Books in the Elements in Structure and Dynamics of Complex Networks series

This Element presents one of the most recent developments in network science in a highly accessible style. This Element will be of interest to interdisciplinary scientists working in network science, in addition to mathematicians working in discrete topology and geometry and physicists working in quantum gravity.

This Element reviews fundamental models and methods for the geometric description of real networks with a focus on applications of real network maps, including decentralized routing protocols, geometric community detection, and the self-similar multiscale unfolding of networks by geometric renormalization.

In many systems consisting of interacting subsystems, the complex interactions between elements can be represented using multilayer networks. However, percolation is not trivially generalised to multiple layers. This Element describes a generalisation of percolation to multilayer networks: weak multiplex percolation.

Many multiagent dynamics can be modeled as a stochastic process in which the agents in the system change their state over time in interaction with each other. The Gillespie algorithms are popular algorithms that exactly simulate such stochastic multiagent dynamics when each state change is driven by a discrete event, the dynamics is defined in continuous time, and the stochastic law of event occurrence is governed by independent Poisson processes. The first main part of this volume provides a tutorial on the Gillespie algorithms focusing on simulation of social multiagent dynamics occurring in populations and networks. The authors clarify why one should use the continuous-time models and the Gillespie algorithms in many cases, instead of easier-to-understand discrete-time models. The remainder of the Element reviews recent extensions of the Gillespie algorithms aiming to add more reality to the model (i.e., non-Poissonian cases) or to speed up the simulations. This title is also available as open access on Cambridge Core.

Networks are convenient mathematical models to represent the structure of complex systems, from cells to societies. In the last decade, multilayer network science - the branch of the field dealing with units interacting in multiple distinct ways, simultaneously - was demonstrated to be an effective modeling and analytical framework for a wide spectrum of empirical systems, from biopolymers networks (such as interactome and metabolomes) to neuronal networks (such as connectomes), from social networks to urban and transportation networks. In this Element, a decade after one of the most seminal papers on this topic, the authors review the most salient features of multilayer network science, covering both theoretical aspects and direct applications to real-world coupled/interdependent systems, from the point of view of multilayer structure, dynamics and function. The authors discuss potential frontiers for this topic and the corresponding challenges in the field for the next future.