This paper introduces a framework for understanding complex temporal interaction patterns in large-scale scientific collaboration networks. In particular, we investigate how two key concepts in science studies, scientific collaboration and scientific mobility, are related and possibly differ between fields. We do so by analyzing multilayer temporal motifs: small recurring configurations of nodes and edges.

Driven by the problem that many papers share the same publication year, we first provide a methodological contribution: an efficient counting algorithm for multilayer temporal motifs with concurrent edges. Next, we introduce a systematic categorization of the multilayer temporal motifs, such that each category reflects a pattern of behavior relevant to scientific collaboration and mobility. Here, a key question concerns the causal direction: does mobility lead to collaboration or vice versa? Applying this framework to scientific collaboration networks extracted from Web of Science (WoS) consisting of up to 7.7 million nodes (authors) and 94 million edges (collaborations), we find that international collaboration and international mobility reciprocally influence one another. Additionally, we find that Social sciences & Humanities (SSH) scholars co-author to a greater extent with authors at a distance, while Mathematics & Computer science (M&C) scholars tend to continue to collaborate within the established knowledge network and organization.

Thematic analysis of personal networks involves identifying regularities in network structure and content, and grouping networks into types/clusters, to allow for a holistic understanding of social complexities. We propose an inductive approach to network thematic analysis, applying the learnings from qualitative coding, fused mixed-methods analysis, and typology development. It involves framing (changing focus by magnifying, aggregating, and graphical configuration), pattern detection (identification of underlying dimensions, sorting, and clustering), labeling, and triangulating (confirmation and fine-tuning using quantitative and qualitative approaches); applied repeatedly and emergently. We describe this approach utilized in two cases of studying support networks of caregivers.

Even within well-studied organisms, many genes lack useful functional annotations. One way to generate such functional information is to infer biological relationships between genes or proteins, using a network of gene coexpression data that includes functional annotations. Signed distance correlation has proved useful for the construction of unweighted gene coexpression networks. However, transforming correlation values into unweighted networks may lead to a loss of important biological information related to the intensity of the correlation. Here, we introduce a principled method to construct weighted gene coexpression networks using signed distance correlation. These networks contain weighted edges only between those pairs of genes whose correlation value is higher than a given threshold. We analyze data from different organisms and find that networks generated with our method based on signed distance correlation are more stable and capture more biological information compared to networks obtained from Pearson correlation. Moreover, we show that signed distance correlation networks capture more biological information than unweighted networks based on the same metric. While we use biological data sets to illustrate the method, the approach is general and can be used to construct networks in other domains. Code and data are available on https://github.com/javier-pardodiaz/sdcorGCN.

We study the network structure of Wikipedia (restricted to its mathematical portion), MathWorld, and DLMF. We approach these three online mathematical libraries from the perspective of several global and local network-theoretic features, providing for each one the appropriate value or distribution, along with comparisons that, if possible, also include the whole of the Wikipedia or the Web. We identify some distinguishing characteristics of all three libraries, most of them supposedly traceable to the libraries' shared nature of relating to a very specialized domain. Among these characteristics are the presence of a very large strongly connected component in each of the corresponding directed graphs, the complete absence of any clear power laws describing the distribution of local features, and the rise to prominence of some local features (e.g., stress centrality) that can be used to effectively search for keywords in the libraries.

Social influence is frequently measured through an ego's direct ties. Although influence may also stem from an ego's indirect ties, reference group, and casual contacts, it is difficult to capture their impact using existing network methods. We identify and trace the influence stemming from an ego's “familiar others,” consisting of those socially similar individuals with whom the ego comes in contact at school, but does not necessarily share a relationship. To evaluate the role of familiar others, we investigate unhealthy weight behaviors in adolescence using data from the National Longitudinal Study of Adolescent to Adult Health. Our results demonstrate that familiar others' unhealthy weight-related behaviors are strong predictors of the ego's own weight behaviors, net of immediate alters' behaviors, and individual-level characteristics. Further, we find that this relationship is stronger and more robust than that between egos and their direct ties. These results suggest that familiar others constitute a key source of social influence that is distinct from the influence of network alters.

