Related papers: Geometric evolution of complex networks
Degree heterogeneity and latent geometry, also referred to as popularity and similarity, are key explanatory components underlying the structure of real-world networks. The relationship between these components and the statistical…
We develop a geometric framework to study the structure and function of complex networks. We assume that hyperbolic geometry underlies these networks, and we show that with this assumption, heterogeneous degree distributions and strong…
Approaches from statistical physics are applied to investigate the structure of network models whose growth rules mimic aspects of the evolution of the world-wide web. We first determine the degree distribution of a growing network in which…
Structure and dynamics of complex networks usually deal with degree distributions, clustering, shortest path lengths and other graph properties. Although these concepts have been analysed for graphs on abstract spaces, many networks happen…
We show that heterogeneous degree distributions in observed scale-free topologies of complex networks can emerge as a consequence of the exponential expansion of hidden hyperbolic space. Fermi-Dirac statistics provides a physical…
Many real-world networks exhibit scale-free feature, have a small diameter and a high clustering tendency. We have studied the properties of a growing network, which has all these features, in which an incoming node is connected to its…
Many complex networks from the World-Wide-Web to biological networks are growing taking into account the heterogeneous features of the nodes. The feature of a node might be a discrete quantity such as a classification of a URL document as…
We investigate a network model based on an infinite regular square lattice embedded in the Euclidean plane where the node connection probability is given by the geometrical distance of nodes. We show that the degree distribution in the…
Complex systems, ranging from soft materials to wireless communication, are often organised as random geometric networks in which nodes and edges evenly fill up the volume of some space. Studying such networks is difficult because they…
Clustering $\unicode{x2013}$ the tendency for neighbors of nodes to be connected $\unicode{x2013}$ quantifies the coupling of a complex network to its latent metric space. In random geometric graphs, clustering undergoes a continuous phase…
We introduce a growing network model in which a new node attaches to a randomly-selected node, as well as to all ancestors of the target node. This mechanism produces a sparse, ultra-small network where the average node degree grows…
Due to the fact that the numbers of annually published papers have witnessed a linear growth in some citation networks, a geometric model is thus proposed to predict some statistical features of those networks, in which the academic…
We introduce a model for the randomization of complex networks with geometric structure. The geometric randomization (GR) model assumes a homogeneous distribution of the nodes in an underlying similarity space and uses rewirings of the…
In this article, we propose a growing network model based on an optimal policy involving both topological and geographical measures. In this model, at each time step, a new node, having randomly assigned coordinates in a $1 \times 1$…
We define a dynamic model of random networks, where new vertices are connected to old ones with a probability proportional to a sublinear function of their degree. We first give a strong limit law for the empirical degree distribution, and…
Network models with latent geometry have been used successfully in many applications in network science and other disciplines, yet it is usually impossible to tell if a given real network is geometric, meaning if it is a typical element in…
We present analytical results for the emerging structure of networks that evolve via a combination of growth (by node addition and random attachment) and contraction (by random node deletion). To this end we consider a network model in…
Temporal dynamics, characterised by time-varying degree heterogeneity and homophily effects, are often exhibited in many real-world networks. As observed in an MIT Social Evolution study, the in-degree and out-degree of the nodes show…
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…
Based on the empirical analysis of the dependency network in 18 Java projects, we develop a novel model of network growth which considers both: an attachment mechanism and the addition of new nodes with a heterogeneous distribution of their…