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Networks are fundamental to the study of complex systems, ranging from social contacts, message transactions, to biological regulations and economical networks. In many realistic applications, these networks may vary over time. Modeling and…
Pseudospectra and structured pseudospectra are important tools for the analysis of matrices. Their computation, however, can be very demanding for all but small matrices. A new approach to compute approximations of pseudospectra and…
Random networks are increasingly used to analyse complex transportation networks, such as airline routes, roads and rail networks. So far, this research has been focused on describing the properties of the networks with the help of random…
From the perspective of network analysis, the ubiquitous networks are comprised of regular and irregular components, which makes uncovering the complexity of network structures to be a fundamental challenge. Exploring the regular…
Understanding the structural complexity and predictability of complex networks is a central challenge in network science. Although recent studies have revealed a relationship between compression-based entropy and link prediction…
Stochastic network influences complicate graph filter design by producing uncertainty in network iteration matrix eigenvalues, the points at which the graph filter response is defined. While joint statistics for the eigenvalues typically…
Most of the real world complex networks such as the Internet, World Wide Web and collaboration networks are huge; and to infer their structure and dynamics one requires handling large connectivity (adjacency) matrices. Also, to find out the…
Driven by growing interest in the sciences, industry, and among the broader public, a large number of empirical studies have been conducted in recent years of the structure of networks ranging from the internet and the world wide web to…
A simple but efficient spectral approach for analyzing the community structure of complex networks is introduced. It works the same way for all types of networks, by spectrally splitting the adjacency matrix into a "unipartite" and a…
For many networks of scientific interest we know both the connections of the network and information about the network nodes, such as the age or gender of individuals in a social network, geographic location of nodes in the Internet, or…
Many network systems are composed of interdependent but distinct types of interactions, which cannot be fully understood in isolation. These different types of interactions are often represented as layers, attributes on the edges or as a…
Spectral analysis connects graph structure to the eigenvalues and eigenvectors of associated matrices. Much of spectral graph theory descends directly from spectral geometry, the study of differentiable manifolds through the spectra of…
Networks of genetic expression can be modelled by hypergraphs with the additional structure that real coefficients are given to each vertex-edge incidence. The spectra, i.e. the multiset of the eigenvalues, of such hypergraphs, are known to…
Studies of the effect of network structure on performance have, thus far, been restricted to examining ensembles of synthetic networks generated by canonical models from the Network Science literature, which do not plausibly represent real…
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…
We consider synchronization of weighted networks, possibly with asymmetrical connections. We show that the synchronizability of the networks cannot be directly inferred from their statistical properties. Small local changes in the network…
Random networks are a powerful tool in the analytical modeling of complex networks as they allow us to write approximate mathematical models for diverse properties and behaviors of networks. One notable shortcoming of these models is that…
We study the structural characteristics of complex networks using the representative eigenvectors of the adjacent matrix. The probability distribution function of the components of the representative eigenvectors are proposed to describe…
We address the problem of identifying a graph structure from the observation of signals defined on its nodes. Fundamentally, the unknown graph encodes direct relationships between signal elements, which we aim to recover from observable…
Understanding the localization properties of eigenvectors of complex networks is important to get insight into various structural and dynamical properties of the corresponding systems. Here, we analytically develop a scheme to construct a…