"Supracentrality Analysis of Temporal Networks with Directed Interlayer Coupling" (Second Edition)

The unnecessary second edition of the book Temporal Network Theory is now out. It includes a second edition of a chapter that I coauthored. Here are a few details.

Title: 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 with 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 with 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 importances 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.

"Classical and Quantum Random-Walk Centrality Measures in Multilayer Networks"

Another paper of mine just came out in final form. Here are some details about it.

Title: Classical and Quantum Random-Walk Centrality Measures in Multilayer Networks

Authors: Lucas Böttcher and Mason A. Porter

Abstract: Multilayer network analysis is a useful approach for studying networks of entities that interact with each other via multiple relationships. Classifying the importance of nodes and node-layer tuples is an important aspect of the study of multilayer networks. To do this, it is common to calculate various centrality measures, which allow one to rank nodes and node-layers according to a variety of structural features. In this paper, we formulate occupation, PageRank, betweenness, and closeness centralities in terms of node-occupation properties of different types of continuous-time classical and quantum random walks on multilayer networks. We apply our framework to a variety of synthetic and real-world multilayer networks, and we identify notable differences between classical and quantum centrality measures. Our computations give insights into the correlations between certain centralities that are based on random walks and associated centralities that are based on geodesic paths.

"Tie-Decay Networks in Continuous Timeand Eigenvector-Based Centralities"

The paper based on one of my old projects finally appeared in final form. Here are some details.

Title: Tie-Decay Networks in Continuous Timeand Eigenvector-Based Centralities

Authors: Walid Ahmad, Mason A. Porter, and Mariano Beguerisse-Díaz

Abstract: Network theory is a useful framework for studying interconnected systems of interacting entities. Many networked systems evolve continuously in time, but most existing methods for the analysis of time-dependent networks rely on discrete or discretized time. In this paper, we propose an approach for studying networks that evolve in continuous time by distinguishing between interactions, which we model as discrete contacts, and ties, which encode the strengths of relationships over time. To illustrate our tie-decay network formalism, we adapt the well-known PageRank centrality score to our tie-decay framework in a mathematically tractable and computationally efficient way. We apply this framework to a synthetic example and then use it to study a network of retweets during the 2012 National Health Service controversy in the United Kingdom. Our work also provides guidance for similar generalizations of other tools from network theory to continuous-time networks with tie decay, including for applications to streaming data.

"Tunable Eigenvector-Based Centralities for Multiplex and Temporal Networks"

One of my papers just came out in final form. Here are the details.

Title: Tunable Eigenvector-Based Centralities for Multiplex and Temporal Networks

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

"Who is the Most Important Character in Frozen? What Networks Can Tell Us about the World"

Petter Holme, Hiroki Sayama, and I decided to take on the challenge of writing a mathematics paper for Frontiers for Young Minds, a scientific journal for young readers. Only a handful of mathematics papers have been published among their many hundreds of articles. We decided to give an introduction to networks through the movie Frozen and calculation of centralities. Our paper came out today, and here are some details. You can take a look at our paper either at their website or in .pdf form.

Title: Who is the Most Important Character in Frozen? What Networks Can Tell Us about the World

Authors: Petter Holme, Mason A. Porter, and Hiroki Sayama

Abstract: How do we determine the important characters in a movie like Frozen? We can watch it, of course, but there are also other ways—using mathematics and computers—to see who is important in the social network of a story. The idea is to compute numbers called centralities, which are ways of measuring who is important in social networks. In this paper, we talk about how different types of centralities measure importance in different ways. We also discuss how people use centralities to study many kinds of networks, not just social ones. Scientists are now developing centrality measures that also consider changes over time and different types of relationships.

The Multiplex Social–Slayage Network of Buffy the Vampire Slayer

Here is the multiplex social–slayage network of Buffy the Vampire Slayer.

The Buffy social network: slayage and love links. https://t.co/xwQ0DoKpAG

— Peter Sheridan Dodds (@peterdodds) March 11, 2018

This figure is definite fodder for talks. Also, if somebody sets up the adjacencies, we should compute some centrality and versatility measures.

XKCD: Academic Imposters

This old xkcd comic is amusing. It also includes an (I believe) unintended joke about centrality measures.

(Tip of the cap to Carlos Castillo Chavez.)

Periodic Table of Network Centrality

Yes, really.

I wonder what new "elements" will be discovered this year? :)

Note: Many centrality measures are missing (unsurprising, given how many there are), and quite a few of them have incorrect citations attached to them.