Researchers theorize that many real-world networks exhibit community structure where within-community edges are more likely than between-community edges. While numerous methods exist to cluster nodes into different communities, less work has addressed this question: given some network, does it exhibit statistically meaningful community structure? We answer this question in a principled manner by framing it as a statistical hypothesis test in terms of a general and model-agnostic community structure parameter. Leveraging this parameter, we propose a simple and interpretable test statistic used to formulate two separate hypothesis testing frameworks. The first is an asymptotic test against a baseline value of the parameter while the second tests against a baseline model using bootstrap-based thresholds. We prove theoretical properties of these tests and demonstrate how the proposed method yields rich insights into real-world datasets.

Various important and useful quantities or measures that characterize the topological network structure are usually investigated for a network, then they are averaged over the samples. In this paper, we propose an explicit representation by the beforehand averaged adjacency matrix over samples of growing networks as a new general framework for investigating the characteristic quantities. It is applied to some network models, and shows a good approximation of degree distribution asymptotically. In particular, our approach will be applicable through the numerical calculations instead of intractable theoretical analyses, when the time-course of degree is a monotone increasing function like power law or logarithm.

The 2011 policy pivot of the German government, from extending nuclear power plants terms to securing their shutdown for 2022, cannot be explained without looking at how the German political discourse network shifted in the months following Fukushima. This paper seeks to model and identify mechanisms that help explain how the two-mode network of political actors’ support for claims developed. We identify possible mechanisms to explain discourse dynamics from literature on political discourse and discourse networks, and extend homophily mechanisms to two-mode networks as “tertius” effects. We then introduce and employ a multimodal extension of dynamic network actor models to answer two questions key to how the discourse has evolved: which actors support claims more frequently and which claims they support. Our results indicate that mechanisms vary according to the discursive phase, but that powerful actors participate in the discourse more often, and actors tend to support claims that have already found support by cross-party coalitions. These are the two most prominent mechanisms that help to explain the dramatic nuclear policy change in Germany after Fukushima.

Dense networks with weighted connections often exhibit a community-like structure, where although most nodes are connected to each other, different patterns of edge weights may emerge depending on each node’s community membership. We propose a new framework for generating and estimating dense weighted networks with potentially different connectivity patterns across different communities. The proposed model relies on a particular class of functions which map individual node characteristics to the edges connecting those nodes, allowing for flexibility while requiring a small number of parameters relative to the number of edges. By leveraging the estimation techniques, we also develop a bootstrap methodology for generating new networks on the same set of vertices, which may be useful in circumstances where multiple data sets cannot be collected. Performance of these methods is analyzed in theory, simulations, and real data.

With the increasing availability of behavioral data from diverse digital sources, such as social media sites and cell phones, it is now possible to obtain detailed information about the structure, strength, and directionality of social interactions in varied settings. While most metrics of network structure have traditionally been defined for unweighted and undirected networks only, the richness of current network data calls for extending these metrics to weighted and directed networks. One fundamental metric in social networks is edge overlap, the proportion of friends shared by two connected individuals. Here, we extend definitions of edge overlap to weighted and directed networks and present closed-form expressions for the mean and variance of each version for the Erdős–Rényi random graph and its weighted and directed counterparts. We apply these results to social network data collected in rural villages in southern Karnataka, India. We use our analytical results to quantify the extent to which the average overlap of the empirical social network deviates from that of corresponding random graphs and compare the values of overlap across networks. Our novel definitions allow the calculation of edge overlap for more complex networks, and our derivations provide a statistically rigorous way for comparing edge overlap across networks.

In urban systems, there is an interdependency between neighborhood roles and transportation patterns between neighborhoods. In this paper, we classify docking stations in bicycle-sharing networks to gain insight into the human mobility patterns of three major cities in the United States. We propose novel time-dependent stochastic block models, with degree-heterogeneous blocks and either mixed or discrete block membership, which classify nodes based on their time-dependent activity patterns. We apply these models to (1) detect the roles of bicycle-sharing stations and (2) describe the traffic within and between blocks of stations over the course of a day. Our models successfully uncover work blocks, home blocks, and other blocks; they also reveal activity patterns that are specific to each city. Our work gives insights for the design and maintenance of bicycle-sharing systems, and it contributes new methodology for community detection in temporal and multilayer networks with heterogeneous degrees.

