"Nonlinearity + Networks: A 2020 Vision"

Here is the final, published version of my forward-looking book chapter about where network science and some directions that it is heading. It appears in the book Emerging Frontiers in Nonlinear Science.

Title: Nonlinearity + Networks: A 2020 Vision

Abstract: I briefly survey several fascinating topics in networks and nonlinearity. I highlight a few methods and ideas, including several of personal interest, that I anticipate to be especially important during the next several years. These topics include temporal networks (in which a network’s entities and/or their interactions change in time), stochastic and deterministic dynamical processes on networks, adaptive networks (in which a dynamical process on a network is coupled to dynamics of network structure), and network structure and dynamics that include “higher-order” interactions (which involve three or more entities in a network). I draw examples from a variety of scenarios, including contagion dynamics, opinion models, waves, and coupled oscillators.

And in case you want to help spread the word, here is my recent tweet.

Here's the final, published version of my forward-looking chapter, "Nonlinearity + Networks: A 2020 Vision": https://t.co/eLdlD45oe8

It appears in the book "Emerging Frontiers in Nonlinear Science" (https://t.co/IBGX7bMyeA)

— Mason Porter (@masonporter) May 30, 2020

"Supracentrality Analysis of Temporal Networks with Directed Interlayer Coupling"

A new book chapter in the edited book Temporal Network Theory was just published in final form. Here are some details.

Titles: Supracentrality Analysis of Temporal Networks with Directed Interlayer Coupling

Authors: Dane Taylor, Mason A. Porter, and Peter J. Mucha

Abstract: We describe centralities in temporal networks using a supracentrality framework to study centrality trajectories, which characterize how the importances of nodes change in time. We study supracentrality generalizations of eigenvector-based centralities, a family of centrality measures for time-independent networks that includes PageRank, hub and authority scores, and eigenvector centrality. We start with a sequence of adjacency matrices, each of which represents a time layer of a network at a different point or interval of time. Coupling centrality matrices across time layers with weighted interlayer edges yields a supracentrality matrix ℂ(𝜔), where ω controls the extent to which centrality trajectories change over time. We can flexibly tune the weight and topology of the interlayer coupling to cater to different scientific applications. The entries of the dominant eigenvector of ℂ(𝜔) represent joint centralities, which simultaneously quantify the importance of every node in every time layer. Inspired by probability theory, we also compute marginal and conditional centralities. We illustrate how to adjust the coupling between time layers to tune the extent to which nodes’ centrality trajectories are influenced by the oldest and newest time layers. We support our findings by analysis in the limits of small and large ω.