Related papers: Integer Networks
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 introduce a new class of deterministic networks by associating networks with Diophantine equations, thus relating network topology to algebraic properties. The network is formed by representing integers as vertices and by drawing cliques…
We derive the finite size dependence of the clustering coefficient of scale-free random graphs generated by the configuration model with degree distribution exponent $2<\gamma<3$. Degree heterogeneity increases the presence of triangles in…
We develop a network in which the natural numbers are the vertices. We use the decomposition of natural numbers by prime numbers to establish the connections. We perform data collapse and show that the degree distribution of these networks…
A wealth of evidence shows that real world networks are endowed with the small-world property i.e., that the maximal distance between any two of their nodes scales logarithmically rather than linearly with their size. In addition, most…
We study the statistical properties of the sampled networks by a random walker. We compare topological properties of the sampled networks such as degree distribution, degree-degree correlation, and clustering coefficient with those of the…
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…
Many real-world network are multilayer, with nontrivial correlations across layers. Here we show that these correlations amplify geometry in networks. We focus on mutual clustering--a measure of the amount of triangles that are present in…
We investigate the nature of written human language within the framework of complex network theory. In particular, we analyse the topology of Orwell's \textit{1984} focusing on the local properties of the network, such as the properties of…
Detecting the dimensionality of graphs is a central topic in machine learning. While the problem has been tackled empirically as well as theoretically, existing methods have several drawbacks. On the one hand, empirical tools are…
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…
We study scale free simple graphs with an exponent of the degree distribution $\gamma$ less than two. Generically one expects such extremely skewed networks -- which occur very frequently in systems of virtually or logically connected units…
We study the effects of spatial constraints on the structural properties of networks embedded in one or two dimensional space. When nodes are embedded in space, they have a well defined Euclidean distance $r$ between any pair. We assume…
A new family of graphs, {\it entangled networks}, with optimal properties in many respects, is introduced. By definition, their topology is such that optimizes synchronizability for many dynamical processes. These networks are shown to have…
Networks are mathematical structures that are universally used to describe a large variety of complex systems such as the brain or the Internet. Characterizing the geometrical properties of these networks has become increasingly relevant…
Can one hear the 'sound' of a growing network? We address the problem of recognizing the topology of evolving biological or social networks. Starting from percolation theory, we analytically prove a linear inverse relationship between two…
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…
Network topologies can be non-trivial, due to the complex underlying behaviors that form them. While past research has shown that some processes on networks may be characterized by low-order statistics describing nodes and their neighbors,…
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 $1 \times 1$…
The entropy of network ensembles characterizes the amount of information encoded in the network structure, and can be used to quantify network complexity, and the relevance of given structural properties observed in real network datasets…