Related papers: Metcalfe's Law Revisited
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…
Many real networks are equipped with short diameters, high clustering, and power-law degree distributions. With preferential attachment and network growth, the model by Barabasi and Albert simultaneously reproduces these properties, and…
Several studies on real complex networks from different fields as biology, economy, or sociology have shown that the degree of nodes (number of edges connected to each node) follows a scale-free power-law distribution like $P(k)\approx…
Unlike the well-studied models of growing networks, where the dominant dynamics consist of insertions of new nodes and connections, and rewiring of existing links, we study {\em ad hoc} networks, where one also has to contend with rapid and…
The IEEE 802.11 standard offers a cheap and promising solution for small scale wireless networks. Due to the self configuring nature, WLANs do not require large scale infrastructure deployment, and are scalable and easily maintainable which…
One of the most important features observed in real networks is that, as a network's topology evolves so does the network's ability to perform various complex tasks. To explain this, it has also been observed that as a network grows certain…
Dynamical networks are powerful tools for modeling a broad range of complex systems, including financial markets, brains, and ecosystems. They encode how the basic elements (nodes) of these systems interact altogether (via links) and evolve…
As individuals communicate, their exchanges form a dynamic network. We demonstrate, using time series analysis of communication in three online settings, that network structure alone can be highly revealing of the diversity and novelty of…
We introduce a new mechanism of connectivity evolution in networks to account for the emergence of scale-free behavior. The mechanism works on a fixed set of nodes and promotes growth from a minimally connected initial topology by the…
The parallel computational complexity or depth of growing network models is investigated. The networks considered are generated by preferential attachment rules where the probability of attaching a new node to an existing node is given by a…
We propose a metric, Layer Saturation, defined as the proportion of the number of eigenvalues needed to explain 99% of the variance of the latent representations, for analyzing the learned representations of neural network layers.…
The rapidly developing theory of complex networks indicates that real networks are not random, but have a highly robust large-scale architecture, governed by strict organizational principles. Here, we focus on the properties of biological…
Financial networks help firms manage risk but also enable financial shocks to spread. Despite their importance, existing models of financial networks have several limitations. Prior works often consider a static network with a simple…
What makes economic and ecological networks so unlike other highly skewed networks in their tendency toward turbulence and collapse? Here, we explore the consequences of a defining feature of these networks: their nodes are tied together by…
We apply statistical physics to study the task of resource allocation in random networks with limited bandwidths along the transportation links. The mean-field approach is applicable when the connectivity is sufficiently high. It allows us…
Densifying networks and deploying more antennas at each access point are two principal ways to boost the capacity of wireless networks. However, the complicated distributions of the signal power and the accumulated interference power,…
Modularity structures are common in various social and biological networks. However, its dynamical origin remains an open question. In this work, we set up a dynamical model describing the evolution of a social network. Based on the…
This article reviews and evaluates models of network evolution based on the notion of structural diversity. We show that diversity is an underlying theme of three principles of network evolution: the preferential attachment model,…
We propose a geometric growth model for weighted scale-free networks, which is controlled by two tunable parameters. We derive exactly the main characteristics of the networks, which are partially determined by the parameters. Analytical…
We introduce a new framework for the analysis of the dynamics of networks, based on randomly reinforced urn (RRU) processes, in which the weight of the edges is determined by a reinforcement mechanism. We rigorously explain the empirical…