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In most networks, the connection between a pair of nodes is the result of their mutual affinity and attachment. In this letter, we will propose a Mutual Attraction Model to characterize weighted evolving networks. By introducing the initial…
Scale-free networks are abundant in nature and society, describing such diverse systems as the world wide web, the web of human sexual contacts, or the chemical network of a cell. All models used to generate a scale-free topology are…
A probabilistic generative network model with $n$ nodes and $m$ overlapping layers is obtained as a superposition of $m$ mutually independent Bernoulli random graphs of varying size and strength. When $n$ and $m$ are large and of the same…
Network control refers to a very large and diverse set of problems including controllability of linear time-invariant dynamical systems, where the objective is to select an appropriate input to steer the network to a desired state. There…
Clustering, assortativity, and communities are key features of complex networks. We probe dependencies between these attributes and find that ensembles with strong clustering display both high assortativity by degree and prominent community…
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…
Community detection is a crucial task in network analysis that can be significantly improved by incorporating subject-level information, i.e. covariates. However, current methods often struggle with selecting tuning parameters and analyzing…
It has been shown that many networks associated with complex systems are small-world (they have both a large local clustering coefficient and a small diameter) and they are also scale-free (the degrees are distributed according to a power…
Graph clustering is a fundamental computational problem with a number of applications in algorithm design, machine learning, data mining, and analysis of social networks. Over the past decades, researchers have proposed a number of…
Scale-free networks, in which the distribution of the degrees obeys a power-law, are ubiquitous in the study of complex systems. One basic network property that relates to the structure of the links found is the degree assortativity, which…
Degree distribution, or equivalently called degree sequence, has been commonly used to be one of most significant measures for studying a large number of complex networks with which some well-known results have been obtained. By contrast,…
Using a maximum entropy principle to assign a statistical weight to any graph, we introduce a model of random graphs with arbitrary degree distribution in the framework of standard statistical mechanics. We compute the free energy and the…
This paper proposes a simple but effective graph-based agglomerative algorithm, for clustering high-dimensional data. We explore the different roles of two fundamental concepts in graph theory, indegree and outdegree, in the context of…
The stochastic block model is able to generate different network partitions, ranging from traditional assortative communities to disassortative structures. Since the degree-corrected stochastic block model does not specify which mixing…
The bivariate distribution of degrees of adjacent vertices (degree-degree distribution) is an important network characteristic defining the statistical dependencies between degrees of adjacent vertices. We show the asymptotic degree-degree…
We provide a novel family of generative block-models for random graphs that naturally incorporates degree distributions: the block-constrained configuration model. Block-constrained configuration models build on the generalised…
The Barab\'{a}si-Albert (BA) model is extended to include the concept of local world and the microscopic event of adding edges. With probability $p$, we add a new node with $m$ edges which preferentially link to the nodes presented in 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…
Triadic closure, the formation of a connection between two nodes in a network sharing a common neighbor, is considered a fundamental mechanism determining the clustered nature of many real-world topologies. In this work we define a static…
We consider the problem of graph generation guided by network statistics, i.e., the generation of graphs which have given values of various numerical measures that characterize networks, such as the clustering coefficient and the number of…