While logistic regression models are easily accessible to researchers, when applied to network data there are unrealistic assumptions made about the dependence structure of the data. For temporal networks measured in discrete time, recent work has made good advances (Almquist & Butts, 2014), but there is still the assumption that the dyads are conditionally independent given the edge histories. This assumption can be quite strong and is sometimes difficult to justify. If time steps are rather large, one would typically expect not only the existence of temporal dependencies among the dyads across observed time points but also the existence of simultaneous dependencies affecting how the dyads of the network co-evolve. We propose a general observation-driven model for dynamic networks that overcomes this problem by modeling both the mean and the covariance structures as functions of the edge histories using a flexible autoregressive approach. This approach can be shown to fit into a generalized linear mixed model framework. We propose a visualization method that provides evidence concerning the existence of simultaneous dependence. We describe a simulation study to determine the method's performance in the presence and absence of simultaneous dependence, and we analyze both a proximity network from conference attendees and a world trade network. We also use this last data set to illustrate how simultaneous dependencies become more prominent as the time intervals become coarser.

We study the detection and the reconstruction of a large very dense subgraph in a social graph with n nodes and m edges given as a stream of edges, when the graph follows a power law degree distribution, in the regime when $m=O(n. \log n)$ . A subgraph S is very dense if it has $\Omega(|S|^2)$ edges. We uniformly sample the edges with a Reservoir of size $k=O(\sqrt{n}.\log n)$ . Our detection algorithm checks whether the Reservoir has a giant component. We show that if the graph contains a very dense subgraph of size $\Omega(\sqrt{n})$ , then the detection algorithm is almost surely correct. On the other hand, a random graph that follows a power law degree distribution almost surely has no large very dense subgraph, and the detection algorithm is almost surely correct. We define a new model of random graphs which follow a power law degree distribution and have large very dense subgraphs. We then show that on this class of random graphs we can reconstruct a good approximation of the very dense subgraph with high probability. We generalize these results to dynamic graphs defined by sliding windows in a stream of edges.

GLOBALink, a large online network of tobacco control professionals, was active in the promotion of the World Health Organization's Framework Convention on Tobacco Control treaty, an international treaty aimed at reducing the global burden of tobacco-related death and disease. We examined and compared the roles that different countries served in the GLOBALink community during FCTC negotiation and ratification. Previous studies of FCTC ratification found the process adhered to a diffusion of innovation model (Valente et al., 2015). We followed that work by conducting content analyses of discussion messages posted by GLOBALink members representing different countries. Based on the time when they ratified the FCTC, each country was labeled by one of the four adoption stages of the diffusion model and we investigated the amount of shared word use between the different stages. A goodness-of-fit chi-squared test indicated that content was not shared in an expected manner between stages (χ2 = 11,856.45, N = 51,447, p < 0.001). A deeper look at the specific words shared between countries within and between adoption stages provided insight into how interactions between certain countries might have served to support the ratification process.

Machine learning applications on large-scale network-structured data commonly encode network information in the form of node embeddings. Network embedding algorithms map the nodes into a low-dimensional space such that the nodes that are “similar” with respect to network topology are also close to each other in the embedding space. Real-world networks often have multiple versions or can be “multiplex” with multiple types of edges with different semantics. For such networks, computation of Consensus Embeddings based on the node embeddings of individual versions can be useful for various reasons, including privacy, efficiency, and effectiveness of analyses. Here, we systematically investigate the performance of three dimensionality reduction methods in computing consensus embeddings on networks with multiple versions: singular value decomposition, variational auto-encoders, and canonical correlation analysis (CCA). Our results show that (i) CCA outperforms other dimensionality reduction methods in computing concensus embeddings, (ii) in the context of link prediction, consensus embeddings can be used to make predictions with accuracy close to that provided by embeddings of integrated networks, and (iii) consensus embeddings can be used to improve the efficiency of combinatorial link prediction queries on multiple networks by multiple orders of magnitude.

