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Online social networks provide a forum where people make new connections, learn more about the world, get exposed to different points of view, and access information that were previously inaccessible. It is natural to assume that content-delivery algorithms in social networks should not only aim to maximize user engagement but also to offer opportunities for increasing connectivity and enabling social networks to achieve their full potential. Our motivation and aim is to develop methods that foster the creation of new connections, and subsequently, improve the flow of information in the network. To achieve our goal, we propose to leverage the strong triadic closure principle, and consider violations to this principle as opportunities for creating more social links. We formalize this idea as an algorithmic problem related to the densest k-subgraph problem. For this new problem, we establish hardness results and propose approximation algorithms. We identify two special cases of the problem that admit a constant-factor approximation. Finally, we experimentally evaluate our proposed algorithm on real-world social networks, and we additionally evaluate some simpler but more scalable algorithms.

The structure of scientific collaborations has been the object of intense study both for its importance for innovation and scientific advancement, and as a model system for social group coordination and formation thanks to the availability of authorship data. Over the last years, complex networks approach to this problem have yielded important insights and shaped our understanding of scientific communities. In this paper we propose to complement the picture provided by network tools with that coming from using simplicial descriptions of publications and the corresponding topological methods. We show that it is natural to extend the concept of triadic closure to simplicial complexes and show the presence of strong simplicial closure. Focusing on the differences between scientific fields, we find that, while categories are characterized by different collaboration size distributions, the distributions of how many collaborations to which an author is able to participate is conserved across fields pointing to underlying attentional and temporal constraints. We then show that homological cycles, that can intuitively be thought as hole in the network fabric, are an important part of the underlying community linking structure.

Organizational theorists have extensively documented the increased likelihood that two organizations will form a relationship if they have preexisting relationships with the same third party, a phenomenon known as triadic closure. They have neglected, however, the importance of the shared third party in facilitating or reversing this process. I theorize that the collaboration outcomes and competitive concerns of the intermediary spanning an open triad play a crucial role in whether that triad closes. Using a longitudinal dataset of the investment decisions of limited partners investing in U.S. venture capital firms in the period 1997–2007, I find that an intermediary is less likely to facilitate a direct connection under two conditions: (1) the intermediary has experienced failed collaborations with one of the indirectly connected parties or (2) the intermediary has competitive concerns—driven by its replaceability and relative attractiveness—that it may lose future business to one of the indirectly connected parties. The paper goes beyond the conceptualization of indirect ties as passive scaffolding that supports creating direct ties and instills a greater appreciation for the role of the intermediary that sits across them.

Applying the concept of triadic closure to coauthorship networks means that scholars are likely to publish a joint paper if they have previously coauthored with the same people. Prior research has identified moderate to high (20 to 40%) closure rates; suggesting this mechanism is a reasonable explanation for tie formation between future coauthors. We show how calculating triadic closure based on prior operationalizations of closure, namely Newman’s measure for one-mode networks (NCC) and Opsahl’s measure for two-mode networks (OCC) may lead to higher amounts of closure compared to measuring closure over time via a metric that we introduce and test in this paper. Based on empirical experiments using four large-scale, longitudinal datasets, we find a lower bound of 1–3% closure rates and an upper bound of 4–7%. These results motivate research on new explanatory factors for the formation of coauthorship links.

The modeling and analysis of networks and network data has seen an explosion of interest in recent years and represents an exciting direction for potential growth in statistics. Despite the already substantial amount of work done in this area to date by researchers from various disciplines, however, there remain many questions of a decidedly foundational nature—natural analogues of standard questions already posed and addressed in more classical areas of statistics—that have yet to even be posed, much less addressed. Here we raise and consider one such question in connection with network modeling. Specifically, we ask, \"Given an observed network, what is the sample size?\" Using simple, illustrative examples from the class of exponential random graph models, we show that the answer to this question can very much depend on basic properties of the networks expected under the model, as the number of vertices nV in the network grows. In particular, adopting the (asymptotic) scaling of the variance of the maximum likelihood parameter estimates as a notion of effective sample size (neff), we show that when modeling the overall propensity to have ties and the propensity to reciprocate ties, whether the networks are sparse or not under the model (i.e., having a constant or an increasing number of ties per vertex, respectively) is sufficient to yield an order of magnitude difference in neff, from O(nV) to $O(n^2_v)$. In addition, we report simulation study results that suggest similar properties for models for triadic (friend-of-a-friend) effects. We then explore some practical implications of this result, using both simulation and data on food-sharing from Lamalera, Indonesia.

