Related papers: Networks with arbitrary edge multiplicities

The coexistence of sparsity and clustering (non-vanishing average fraction of triangles per node) is one of the few structural features that, irrespective of finer details, are ubiquitously observed across large real-world networks. This…

We develop a full theoretical approach to clustering in complex networks. A key concept is introduced, the edge multiplicity, that measures the number of triangles passing through an edge. This quantity extends the clustering coefficient in…

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 uncover the global organization of clustering in real complex networks. As it happens with other fundamental properties of networks such as the degree distribution, we find that real networks are neither completely random nor ordered…

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 propose a model for growing networks based on a finite memory of the nodes. The model shows stylized features of real-world networks: power law distribution of degree, linear preferential attachment of new links and a negative…

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…

Systems as diverse as genetic networks or the world wide web are best described as networks with complex topology. A common property of many large networks is that the vertex connectivities follow a scale-free power-law distribution. This…

A fundamental property of complex networks is the tendency for edges to cluster. The extent of the clustering is typically quantified by the clustering coefficient, which is the probability that a length-2 path is closed, i.e., induces a…

Many real networks in nature and society share two generic properties: they are scale-free and they display a high degree of clustering. We show that these two features are the consequence of a hierarchical organization, implying that small…

Clustering is the propensity of nodes that share a common neighbour to be connected. It is ubiquitous in many networks but poses many modelling challenges. Clustering typically manifests itself by a higher than expected frequency of…

Clustering is well-known to play a prominent role in the description and understanding of complex networks, and a large spectrum of tools and ideas have been introduced to this end. In particular, it has been recognized that the abundance…

A large number of complex networks, both natural and artificial, share the presence of highly heterogeneous, scale-free degree distributions. A few mechanisms for the emergence of such patterns have been suggested, optimization not being…

It appeared recently that the classical random graph model used to represent real-world complex networks does not capture their main properties. Since then, various attempts have been made to provide accurate models. We study here a model…

We investigate the properties of the spanning trees of various real-world and model networks. The spanning tree representing the communication kernel of the original network is determined by maximizing total weight of edges, whose weights…

Triangles are an important building block and distinguishing feature of real-world networks, but their structure is still poorly understood. Despite numerous reports on the abundance of triangles, there is very little information on what…

Complex networks of real-world systems are believed to be controlled by common phenomena, producing structures far from regular or random. These include scale-free degree distributions, small-world structure and assortative mixing by…

Generative mechanisms which lead to empirically observed structure of networked systems from diverse fields like biology, technology and social sciences form a very important part of study of complex networks. The structure of many…

Real complex systems are not rigidly structured; no clear rules or blueprints exist for their construction. Yet, amidst their apparent randomness, complex structural properties universally emerge. We propose that an important class of…

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…