Related papers: Asymmetric evolving random networks
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…
Models for generating simple graphs are important in the study of real-world complex networks. A well established example of such a model is the erased configuration model, where each node receives a number of half-edges that are connected…
We investigate a network model based on an infinite regular square lattice embedded in the Euclidean plane where the node connection probability is given by the geometrical distance of nodes. We show that the degree distribution in the…
We study the emergence of coherence in complex networks of mutually coupled non-identical elements. We uncover the precise dependence of the dynamical coherence on the network connectivity, on the isolated dynamics of the elements and the…
Understanding information exchange and aggregation on networks is a central problem in theoretical economics, probability and statistics. We study a standard model of economic agents on the nodes of a social network graph who learn a binary…
We determine the phase diagram of the Anderson tight-binding model on random regular graphs with Gaussian disorder and sufficiently large degree. In particular, we prove that if the degree is fixed and the number of vertices goes to…
Epidemics on complex networks is a widely investigated topic in the last few years, mainly due to the last pandemic events. Usually, real contact networks are dynamic, hence much effort has been invested in studying epidemics on evolving…
We discuss two sampling schemes for selecting random subnets from a network: Random sampling and connectivity dependent sampling, and investigate how the degree distribution of a node in the network is affected by the two types of sampling.…
Understanding the mathematical properties of graphs underling biological systems could give hints on the evolutionary mechanisms behind these structures. In this article we perform a complete statistical analysis over thousands of graphs…
In this paper we study the component structure of random graphs with independence between the edges. Under mild assumptions, we determine whether there is a giant component, and find its asymptotic size when it exists. We assume that the…
Population structure affects the outcome of natural selection. Static population structures can be described by graphs, where individuals occupy the nodes, and interactions occur along the edges. General conditions for evolutionary success…
We demonstrate how sophisticated graph properties, such as small distances and scale-free degree distributions, arise naturally from a reinforcement mechanism on layered graphs. Every node is assigned an a-priori i.i.d. fitness with…
In a graph, nodes can be characterized locally (with their degree $k$) or globally (e.g. with their average length path $\xi$ to other nodes). Here we investigate how $\xi$ depends on $k$. Our earlier algorithm of the construction of the…
We study network growth from a fixed set of initially isolated nodes placed at random on the surface of a sphere. The growth mechanism we use adds edges to the network depending on strictly local gain and cost criteria. Only nodes that are…
In the stochastic network model of Britton and Lindholm [Dynamic random networks in dynamic populations. Journal of Statistical Physics, 2010], the number of individuals evolves according to a supercritical linear birth and death process,…
The weak component generalizes the idea of connected components to directed graphs. In this paper, an exact criterion for existence of the giant weak component is derived for directed graphs with arbitrary bivariate degree distributions. In…
Dynamical processes taking place on networks have received much attention in recent years, especially on various models of random graphs (including small world and scale free networks). They model a variety of phenomena, including the…
A random graph evolution based on the interactions of N vertices is studied. During the evolution both the preferential attachment method and the uniform choice of vertices are allowed. The weight of a vertex means the number of its…
We study the problem of maintaining robust and sparse overlay networks in fully distributed settings where nodes continuously join and leave the system. This scenario closely models real-world unstructured peer-to-peer networks, where…
Bounded-size rules are dynamic random graph processes which incorporate limited choice along with randomness in the evolution of the system. One starts with the empty graph and at each stage two edges are chosen uniformly at random. One of…