Within US professional sports, trades within one’s own division are often perceived to be disadvantageous. We ask how common this practice is. To examine this question, we construct a date-stamped network of all trades in the National Basketball Association between June 1976 and May 2019. We then use season-specific weighted exponential random graph models to estimate the likelihood of teams avoiding within-division trade partners, and how consistent that pattern is across the observed period. In addition to the empirical question, this analysis serves to demonstrate the necessity and difficulty of constructing the proper baseline for statistical comparison. We find limited-to-no support for the popular perception.

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.

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.

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.

This paper studies the friendship paradox for weighted and directed networks, from a probabilistic perspective. We consolidate and extend recent results of Cao and Ross and Kramer, Cutler and Radcliffe, to weighted networks. Friendship paradox results for directed networks are given; connections to detailed balance are considered.

There is a growing consensus that dark networks require special methodological considerations, but little attention has been devoted to determining which data transformation processes are best suited to the study of dark networks. Standard approaches to the transformation of multi-modal data “fold” matrices, by binarizing the network and multiplying it against its transpose. Unfortunately, this process produces exaggerated results when applied to weighted networks, and consequently researchers often disregard information on tie-strength when transforming data. This paper evaluates previous attempts to overcome this limitation and assesses projection methods discovered by biologists and physicists, who have studied the problem of transforming weighted multi-modal networks within the specific context of these disciplines. However, the assumptions underlying these transformation processes limit their applicability to dark networks. This paper, therefore, offers the Median Additive Projection Process (MAPP), an approach to data transformation specifically designed for implementation in weighted, multi-modal dark networks. MAPP accounts for the ambiguity inherent to clandestine subject matter by treating relationship strength in a probabilistic fashion. Because agents' one-mode centrality rankings change significantly when different projection processes are applied to the same two-mode network, MAPP allows researchers to more accurately identify central actors in dark networks.

A wide variety of networked systems in human societies are composed of repeated communications between actors. A dyadic relationship made up of repeated interactions may be reciprocal (both actors have the same probability of directing a communication attempt to the other) or non-reciprocal (one actor has a higher probability of initiating a communication attempt than the other). In this paper we propose a theoretically motivated index of reciprocity appropriate for networks formed from repeated interactions based on these probabilities. We go on to examine the distribution of reciprocity in a large-scale social network built from trace-logs of over a billion cell-phone communication events across millions of actors in a large industrialized country. We find that while most relationships tend toward reciprocity, a substantial minority of relationships exhibit large levels of non-reciprocity. This is puzzling because behavioral theories in social science predict that persons will selectively terminate non-reciprocal relationships, keeping only those that approach reciprocity. We point to two structural features of human communication behavior and relationship formation—the division of contacts into strong and weak ties and degree-based assortativity—that either help or hinder the ability of persons to obtain communicative balance in their relationships. We examine the extent to which deviations from reciprocity in the observed network are partially traceable to the operation of these countervailing tendencies.