Related papers: Finiteness and Fluctuations in Growing Networks
Networks growing according to the rule that every new node has a probability p_k of being attached to k preexisting nodes, have a universal phase diagram and exhibit power law decays of the distribution of cluster sizes in the…
In this note we make some specific observations on the distribution of the degree of a given vertex in certain model of randomly growing networks. The rule for network growth is the following. Starting with an initial graph of minimum…
Gaussian macroscopic fluctuation theory underpins the understanding of noise in a broad class of nonequilibrium systems. We derive exact fluctuation-response relations linking the power spectral density of stationary fluctuations to the…
We introduce a new class of networks that grow by enhanced redirection. Nodes are introduced sequentially, and each either attaches to a randomly chosen target node with probability 1-r or to the ancestor of the target with probability r,…
It is often claimed that the entropy of a network's degree distribution is a proxy for its robustness. Here, we clarify the link between degree distribution entropy and giant component robustness to node removal by showing that the former…
We investigate the propagation of random fluctuations through biochemical networks in which the concentrations of species are large enough so that the unperturbed problem is well-described by ordinary differential equation. We characterize…
In the infinite configuration network the links between nodes are assigned randomly with the only restriction that the degree distribution has to match a predefined function. This work presents a simple equation that gives for an arbitrary…
We compute the stationary in-degree probability, $P_{in}(k)$, for a growing network model with directed edges and arbitrary out-degree probability. In particular, under preferential linking, we find that if the nodes have a light tail…
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…
Information propagation characterizes how input correlations evolve across layers in deep neural networks. This framework has been well studied using mean-field theory, which assumes infinitely wide networks. However, these assumptions…
We review the recent fast progress in statistical physics of evolving networks. Interest has focused mainly on the structural properties of random complex networks in communications, biology, social sciences and economics. A number of giant…
We generalize the poissonian evolving random graph model of Bauer and Bernard to deal with arbitrary degree distributions. The motivation comes from biological networks, which are well-known to exhibit non poissonian degree distribution. A…
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 this study, we investigate bond percolation in networks that have the Poisson degree distribution and a nearest-neighbor degree-degree correlation. Previous numerical studies on percolation critical behaviors of degree-correlated…
We propose a possible relation between complex networks and gravity. Our guide in our proposal is the power-law distribution of the node degree in network theory and the information approach to gravity. The established bridge may allow us…
We study the statistical properties of large random networks with specified degree distributions. New techniques are presented for analyzing the structure of social networks. Specifically, we address the question of how many nodes exist at…
The structure of a river network may be seen as a discrete set of nested sub-networks built out of individual stream segments. These network components are assigned an integral stream order via a hierarchical and discrete ordering method.…
At the macroscopic scale, many important models of collective motion fall into the class of kinematic flows for which both velocity and diffusion terms depend only on particle density. When total particle numbers are fixed and finite,…
We study a coupled dynamics of a network and a particle system. Particles of density $\rho$ diffuse freely along edges, each of which is rewired at a rate given by a decreasing function of particle flux. We find that the coupled dynamics…
Many real world networks, such as social networks, are primarily formed through local interactions between agents. Additionally, in contrast with common network models, social and biological networks exhibit a high degree of clustering.…