Related papers: Multi-directed Eulerian growing networks
We introduce the notion of balance for directed graphs: a weighted directed graph is $\alpha$-balanced if for every cut $S \subseteq V$, the total weight of edges going from $S$ to $V\setminus S$ is within factor $\alpha$ of the total…
Highly dynamic networks are characterized by frequent changes in the availability of communication links. These networks are often partitioned into several components, which split and merge unpredictably. We present a distributed algorithm…
Networked structures arise in a wide array of different contexts such as technological and transportation infrastructures, social phenomena, and biological systems. These highly interconnected systems have recently been the focus of a great…
We study a generic family of nonlinear dynamics on undirected networks generalising linear consensus. We find a compact expression for its equilibrium points in terms of the topology of the network and classify their stability using the…
Networks constitute efficient tools for assessing universal features of complex systems. In physical contexts, classical as well as quantum, networks are used to describe a wide range of phenomena, such as phase transitions, intricate…
This paper proposes a simple procedure to decide whether the empirically-observed adjacency or weights matrix, which characterizes the graph underlying a socio-economic network, is sufficiently symmetric (respectively, asymmetric) to…
In this paper, we propose a discontinuous distributed model-independent algorithm for a directed network of Euler-Lagrange agents to track the trajectory of a leader with non-constant velocity. We initially study a fixed network and show…
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…
Online social networks are a dominant medium in everyday life to stay in contact with friends and to share information. In Twitter, users can connect with other users by following them, who in turn can follow back. In recent years,…
Neural networks have seen an explosion of usage and research in the past decade, particularly within the domains of computer vision and natural language processing. However, only recently have advancements in neural networks yielded…
We study a model of wealth dynamics [Bouchaud and M\'ezard 2000, \emph{Physica A} \textbf{282}, 536] which mimics transactions among economic agents. The outcomes of the model are shown to depend strongly on the topological properties of…
We propose a model for evolving networks by merging building blocks represented as complete graphs, reminiscent of modules in biological system or communities in sociology. The model shows power-law degree distributions, power-law…
In multiplex networks with a large number of layers, the nodes can have different activities, indicating the total number of layers in which the nodes are present. Here we model multiplex networks with heterogeneous activity of the nodes…
In networks that grow by isotropic redirection (IR), a new node selects an initial target node uniformly at random and attaches to a randomly chosen neighbor of the target. The emerging networks exhibit leaf proliferation, in which the…
We give a randomized algorithm that samples a nearly uniform Eulerian tour of a directed Eulerian multigraph with $m$ arcs in $\widetilde O(m^{3/2})$ time. The guarantee is worst-case, applies to arbitrary directed Eulerian multigraphs, and…
The configuration model is one of the most successful models for generating uncorrelated random networks. We analyze its behavior when the expected degree sequence follows a power law with exponent smaller than two. In this situation, the…
Networks are widely used to represent interaction pattern among the components in complex systems. Structures of real networks from differ- ent domains may vary quite significantly. Since there is an interplay be- tween network architecture…
Functional networks of complex systems are obtained from the analysis of the temporal activity of their components, and are often used to infer their unknown underlying connectivity. We obtain the equations relating topology and function in…
Graph neural networks (GNNs) have recently become the standard approach for learning with graph-structured data. Prior work has shed light into their potential, but also their limitations. Unfortunately, it was shown that standard GNNs are…
Existing cellular network analyses, and even simulations, typically use the standard path loss model where received power decays like $\|x\|^{-\alpha}$ over a distance $\|x\|$. This standard path loss model is quite idealized, and in most…