Related papers: Matrix representation of evolving networks
The study of random graphs has become very popular for real-life network modeling such as social networks or financial networks. Inhomogeneous long-range percolation (or scale-free percolation) on the lattice $\mathbb Z^d$, $d\ge1$, is a…
Phylogenetic networks are a generalization of phylogenetic trees that allow for the representation of non-treelike evolutionary events, like recombination, hybridization, or lateral gene transfer. In this paper, we present and study a new…
We study the evolution of a random graph under the constraint that the diameter remain constant as the graph grows. We show that if the graph maintains the form of its link distribution it must be scale-free with exponent between 2 and 3.…
Introduced recently, the concept of hierarchical degree allows a more complete characterization of the topological context of a node in a complex network than the traditional node degree. This article presents analytical characterization…
Adaptive networks appear in many biological applications. They combine topological evolution of the network with dynamics in the network nodes. Recently, the dynamics of adaptive networks has been investigated in a number of parallel…
Scale-free networks contain many small cliques and cycles. We model such networks as inhomogeneous random graphs with regularly varying infinite-variance weights. For these models, the number of cliques and cycles have exact integral…
We develop the theory of linear evolution equations associated with the adjacency matrix of a graph, focusing in particular on infinite graphs of two kinds: uniformly locally finite graphs as well as locally finite line graphs. We discuss…
A fundamental method of reconstructing networks, e.g. in the context of gene regulation, relies on the precision matrix (the inverse of the variance-covariance matrix) as an indicator which variables are associated with each other. The…
Conventional studies of network growth models mainly look at the steady state degree distribution of the graph. Often long time behavior is considered, hence the initial condition is ignored. In this contribution, the time evolution of the…
Across the sciences, the statistical analysis of networks is central to the production of knowledge on relational phenomena. Because of their ability to model the structural generation of networks, exponential random graph models are a…
Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical…
This study examines long-term trends and shifting behavior in the collaboration network of mathematics literature, using a subset of data from Mathematical Reviews spanning 1985-2009. Rather than modeling the network cumulatively, this…
Many real systems possess accelerating statistics where the total number of edges grows faster than the network size. In this paper, we propose a simple weighted network model with accelerating growth. We derive analytical expressions for…
Combinations of random and preferential growth for both on-growing and stationary networks are studied and a hierarchical topology is observed. Thus for real world scale-free networks which do not exhibit hierarchical features preferential…
Many real-world networks display a natural bipartite structure. Investigating it based on the original structure is helpful to get deep understanding about the networks. In this paper, some real-world bipartite networks are collected and…
Using each node's degree as a proxy for its importance, the topological hierarchy of a complex network is introduced and quantified. We propose a simple dynamical process used to construct networks which are either maximally or minimally…
Networks effectively capture interactions among components of complex systems, and have thus become a mainstay in many scientific disciplines. Growing evidence, especially from biology, suggest that networks undergo changes over time, and…
A general population evolution model is considered. Any individual of the population is characterized by its score. Certain general conditions are assumed concerning the number of the individuals and their scores. Asymptotic theorems are…
In this paper, we study a class of stochastic processes, called evolving network Markov chains, in evolving networks. Our approach is to transform the degree distribution problem of an evolving network to a corresponding problem of evolving…
The extreme eigenvalues of adjacency matrices are important indicators on the influences of topological structures to collective dynamical behavior of complex networks. Recent findings on the ensemble averageability of the extreme…