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Temporal networks consist of timestamped directed interactions that may appear continuously in time, yet few studies have directly tackled the continuous-time modeling of networks. Here, we introduce a maximum-entropy approach to temporal…
Traditional mathematical models of epidemic disease had for decades conventionally considered static structure for contacts. Recently, an upsurge of theoretical inquiry has strived towards rendering the models more realistic by…
In this paper, we present a method for characterizing the evolution of time-varying complex networks by adopting a thermodynamic representation of network structure computed from a polynomial (or algebraic) characterization of graph…
Temporal networks have been increasingly used to model a diversity of systems that evolve in time; for example human contact structures over which dynamic processes such as epidemics take place. A fundamental aspect of real-life networks is…
Measuring the topological overlap of two graphs becomes important when assessing the changes between temporally adjacent graphs in a time-evolving network. Current methods depend on the fraction of nodes that have persisting edges. This…
A cross-diffusion system modeling the information herding of individuals is analyzed in a bounded domain with no-flux boundary conditions. The variables are the species' density and an influence function which modifies the information state…
Researchers, policy makers, and engineers need to make sense of data on spreading processes as diverse as viral infections, water contamination, and misinformation in social networks. Classical questions include predicting infection…
Recent advances in data collection and storage have allowed both researchers and industry alike to collect data in real time. Much of this data comes in the form of 'events', or timestamped interactions, such as email and social media…
Human dynamical social networks encode information and are highly adaptive. To characterize the information encoded in the fast dynamics of social interactions, here we introduce the entropy of dynamical social networks. By analysing a…
Network data has emerged as an active research area in statistics. Much of the focus of ongoing research has been on static networks that represent a single snapshot or aggregated historical data unchanging over time. However, most networks…
Network theory provides various tools for investigating the structural or functional topology of many complex systems found in nature, technology and society. Nevertheless, it has recently been realised that a considerable number of systems…
Social contact networks underlying epidemic processes in humans and animals are highly dynamic. The spreading of infections on such temporal networks can differ dramatically from spreading on static networks. We theoretically investigate…
Dynamic networks consist of a sequence of time-varying networks, and it is of great importance to detect the network change points. Most existing methods focus on detecting abrupt change points, necessitating the assumption that the…
The customary perspective to reason about epidemic mitigation in temporal networks hinges on the identification of nodes with specific features or network roles. The ensuing individual-based control strategies, however, are difficult to…
Fluctuations in biochemical networks, e.g., in a living cell, have a complex origin that precludes a description of such systems in terms of bipartite or multipartite processes, as is usually done in the framework of stochastic and/or…
Understanding how information, diseases, or influence spread across networks is a fundamental challenge in complex systems. While network diameter has been extensively studied in static networks, its definition and behavior in temporal…
We extend the well-known $\beta$-model for directed graphs to dynamic network setting, where we observe snapshots of adjacency matrices at different time points. We propose a kernel-smoothed likelihood approach for estimating $2n$…
The entropy of network ensembles characterizes the amount of information encoded in the network structure, and can be used to quantify network complexity, and the relevance of given structural properties observed in real network datasets…
The time variation of entropy, as an alternative to the variance, is proposed as a measure of the diffusion rate. It is shown that for linear and time-translationally invariant systems having a large-time limit for the density, at large…
The structure of the network can be described by motifs, which are subgraphs that often repeat themselves. In order to understand the structure of network motifs, it is of great importance to study subgraphs from the perspective of…