Related papers: Growing a Network on a Given Substrate

How do real graphs evolve over time? What are ``normal'' growth patterns in social, technological, and information networks? Many studies have discovered patterns in static graphs, identifying properties in a single snapshot of a large…

A model for growing information networks is introduced where nodes receive new links through j-redirection, i.e. the probability for a node to receive a link depends on the number of paths of length j arriving at this node. In detail, when…

Power law distribution seems to be an important characteristic of web graphs. Several existing web graph models generate power law graphs by adding new vertices and non-uniform edge connectivities to existing graphs. Researchers have…

The characterization of the "most connected" nodes in static or slowly evolving complex networks has helped in understanding and predicting the behavior of social, biological, and technological networked systems, including their robustness…

We introduce a dynamical network model which unifies a number of network families which are individually known to exhibit $q$-exponential degree distributions. The present model dynamics incorporates static (non-growing) self-organizing…

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…

Dynamical processes taking place on real networks define on them evolving subnetworks whose topology is not necessarily the same of the underlying one. We investigate the problem of determining the emerging degree distribution, focusing on…

There has been considerable recent interest in the properties of networks, such as citation networks and the worldwide web, that grow by the addition of vertices, and a number of simple solvable models of network growth have been studied.…

In a recent work \cite{LiuJoladSchZia13}, we introduced dynamic networks with preferred degrees and presented simulation and analytic studies of a single, homogeneous system as well as two interacting networks. Here, we extend these studies…

We study collaboration networks in terms of evolving, self-organizing bipartite graph models. We propose a model of a growing network, which combines preferential edge attachment with the bipartite structure, generic for collaboration…

Complex networks in different areas exhibit degree distributions with heavy upper tail. A preferential attachment mechanism in a growth process produces a graph with this feature. We herein investigate a variant of the simple preferential…

Random graphs are more and more used for modeling real world networks such as evolutionary networks of proteins. For this purpose we look at two different models and analyze how properties like connectedness and degree distributions are…

We analyze a minimal model of a growing network. At each time step, a new vertex is added; then, with probability delta, two vertices are chosen uniformly at random and joined by an undirected edge. This process is repeated for t time…

Since their inception about a decade ago, dynamic networks which adapt to the state of the nodes have attracted much attention. One simple case of such an adaptive dynamics is a model of social networks in which individuals are typically…

Gradient-based learning in multi-layer neural networks displays a number of striking features. In particular, the decrease rate of empirical risk is non-monotone even after averaging over large batches. Long plateaus in which one observes…

We study a general set of models of social network evolution and dynamics. The models consist of both a dynamics on the network and evolution of the network. Links are formed preferentially between 'similar' nodes, where the similarity is…

In this paper we investigate networks whose evolution is governed by the interaction of a random assembly process and an optimization process. In the first process, new nodes are added one at a time and form connections to randomly selected…

Degree distributions of many real networks are known to follow the Mandelbrot law, which can be considered as an extension of the power law and is determined by not only the power-law exponent, but also the shifting coefficient. Although…

We provide a framework for modeling social network formation through conditional multinomial logit models from discrete choice and random utility theory, in which each new edge is viewed as a "choice" made by a node to connect to another…

Using a simple model with link removals as well as link additions, we show that an evolving network is scale free with a degree exponent in the range of (2, 4]. We then establish a relation between the network evolution and a set of…