The special issue of “Networks in space and in time: methods and applications” contributes to the debate on contextual analysis in network science. It includes seven research papers that shed light on the analysis of network phenomena studied within geographic space and across temporal dimensions. In these papers, methodological issues as well as specific applications are described from different fields. We take the seven papers, study their citations and texts, and relate them to the broader literature. By exploiting the bibliographic information and the textual data of these seven documents, citation analysis and lexical correspondence analysis allow us to evaluate the connections among the papers included in this issue.

Most social networks present complex structures. They can be both multi-modal and multi-relational. In addition, each relationship can be observed across time occasions. Relational data observed in such conditions can be organized into multidimensional arrays and statistical methods from the theory of multiway data analysis may be exploited to reveal the underlying data structure. In this paper, we adopt an exploratory data analysis point of view, and we present a procedure based on multiple factor analysis and multiple correspondence analysis to deal with time-varying two-mode networks. This procedure allows us to create static displays in order to explore network evolutions and to visually analyze the degree of similarity of actor/event network profiles over time while preserving the different statuses of the two modes.

Dynamic network models describe many important scientific processes, from cell biology and epidemiology to sociology and finance. Estimating dynamic networks from noisy time series data is a difficult task since the number of components involved in the system is very large. As a result, the number of parameters to be estimated is typically larger than the number of observations. However, a characteristic of many real life networks is that they are sparse. For example, the molecular structure of genes make interactions with other components a highly-structured and, therefore, a sparse process. Until now, the literature has focused on static networks, which lack specific temporal interpretations.

We propose a flexible collection of ANOVA-like dynamic network models, where the user can select specific time dynamics, known presence or absence of links, and a particular autoregressive structure. We use undirected graphical models with block equality constraints on the parameters. This reduces the number of parameters, increases the accuracy of the estimates and makes interpretation of the results more relevant. We illustrate the flexibility of the method on both synthetic and real data.

In dynamic networks, the presence of ties are subject both to endogenous network dependencies and spatial dependencies. Current statistical models for change over time are typically defined relative to some initial condition, thus skirting the issue of where the first network came from. Additionally, while these longitudinal network models may explain the dynamics of change in the network over time, they do not explain the change in those dynamics. We propose an extension to the longitudinal exponential random graph model that allows for simultaneous inference of the changes over time and the initial conditions, as well as relaxing assumptions of time-homogeneity. Estimation draws on recent Bayesian approaches for cross-sectional exponential random graph models and Bayesian hierarchical models. This is developed in the context of foreign direct investment relations in the global electricity industry in 1995–2003. International investment relations are known to be affected by factors related to: (i) the initial conditions determined by the geographical locations; (ii) time-dependent fluctuations in the global intensity of investment flows; and (iii) endogenous network dependencies. We rely on the well-known gravity model used in research on international trade to represent how spatial embedding and endogenous network dependencies jointly shape the dynamics of investment relations.

We compare and contrast the network formation of interest groups across industry and issue area. We focus on membership interest groups, which by virtue of representing the interests of voluntary members face particular organizational and maintenance constraints. To reveal their cooperative behavior we build a network dataset based on cosigner status to United States Supreme Court amicus curiae briefs and analyze it with exponential random graph models and multidimensional scaling. Our methodological approach culminates in a clear and compact spatial representation of network similarities and differences. We find that while many of the same factors shape membership networks, religious, labor, and political organizations do not share the same structure as each other or as the business, civic and professional groups.

This paper proposes a model of network interactions in the interbank market. Our innovation is to model systemic risk in the interbank network as the propagation of incentives or strategic behavior rather than the propagation of losses after default. Transmission in our model is not based on default. Instead, we explain bank profitability based on competition incentives and the outcome of a strategic game. As competitors' lending decisions change, banks adjust their own decisions as a result: generating a “transmission” of shocks through the system. We provide a unique equilibrium characterization of a static model, and embed this model into a full dynamic model of network formation. We also determine the key bank, which is the bank that is crucial for the stability of the financial network.

Digital technologies have created the potential for new forms of organizing among geographically dispersed individuals by connecting their ideas across the time and space in complex multiteam systems (MTSs). Realizing this potential requires novel forms of shared leadership structures to shepherd divergent and convergent thinking necessary to nurture innovation. While there is limited research on how space influences leadership and how the time influences leadership, there is virtually no theorizing on how space and time interact together to influence the emergence of shared leadership structures that facilitates innovation. A key contribution of this study is to utilize an agent-based model (ABM) that draws upon the research on leadership, networks, and innovation to specify generative mechanisms (or micro-processes) through which shared leadership structures emerge over space and time. The parameters in this model were estimated from empirical data. Results of virtual experiments (VE) yielded testable hypotheses suggesting that, over time, leadership capacity and between-team ties are negatively influenced by space. Furthermore, the computational model suggests that space increases the concentration of divergent leadership but decreases the concentration of convergent leadership. The study concludes by discussing the implications for the design of effective leadership structures to nurture innovation in MTSs.

City road networks have been extensively studied for their social significance or to quantify their connections and centralities, but often their geographical origin is forgotten. This work focuses on the spatial-geographical and geometrical aspects of the road network skeleton. Following previous work, a multi-scale object, the way, is constructed, based only on the local geometry at road crossings. The best method to reconstruct significant elements is investigated. The results show that this object is geographically meaningful, with many particular characteristics. A new indicator, structurality, is introduced and compared with previous indicators, on the cities of Paris and Avignon. Structurality appears to be stable over the borders of the map sample, and is able to reveal the underlying coherence of the road network. This stability can be interpreted as coming from the particular way the network developed in time, and was later preserved. This link with the historical development of the cites, which deserves to be further studied, is exemplified in the cases of Villers-sur-Mer (France) and Manaus (Brazil). The construction method, the results, and their potential meaning are discussed in detail so that they can be used in various related disciplines, such as sociology, town planning, geomatics, and physics.