In social media, ties between content providers as an organic recommendation mechanism enable users to explore content. A provider can initiate outgoing ties to other providers to cross-promote their content. On receiving the incoming ties, these responding providers then decide whether to reciprocate. Confirming that reciprocation is beneficial for the initiator to attract more subscribers, we find that the reciprocation benefit is negatively moderated by content similarity between the two providers and their common ties with other providers, although both content similarity and common ties increase reciprocation probability. Specifically, a 10% increase in content similarity decreases the reciprocation benefit by 27.2%, and one additional common tie reduces the reciprocation benefit by 12.6% on average. Therefore, providers can take different networking strategies for different objectives. New providers aiming for more reciprocations can initiate ties to providers with similar content or more common ties, whereas well-established providers can reach out to providers with fewer common ties to gain subscribers or to providers with similar content to grow views. To maximize the expected benefit of integrating both reciprocation probability and benefit, a provider should link to more content-similar providers among those with few common ties and more content-different providers among those with many common ties. In social media, a content provider can initiate outgoing ties to other providers to promote their content, thus inviting reciprocal promotion. We investigate how the reciprocation benefit for the initiating provider is affected by homophily and triadic closure, the two major mechanisms of tie formation. Specifically, we examine how the increase in subscribers and viewership of the initiating provider’s content attributable to the responding providers’ reciprocation is moderated by common ties and content similarity between the two linked providers. Using panel data on 27,356 YouTube video providers, we specify a switching regression model to estimate the influence of content similarity and common ties on reciprocation impact while correcting for their influence on reciprocation probability. Confirming that reciprocation is generally beneficial for the initiator, we find that although content similarity and common ties increase reciprocation probability, they reduce the reciprocation benefit for the initiator in terms of subscriber growth. We also find a positive interaction effect between content similarity and common ties on reciprocation impact, reducing their individual effects. Combining their respective influence on reciprocation probability and benefit, we further examine how content similarity and common ties affect the expected benefit for the initiator and derive practical implications for content providers and social media platforms.

We investigate how homophily in adherence to anti-epidemic measures affects the final size of epidemics in social networks. Using a modified SIR model, we divide agents into two behavioral groups—compliant and non-compliant—and introduce transmission probabilities that depend asymmetrically on the behavior of both the infected and susceptible individuals. We simulate epidemic dynamics on two types of synthetic networks with tunable inter-group connection probability: stochastic block models (SBM) and networks with triadic closure (TC) that better capture local clustering. Our main result reveals a counterintuitive effect: under conditions where compliant infected agents significantly reduce transmission, increasing the separation between groups may lead to a higher fraction of infections in the compliant population. This paradoxical outcome emerges only in networks with clustering (TC), not in SBM, suggesting that local network structure plays a crucial role. These findings highlight that increasing group separation does not always confer protection, especially when behavioral traits amplify within-group transmission.

Purpose This study aims to investigate how and to what extent structural network properties affect dyadic negotiation behavior in tourism destination ecosystems. Specifically, this study addresses negotiation behavior in terms of problem-solving and contending, because these two key strategies reflect the integrative and distributive aspects of dyadic interactions. Design/methodology/approach This study relies on network data and dyadic survey data from nine mountain tourism destinations in Southeastern Norway. The structural network properties the authors research are triadic closure – the extent to which a dyad has common ties to other actors – and structural equivalence – the similarities in networking patterns that capture firms’ competition for similar resources. In addition, the authors also study a possible effect of relationship duration on negotiation behavior. Findings Triadic closure and relationship duration have positive effects on problem-solving, and structural equivalence tends to decrease problem-solving, although the effect is inconsistent; none of these three independent variables was found to affect contending negotiation behavior. Research limitations/implications This study shows that a dyad’s structural network embeddedness has implications for negotiation behavior. Further research is encouraged to develop this theoretical perspective. Originality/value This study is a pioneering investigation of how structural network properties affect dyadic negotiation behavior in ongoing coproducing relationships in real-world destination ecosystems.

Recent work studying triadic closure in undirected graphs has drawn attention to the distinction between measures that focus on the “center” node of a wedge (i.e., length-2 path) versus measures that focus on the “initiator,” a distinction with considerable consequences. Existing measures in directed graphs, meanwhile, have all been center-focused. In this work, we propose a family of eight directed closure coefficients that measure the frequency of triadic closure in directed graphs from the perspective of the node initiating closure. The eight coefficients correspond to different labeled wedges, where the initiator and center nodes are labeled, and we observe dramatic empirical variation in these coefficients on real-world networks, even in cases when the induced directed triangles are isomorphic. To understand this phenomenon, we examine the theoretical behavior of our closure coefficients under a directed configuration model. Our analysis illustrates an underlying connection between the closure coefficients and moments of the joint in- and out-degree distributions of the network, offering an explanation of the observed asymmetries. We also use our directed closure coefficients as predictors in two machine learning tasks. We find interpretable models with AUC scores above 0.92 in class-balanced binary prediction, substantially outperforming models that use traditional center-focused measures.

Community detection is a fundamental task for understanding network structures, crucial for identifying groups of nodes with close connections. However, existing methods generally treat all connections in networks as equally important, overlooking the inherent inequality of connection strengths in social networks, and often require large quantities of labeled data. To address these challenges, we propose a few-shot community detection framework, Strong Triadic Closure Community Detection with Prompt (STC-CDP), which combines the Strong Triadic Closure (STC) principle, Graph Neural Networks, and prompt learning. The STC principle, derived from social network theory, states that if two nodes share strong connections with a third node, they are likely to be connected with each other. By incorporating STC constraints during the pre-training phase, STC-CDP can differentiate between strong and weak connections in networks, thereby more accurately capturing community structures. We design an innovative prompt learning mechanism that enables the model to extract key features from a small number of labeled communities and transfer them to the identification of unlabeled communities. Experiments on multiple real-world datasets demonstrate that STC-CDP significantly outperforms existing state-of-the-art methods under few-shot conditions, achieving higher F1 scores and Jaccard similarity particularly on Facebook, Amazon, and DBLP datasets. Our approach not only improves the precision of community detection but also provides new insights into understanding connection inequality in social networks.