Related papers: A General Formalism for Inhomogeneous Random Graph…
We investigate the dynamic formation of regular random graphs. In our model, we pick a pair of nodes at random and connect them with a link if both of their degrees are smaller than d. Starting with a set of isolated nodes, we repeat this…
Random walks on graphs are widely used in all sciences to describe a great variety of phenomena where dynamical random processes are affected by topology. In recent years, relevant mathematical results have been obtained in this field, and…
Structure learning methods for covariance and concentration graphs are often validated on synthetic models, usually obtained by randomly generating: (i) an undirected graph, and (ii) a compatible symmetric positive definite (SPD) matrix. In…
We are interested in modeling networks in which the connectivity among the nodes and node attributes are random variables and interact with each other. We propose a probabilistic model that allows one to formulate jointly a probability…
Most real-world graphs exhibit a hierarchical structure, which is often overlooked by existing graph generation methods. To address this limitation, we propose a novel graph generative network that captures the hierarchical nature of graphs…
We consider a variant of so called power-law random graph. A sequence of expected degrees corresponds to a power-law degree distribution with finite mean and infinite variance. In previous works the asymptotic picture with number of nodes…
We review a collection of models of random simplicial complexes together with some of the most exciting phenomena related to them. We do not attempt to cover all existing models, but try to focus on those for which many important results…
We study the time-averaged flow in a model of particles that randomly hop on a finite directed graph. In the limit as the number of particles and the time window go to infinity but the graph remains finite, the large-deviation rate…
Generative models for graphs have been typically committed to strong prior assumptions concerning the form of the modeled distributions. Moreover, the vast majority of currently available models are either only suitable for characterizing…
In a graph, nodes can be characterized locally (with their degree $k$) or globally (e.g. with their average length path $\xi$ to other nodes). Here we investigate how $\xi$ depends on $k$. Our earlier algorithm of the construction of the…
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…
This Letter introduces a generalization of known duplication-divergence models for growing random graphs. This general duplication-divergence model includes a new coupled divergence asymmetry rate, which allows to obtain the structure of…
We consider the random hypergraph on a finite vertex set by choosing each set of vertices as an hyperedge independently at random. We express the probability distributions of the (lower-)associated simplicial complex and the…
What does a typical road network look like? Existing generative models tend to focus on one aspect to the exclusion of others. We introduce the general-purpose \emph{quadtree model} and analyze its shortest paths and maximum flow.
A random intersection graph is constructed by assigning independently to each vertex a subset of a given set and drawing an edge between two vertices if and only if their respective subsets intersect. In this paper a model is developed in…
In recent decades, it has been emphasized that the evolving structure of networks may be shaped by interaction principles that yield sparse graphs with a vertex degree distribution exhibiting an algebraic tail, and other structural traits…
This paper is intended as an introductory survey of a newly emerging field: a topological approach to the study of locally finite graphs that crucially incorporates their ends. Topological arcs and circles, which may pass through ends,…
In this paper, we introduce a generalization of graphlets to heterogeneous networks called typed graphlets. Informally, typed graphlets are small typed induced subgraphs. Typed graphlets generalize graphlets to rich heterogeneous networks…
We develop a statistical mechanics approach for random networks with uncorrelated vertices. We construct equilibrium statistical ensembles of such networks and obtain their partition functions and main characteristics. We find simple…
Models of complex networks are generally defined as graph stochastic processes in which edges and vertices are added or deleted over time to simulate the evolution of networks. Here, we define a unifying framework - probabilistic inductive…