We consider a dynamic network cascade process developed by Duncan Watts applied to a class of random networks, developed independently by Newman and Miller, which allows a specified amount of clustering (short loops). We adapt existing methods for locally tree-like networks to formulate an appropriate two-type branching process to describe the spread of a cascade started with a single active node and obtain a fixed-point equation to implicitly express the extinction probability of such a cascade. In so doing, we also recover a formula that has appeared in various forms in works by Hackett et al. and Miller which provides a threshold condition for certain extinction of the cascade. We find that clustering impedes cascade propagation for networks of low average degree by reducing the connectivity of the network, but for networks with high average degree, the presence of small cycles makes cascades more likely.

The presence of unobserved node-specific heterogeneity in exponential random graph models (ERGM) is a general concern, both with respect to model validity as well as estimation instability. We, therefore, include node-specific random effects in the ERGM that account for unobserved heterogeneity in the network. This leads to a mixed model with parametric as well as random coefficients, labelled as mixed ERGM. Estimation is carried out by iterating between approximate pseudolikelihood estimation for the random effects and maximum likelihood estimation for the remaining parameters in the model. This approach provides a stable algorithm, which allows to fit nodal heterogeneity effects even for large scale networks. We also propose model selection based on the Akaike Information Criterion to check for node-specific heterogeneity.

Isolation is a concept originally conceived in the context of clique enumeration in static networks, mostly used to model communities that do not have much contact to the outside world. Herein, a clique is considered isolated if it has few edges connecting it to the rest of the graph. Motivated by recent work on enumerating cliques in temporal networks, we transform the isolation concept to the temporal setting. We discover that the addition of the time dimension leads to six distinct natural isolation concepts. Our main contribution is the development of parameterized enumeration algorithms for five of these six isolation types for clique enumeration, employing the parameter “degree of isolation.” In a nutshell, this means that the more isolated these cliques are, the faster we can find them. On the empirical side, we implemented and tested these algorithms on (temporal) social network data, obtaining encouraging results.

Centralities are a widely studied phenomenon in network science. In policy networks, central actors are of interest because they are assumed to control information flows, to link opposing coalitions and to directly impact decision-making. First, we study what type of actor (e.g., state authorities or interest groups) is able to occupy central positions in the highly institutionalized context of policy networks. Second, we then ask whether bonding or bridging centralities prove to be more stable over time. Third, we investigate how these types of centrality influence actors’ positions in a network over time. We therefore adopt a longitudinal perspective and run exponential random graph models, including lagged central network positions at t1 as the main independent variable for actors’ activity and popularity at t2. Results confirm that very few actors are able to maintain central positions over time.

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.

The validity of network observations is sometimes of concern in empirical studies, since observed networks are prone to error and may not represent the population of interest. This lack of validity is not just a result of random measurement error, but often due to systematic bias that can lead to the misinterpretation of actors’ preferences of network selections. These issues in network observations could bias the estimation of common network models (such as those pertaining to influence and selection) and lead to erroneous statistical inferences. In this study, we proposed a simulation-based sensitivity analysis method that can evaluate the robustness of inferences made in social network analysis to six forms of selection mechanisms that can cause biases in network observations—random, homophily, anti-homophily, transitivity, reciprocity, and preferential attachment. We then applied this sensitivity analysis to test the robustness of inferences for social influence effects, and we derived two sets of analytical solutions that can account for biases in network observations due to random, homophily, and anti-homophily selection.

We introduce new definitions of sectional, Ricci, and scalar curvatures for networks and their higher dimensional counterparts, derived from two classical notions of curvature for curves in general metric spaces, namely, the Menger curvature and the Haantjes curvature. These curvatures are applicable to unweighted or weighted and undirected or directed networks and are more intuitive and easier to compute than other network curvatures. In particular, the proposed curvatures based on the interpretation of Haantjes definition as geodesic curvature allow us to give a network analogue of the classical local Gauss–Bonnet theorem. Furthermore, we propose even simpler and more intuitive proxies for the Haantjes curvature that allow for even faster and easier computations in large-scale networks. In addition, we also investigate the embedding properties of the proposed Ricci curvatures. Lastly, we also investigate the behavior, both on model and real-world networks, of the curvatures introduced herein with more established notions of Ricci curvature and other widely used network measures.

This paper investigates the distributions of triangle counts per vertex and edge, as a means for network description, analysis, model building, and other tasks. The main interest is in estimating these distributions through sampling, especially for large networks. A novel sampling method tailored for the estimation analysis is proposed, with three sampling designs motivated by several network access scenarios. An estimation method based on inversion and an asymptotic method are developed to recover the entire distribution. A single method to estimate the distribution using multiple samples is also considered. Algorithms are presented to sample the network under the various access scenarios. Finally, the estimation methods on synthetic and real-world networks are evaluated in a data study.

Population analyses of functional connectivity have provided a rich understanding of how brain function differs across time, individual, and cognitive task. An important but challenging task in such population analyses is the identification of reliable features that describe the function of the brain, while accounting for individual heterogeneity. Our work is motivated by two particularly important challenges in this area: first, how can one analyze functional connectivity data over populations of individuals, and second, how can one use these analyses to infer group similarities and differences. Motivated by these challenges, we model population connectivity data as a multilayer network and develop the multi-node2vec algorithm, an efficient and scalable embedding method that automatically learns continuous node feature representations from multilayer networks. We use multi-node2vec to analyze resting state fMRI scans over a group of 74 healthy individuals and 60 patients with schizophrenia. We demonstrate how multilayer network embeddings can be used to visualize, cluster, and classify functional regions of the brain for these individuals. We furthermore compare the multilayer network embeddings of the two groups. We identify significant differences between the groups in the default mode network and salience network—findings that are supported by the triple network model theory of cognitive organization. Our findings reveal that multi-node2vec is a powerful and reliable method for analyzing multilayer networks. Data and publicly available code are available at https://github.com/jdwilson4/multi-node2vec.

Critical cascades are found in many self-organizing systems. Here, we examine critical cascades as a design paradigm for logic and learning under the linear threshold model (LTM), and simple biologically inspired variants of it as sources of computational power, learning efficiency, and robustness. First, we show that the LTM can compute logic, and with a small modification, universal Boolean logic, examining its stability and cascade frequency. We then frame it formally as a binary classifier and remark on implications for accuracy. Second, we examine the LTM as a statistical learning model, studying benefits of spatial constraints and criticality to efficiency. We also discuss implications for robustness in information encoding. Our experiments show that spatial constraints can greatly increase efficiency. Theoretical investigation and initial experimental results also indicate that criticality can result in a sudden increase in accuracy.

A number of theoretical results have provided sufficient conditions for the selection of payoff-efficient equilibria in games played on networks when agents imitate successful neighbors and make occasional mistakes (stochastic stability). However, those results only guarantee full convergence in the long-run, which might be too restrictive in reality. Here, we employ a more gradual approach relying on agent-based simulations avoiding the double limit underlying these analytical results. We focus on the circular-city model, for which a sufficient condition on the population size relative to the neighborhood size was identified by Alós-Ferrer & Weidenholzer [(2006) Economics Letters, 93, 163–168]. Using more than 100,000 agent-based simulations, we find that selection of the efficient equilibrium prevails also for a large set of parameters violating the previously identified condition. Interestingly, the extent to which efficiency obtains decreases gradually as one moves away from the boundary of this condition.