Related papers: Correlation effects in a simple model of small-wor…

We review the recent fast progress in statistical physics of evolving networks. Interest has focused mainly on the structural properties of random complex networks in communications, biology, social sciences and economics. A number of giant…

We analyse the so-called small-world network model (originally devised by Strogatz and Watts), treating it, among other things, as a case study of non-linear coupled difference or differential equations. We derive a system of evolution…

Small-world networks are highly clustered networks with small distances among the nodes. There are many biological neural networks that present this kind of connections. There are no special weightings in the connections of most existing…

Global transport and communication networks enable information, ideas and infectious diseases now to spread at speeds far beyond what has historically been possible. To effectively monitor, design, or intervene in such epidemic-like…

Empirical researchers often estimate spillover effects by fitting linear or non-linear regression models to sampled network data. We show that common sampling schemes bias these estimates, potentially upwards, and derive biased-corrected…

The small-world phenomenon has been already the subject of a huge variety of papers, showing its appeareance in a variety of systems. However, some big holes still remain to be filled, as the commonly adopted mathematical formulation…

We investigate the low-dimensional structure of deterministic transformations between random variables, i.e., transport maps between probability measures. In the context of statistics and machine learning, these transformations can be used…

Small-world networks (SWN), obtained by randomly adding to a regular structure additional links (AL), are of current interest. In this article we explore (based on physical models) a new variant of SWN, in which the probability of realizing…

Temporal networks model how the interaction between elements in a complex system evolve over time. Just like complex systems display collective dynamics, here we interpret temporal networks as trajectories performing a collective motion in…

In this paper we study the impact of degree correlations in the subgraphs statistics of scale-free networks. In particular we consider loops: a simple case of network subgraphs which encode the redundancy of the paths passing through every…

In this set of five lectures the authors have presented techniques to analyze open classical and quantum systems using correlation matrices. For diverse reasons we shall see that random matrices play an important role to describe a null…

Percolation theory concerns the emergence of connected clusters that percolate through a networked system. Previous studies ignored the effect that a node outside the percolating cluster may actively induce its inside neighbours to exit the…

We apply random matrix theory to complex networks. We show that nearest neighbor spacing distribution of the eigenvalues of the adjacency matrices of various model networks, namely scale-free, small-world and random networks follow…

Many social, biological, and economic systems can be approached by complex networks of interacting units. The behaviour of several models on small-world networks has recently been studied. These models are expected to capture the essential…

We study a general and simple model for communication processes. In the model, agents in a network (in particular, an organization) interchange information packets following simple rules that take into account the limited capability of the…

Small-world networks are the focus of recent interest because they appear to circumvent many of the limitations of either random networks or regular lattices as frameworks for the study of interaction networks of complex systems. Here, we…

We study proliferation of an action in binary action network coordination games that are generalized to include global effects. This captures important aspects of proliferation of a particular action or narrative in online social networks,…

We quantify the finite size effects in a stochastic network made up of rate neurons, for several kinds of recurrent connectivity matrices. This analysis is performed by means of a perturbative expansion of the neural equations, where the…

Theoretical attempts proposed so far to describe ordinary percolation processes on real-world networks rely on the locally tree-like ansatz. Such an approximation, however, holds only to a limited extent, as real graphs are often…

In a motorway network, correlations between parts or, more precisely, between the sections of (different) motorways, are of considerable interest. Knowledge of flows and velocities on individual motorways is not sufficient, rather, their…