature as convergence to a steady state is important due to stability and performance. However, research is lacking when it comes to the propagation of change that…
Recently it has been shown that a large variety of different networks have power-law (scale-free) distributions of connectivities. We investigate the robustness of such a distribution in discrete threshold networks under neutral evolution.…
Within the conventional statistical physics framework, we study critical phenomena in a class of configuration network models with hidden variables controlling links between pairs of nodes. We find analytical expressions for the average…
We consider propagation models that describe the spreading of an attribute, called "damage", through the nodes of a random network. In some systems, the average fraction of nodes that remain undamaged vanishes in the large system limit, a…
A statistical model of interference in wireless networks is considered, which is based on the traditional propagation channel model and a Poisson model of random spatial distribution of nodes in 1-D, 2-D and 3-D spaces with both uniform and…
We derive a analytic evolution equation for overlap parameters including the effect of degree distribution on the transient dynamics of sequence processing neural networks. In the special case of globally coupled networks, the precisely…
Complex networks have gained more attention from the last few years. The size of real-world complex networks, such as online social networks, WWW network, collaboration networks, is increasing exponentially with time. It is not feasible to…
Networks facilitate the spread of cascades, allowing a local perturbation to percolate via interactions between nodes and their neighbors. We investigate how network structure affects the dynamics of a spreading cascade. By accounting for…
In wireless networks, the knowledge of nodal distances is essential for several areas such as system configuration, performance analysis and protocol design. In order to evaluate distance distributions in random networks, the underlying…
Identifying an optimal set of driver nodes to achieve synchronization via pinning control is a fundamental challenge in complex network science, limited by computational intractability and the lack of general theory. Here, leveraging a…
We present a detailed analytical study of the $A+A\to\emptyset$ diffusion-annihilation process in complex networks. By means of microscopic arguments, we derive a set of rate equations for the density of $A$ particles in vertices of a given…
It was experimentally observed that the majority of real-world networks follow power law degree distribution. The aim of this paper is to study the algorithmic complexity of such "typical" networks. The contribution of this work is twofold.…
We derive a mean-field approximation for the macroscopic dynamics of large networks of pulse-coupled theta neurons in order to study the effects of different network degree distributions, as well as degree correlations (assortativity).…
Degree correlation is an important topological property common to many real-world networks. In this paper, the statistical measures for characterizing the degree correlation in networks are investigated analytically. We give an exact proof…
Degree distribution, or equivalently called degree sequence, has been commonly used to be one of most significant measures for studying a large number of complex networks with which some well-known results have been obtained. By contrast,…
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 power law degree distribution is established for a graph evolution model based on the graph class of k-trees. This k-tree-based graph process can be viewed as an idealized model that captures some characteristics of the preferential…
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…