Related papers: Hamiltonian Dynamics of Preferential Attachment
Hypergraphs have been a useful tool for analyzing population dynamics such as opinion formation and the public goods game occurring in overlapping groups of individuals. In the present study, we propose and analyze evolutionary dynamics on…
We study preferential attachment mechanisms in random graphs that are parameterized by (i) a constant bias affecting the degree-biased distribution on the vertex set and (ii) the distribution of times at which new vertices are created by…
We study information aggregation in networks where agents make binary decisions (labeled incorrect or correct). Agents initially form independent private beliefs about the better decision, which is correct with probability $1/2+\delta$. The…
Proximity networks are time-varying graphs representing the closeness among humans moving in a physical space. Their properties have been extensively studied in the past decade as they critically affect the behavior of spreading phenomena…
We propose a novel model-selection method for dynamic networks. Our approach involves training a classifier on a large body of synthetic network data. The data is generated by simulating nine state-of-the-art random graph models for dynamic…
The recent discovery of universal principles underlying many complex networks occurring across a wide range of length scales in the biological world has spurred physicists in trying to understand such features using techniques from…
This paper presents a comprehensive analysis of the degree statistics in models for growing networks where new nodes enter one at a time and attach to one earlier node according to a stochastic rule. The models with uniform attachment,…
This paper addresses analytical aspects of deterministic, continuous-time dynamical systems defined on networks. The goal is to model and analyze certain phenomena which must be framed beyond the context of networked dynamical systems,…
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.…
We introduce evolving networks where new vertices preferentially connect to the more central parts of a network. This makes such networks compact. Finite networks grown under the preferential compactness mechanism have complex…
The notion of treewidth, introduced by Robertson and Seymour in their seminal Graph Minors series, turned out to have tremendous impact on graph algorithmics. Many hard computational problems on graphs turn out to be efficiently solvable in…
We include complex connectivity structures and heterogeneity in models of multilayer networks or multilayer hypergraphs growing by preferential attachment. We consider the most generic connectivity structure, where the probability of…
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…
The co-authorship network of scientists represents a prototype of complex evolving networks. By mapping the electronic database containing all relevant journals in mathematics and neuro-science for an eight-year period (1991-98), we infer…
Ever since the Barab\'{a}si-Albert (BA) scale-free network has been proposed, network modeling has been studied intensively in light of the network growth and the preferential attachment (PA). However, numerous real systems are featured…
Preferential attachment is an appealing mechanism for modeling power-law behavior of the degree distributions in directed social networks. In this paper, we consider methods for fitting a 5-parameter linear preferential model to network…
In this contribution we introduce local attachment as an universal network-joining protocol for peer-to-peer networks, social networks, or other kinds of networks. Based on this protocol nodes in a finite-size network dynamically create…
Simple growth mechanisms have been proposed to explain the emergence of seemingly universal network structures. The widely-studied model of preferential attachment assumes that new nodes are more likely to connect to highly connected nodes.…
Many growing networks possess accelerating statistics where the number of links added with each new node is an increasing function of network size so the total number of links increases faster than linearly with network size. In particular,…
Concise, accurate descriptions of physical systems through their conserved quantities abound in the natural sciences. In data science, however, current research often focuses on regression problems, without routinely incorporating…