During the last century, networks of several types have been used to model a wide range of physical, biological and social systems. For example, Moreno (1934) studied social networks with multiple types of ties, later called multiplex networks (Verbrugge, 1979; Minor, 1983; Lazega & Pattison, 1999) as well as networks with multiple types of actors. Networks with multiple types of actors and relational ties have often been used together: relevant examples are the extensions of two-mode networks studied by Wasserman & Iacobucci (1991), multi-level networks (Lazega & Snijders, 2016), and heterogeneous information networks (Sun et al., 2012). More recently, researchers in physics and computer science have developed models for different types of interconnected networks known as networks of networks (Buldyrev et al., 2010; D'Agostino & Scala, 2014), multilayer social networks (Magnani & Rossi, 2011), and interconnected networks (Dickison et al., 2012).

The analysis of multilayer networks is among the most active areas of network science, and there are several methods to detect dense “communities” of nodes in multilayer networks. One way to define a community is as a set of nodes that trap a diffusion-like dynamical process (usually a random walk) for a long time. In this view, communities are sets of nodes that create bottlenecks to the spreading of a dynamical process on a network. We analyze the local behavior of different random walks on multiplex networks (which are multilayer networks in which different layers correspond to different types of edges) and show that they have very different bottlenecks, which correspond to rather different notions of what it means for a set of nodes to be a good community. This has direct implications for the behavior of community-detection methods that are based on these random walks.

Network scholars commonly encounter multiple networks, each of which is possibly governed by distinct generation rules while sharing a node group structure. Although the stochastic blockmodeling—detecting such latent group structures with group-specific connection profiles—has been a major topic of recent research, the focus has been given to the assortative group discovery of a single network. Despite its universality, concepts, and techniques for simultaneous characterization of node traits of multilayer networks, constructed by stacking multiple networks into layers, have been limited. Here, we propose a Bayesian multilayer stochastic blockmodeling framework that uncovers layer-common node traits and factors associated with layer-specific network generating functions. Without assuming a priori layer-specific generation rules, our fully Bayesian treatment allows probabilistic inference of latent traits. We extend the approach to detect changes in block structures embedded in temporal layers of network time series. We demonstrate the method using synthetic multilayer networks with assortative, disassortative, core-periphery, and overlapping community structures. Finally, we apply the method to empirical social network datasets, and find that it detects significant latent traits and structural changepoints. In particular, we uncover endogenous historical regimes associated with distinct constellations of states in United States Senate roll call vote similarity patterns.

In this paper, we seek to advance an updated concept of social space that integrates the multilayer and dynamic statistical network methods currently at the disposal of social network researchers. We demonstrate the analytic value of the new concept of social space that we propose with the help of an illustrative analysis of an organizational field involving organizations' external and internal decisions that congeal into a multilevel system of action that shapes the space of possibilities for other participants in the field. Through these internal and external decisions, organizations seek certain positions in their social space while simultaneously modifying that social space over time. We conclude by arguing that network researchers' choices of goodness-of-fit statistics should reflect a consideration about the dimensions of social space of most interest to the nodes involved.

Most people simultaneously belong to several distinct social networks, in which their relations can be different. They have opinions about certain topics, which they share and spread on these networks, and are influenced by the opinions of other persons. In this paper, we build upon this observation to propose a new nodal centrality measure for multiplex networks. Our measure, called Opinion centrality, is based on a stochastic model representing opinion propagation dynamics in such a network. We formulate an optimization problem consisting in maximizing the opinion of the whole network when controlling an external influence able to affect each node individually. We find a mathematical closed form of this problem, and use its solution to derive our centrality measure. According to the opinion centrality, the more a node is worth investing external influence, and the more it is central. We perform an empirical study of the proposed centrality over a toy network, as well as a collection of real-world networks. Our measure is generally negatively correlated with existing multiplex centrality measures, and highlights different types of nodes, accordingly to its definition.

Nowadays, scientific challenges usually require approaches that cross traditional boundaries between academic disciplines, driving many researchers towards interdisciplinarity. Despite its obvious importance, there is a lack of studies on how to quantify the influence of interdisciplinarity on the research impact, posing uncertainty in a proper evaluation for hiring and funding purposes. Here, we propose a method based on the analysis of bipartite interconnected multilayer networks of citations and disciplines, to assess scholars, institutions, and countries interdisciplinary importance. Using data about physics publications and US patents, we show that our method allows to reward, using a quantitative approach, scholars and institutions that have carried out interdisciplinary work and have had an impact in different scientific areas. The proposed method could be used by funding agencies, universities and scientific policy decision makers for hiring and funding purposes, and to complement existing methods to rank universities and countries.

The order of the authors in the published article is incorrect. The authors should appear as follows:

J. Schneider, B. Cornwell, A. Jonas, R. Behler, N. Lancki, B. Skaathun, L. E. Young, E. Morgan, S. Michaels, R. Duvoisin, A. S. Khanna, S. Friedman, P. Schumm, E. Laumann, for the uConnect Study Team

The authors regret the error.