Related papers: Exponential Generalised Network Descriptors
In this paper we define a metric for reciprocity---the degree of balance in a social relationship---appropriate for weighted social networks in order to investigate the distribution of this dyadic feature in a large-scale system built from…
We introduce a new topological descriptor of a network called the density decomposition which is a partition of the nodes of a network into regions of uniform density. The decomposition we define is unique in the sense that a given network…
The contact structure between hosts has a critical influence on disease spread. However, most networkbased models used in epidemiology tend to ignore heterogeneity in the weighting of contacts. This assumption is known to be at odds with…
Many complex systems can be described in terms of networks of interacting units. Recent studies have shown that a wide class of both natural and artificial nets display a surprisingly widespread feature: the presence of highly heterogeneous…
The relations, rather than the elements, constitute the structure of networks. We therefore develop a systematic approach to the analysis of networks, modelled as graphs or hypergraphs, that is based on structural properties of…
The calculation of centrality measures is common practice in the study of networks, as they attempt to quantify the importance of individual vertices, edges, or other components. Different centralities attempt to measure importance in…
Network or graph structures are ubiquitous in the study of complex systems. Often, we are interested in complexity trends of these system as it evolves under some dynamic. An example might be looking at the complexity of a food web as…
We develop a statistical theory to characterize correlations in weighted networks. We define the appropriate metrics quantifying correlations and show that strictly uncorrelated weighted networks do not exist due to the presence of…
The tensor network variety is a variety of tensors associated to a graph and a set of positive integer weights on its edges, called bond dimensions. We determine an upper bound on the dimension of the tensor network variety. A refined upper…
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…
Different network models have been suggested for the topology underlying complex interactions in natural systems. These models are aimed at replicating specific statistical features encountered in real-world networks. However, it is rarely…
Mechanistic network models can capture salient characteristics of empirical networks using a small set of domain-specific, interpretable mechanisms. Yet inference remains challenging because the likelihood is often intractable. We show…
We extend the concept of eigenvector centrality to multiplex networks, and introduce several alternative parameters that quantify the importance of nodes in a multi-layered networked system, including the definition of vectorial-type…
We consider the average-consensus problem in a multi-node network of finite size. Communication between nodes is modeled by a sequence of directed signals with arbitrary communication delays. Four distributed algorithms that achieve…
Real-world complex systems exhibit multiple levels of relationships. In many cases, they require to be modeled by interconnected multilayer networks, characterizing interactions on several levels simultaneously. It is of crucial importance…
Symmetries are ubiquitous in real networks and often characterize network features and functions. Here we present a generalization of network symmetry called \emph{latent symmetry}, which is an extension of the standard notion of symmetry.…
We develop a theory to measure the variance and covariance of probability distributions defined on the nodes of a graph, which takes into account the distance between nodes. Our approach generalizes the usual (co)variance to the setting of…
Exponential-family random graph models (ERGMs) provide a principled and flexible way to model and simulate features common in social networks, such as propensities for homophily, mutuality, and friend-of-a-friend triad closure, through…
Classical results on the statistical complexity of linear models have commonly identified the norm of the weights $\|w\|$ as a fundamental capacity measure. Generalizations of this measure to the setting of deep networks have been varied,…
In the last decade it became apparent that a large number of the most interesting structures and phenomena of the world can be described by networks: separable elements, with connections (or interactions) between certain pairs of them.…