Related papers: Stability in the evolution of random networks
Diverse biological networks exhibit universal features distinguished from those of random networks, calling much attention to their origins and implications. Here we propose a minimal evolution model of Boolean regulatory networks, which…
We determine stability and attractor properties of random Boolean genetic network models with canalyzing rules for a variety of architectures. For all power law, exponential, and flat in-degree distributions, we find that the networks are…
Networks composed from both connectivity and dependency links were found to be more vulnerable compared to classical networks with only connectivity links. Their percolation transition is usually of a first order compared to the second…
For $\alpha \in (1,2]$, the $\alpha$-stable graph arises as the universal scaling limit of critical random graphs with i.i.d. degrees having a given $\alpha$-dependent power-law tail behavior. It consists of a sequence of compact measured…
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…
Motivated by networked systems, stochastic control, optimization, and a wide variety of applications, this work is devoted to systems of switching jump diffusions. Treating such nonlinear systems, we focus on stability issues. First…
The co-evolution of network topology and dynamics is studied in an evolutionary Boolean network model that is a simple model of gene regulatory network. We find that a critical state emerges spontaneously resulting from interplay between…
We introduce a growing network model---the copying model---in which a new node attaches to a randomly selected target node and, in addition, independently to each of the neighbors of the target with copying probability $p$. When…
Graph convolutional neural networks (GCNNs) are nonlinear processing tools to learn representations from network data. A key property of GCNNs is their stability to graph perturbations. Current analysis considers deterministic perturbations…
We propose a simple model of the evolution of a social network which involves local search and volatility (random decay of links). The model captures the crucial role the network plays for information diffusion. This is responsible for a…
There has been a considerable amount of interest in recent years on the robustness of networks to failures. Many previous studies have concentrated on the effects of node and edge removals on the connectivity structure of a static network;…
Turing instability in complex networks have been shown in the literature to be dominated by the distribution of the nodal degrees. The conditions for Turing instability have been derived with an explicit dependence on the eigenvalues of the…
A dynamic model for a random network evolving in continuous time is defined where new vertices are born and existing vertices may die. The fitness of a vertex is defined as the accumulated in-degree of the vertex and a new vertex is…
Graph Neural Networks (GNNs) have become the standard for graph representation learning but remain vulnerable to structural perturbations. We propose a novel framework that integrates persistent homology features with stability…
We study cascading failures in networks using a dynamical flow model based on simple conservation and distribution laws to investigate the impact of transient dynamics caused by the rebalancing of loads after an initial network failure…
A classic measure of ecological stability describes the tendency of a community to return to equilibrium after small perturbation. While many advances show how the network structure of these communities severely constrains such tendencies,…
We prove a metric space scaling limit for a critical random graph with independent and identically distributed degrees having power-law tail behaviour with exponent $\alpha+1$, where $\alpha \in (1,2)$. The limiting components are…
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…
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…
It is known that the stationary distribution of the random walk process is dependent on the structure of the network. This could provide us a solution of the network reconstruction. However, the stationary distribution of the random walk…