Researchers collecting survey data on inter-organizational networks typically choose a single informant with the most senior job title in each organization from whom to obtain a report of the organization’s inter-organizational ties. This approach to informant selection is based on the logic that greater seniority confers greater knowledge of inter-organizational relationships. The present study investigated the wisdom of this logic, using data in which multiple informants’ reports of inter-organizational network ties were collected for each organization. We calculated the degree of agreement in network reports between the informant with the most senior job title and a second informant in the organization. To determine if alternative criteria to seniority serve as better approaches to informant selection, we assessed other potential predictors of agreement in informants’ reports. Results indicated that (1) informants’ perceptions of the network differed significantly according to job title, suggesting little agreement between senior informants and their more junior colleagues; and (2) greater informant tenure in the network and industry were associated with greater agreement among informants. These results call a common data collection practice into question and suggest that tenure may trump title as a criterion for informant selection in inter-organizational network research.

When people are asked to recall their social networks, theoretical and empirical work tells us that they rely on shortcuts, or heuristics. Cognitive social structures (CSSs) are multilayer social networks where each layer corresponds to an individual’s perception of the network. With multiple perceptions of the same network, CSSs contain rich information about how these heuristics manifest, motivating the question, Can we identify people who share the same heuristics? In this work, we propose a method for identifying cognitive structure across multiple network perceptions, analogous to how community detection aims to identify social structure in a network. To simultaneously model the joint latent social and cognitive structure, we study CSSs as three-dimensional tensors, employing low-rank nonnegative Tucker decompositions (NNTuck) to approximate the CSS—a procedure closely related to estimating a multilayer stochastic block model (SBM) from such data. We propose the resulting latent cognitive space as an operationalization of the sociological theory of social cognition by identifying individuals who share relational schema. In addition to modeling cognitively independent, dependent, and redundant networks, we propose a specific model instance and related statistical test for testing when there is social-cognitive agreement in a network: when the social and cognitive structures are equivalent. We use our approach to analyze four different CSSs and give insights into the latent cognitive structures of those networks.

In this paper, we attempt to investigate the attack tolerance of human mobility networks where the mobility is restricted to some extent, for instance, in a hospital, one is not allowed to access all locations. Similar situations also arise in schools. In such a network, we will show that people need to rely upon some intermediate agents, popularly known as the brokers to disseminate information. In order to establish this fact, we have followed the approach of attack in a network which in turn helps to identify important nodes in the network in order to maintain the overall connectivity. In this direction, we have proposed, a new temporal metric, brokerage frequency which significantly outperforms all other state-of-the-art attack strategies reported in Trajanovski et al. (2012), Sur et al. (2015).

We introduce a novel preferential attachment model using the draw variables of a modified Pólya urn with an expanding number of colors, notably capable of modeling influential opinions (in terms of vertices of high degree) as the graph evolves. Similar to the Barabási-Albert model, the generated graph grows in size by one vertex at each time instance; in contrast however, each vertex of the graph is uniquely characterized by a color, which is represented by a ball color in the Pólya urn. More specifically at each time step, we draw a ball from the urn and return it to the urn along with a number of reinforcing balls of the same color; we also add another ball of a new color to the urn. We then construct an edge between the new vertex (corresponding to the new color) and the existing vertex whose color ball is drawn. Using color-coded vertices in conjunction with the time-varying reinforcing parameter allows for vertices added (born) later in the process to potentially attain a high degree in a way that is not captured in the Barabási-Albert model. We study the degree count of the vertices by analyzing the draw vectors of the underlying stochastic process. In particular, we establish the probability distribution of the random variable counting the number of draws of a given color which determines the degree of the vertex corresponding to that color in the graph. We further provide simulation results presenting a comparison between our model and the Barabási-Albert network.

The supplemental online material accompanying this article was not the final version. The final version is now published online. The publisher regrets the error.