Many studies that gather social network data use survey methods that lead to censored, missing, or otherwise incomplete information. For example, the popular fixed rank nomination (FRN) scheme, often used in studies of schools and businesses, asks study participants to nominate and rank at most a small number of contacts or friends, leaving the existence of other relations uncertain. However, most statistical models are formulated in terms of completely observed binary networks. Statistical analyses of FRN data with such models ignore the censored and ranked nature of the data and could potentially result in misleading statistical inference. To investigate this possibility, we compare Bayesian parameter estimates obtained from a likelihood for complete binary networks with those obtained from likelihoods that are derived from the FRN scheme, and therefore accommodate the ranked and censored nature of the data. We show analytically and via simulation that the binary likelihood can provide misleading inference, particularly for certain model parameters that relate network ties to characteristics of individuals and pairs of individuals. We also compare these different likelihoods in a data analysis of several adolescent social networks. For some of these networks, the parameter estimates from the binary and FRN likelihoods lead to different conclusions, indicating the importance of analyzing FRN data with a method that accounts for the FRN survey design.

Thank you for the support in getting Network Science up and running. We are deeply appreciative of the work our associate editors, authors, and reviewers have put into realizing this vision of an interdisciplinary journal for network science. And of course, the journal would not be possible without the hard work of the editors of Network Science, who act as action editors for the submitted articles.

This is the beginning of Network Science. The journal has been created because network science is exploding. As is typical for a field in formation, the discussions about its scope, contents, and foundations are intense. On these first few pages of the first issue of our new journal, we would like to share our own vision of the emerging science of networks.

We use data on a real, large-scale social network of 27 million individuals interacting daily, together with the day-by-day adoption of a new mobile service product, to inform, build, and analyze data-driven simulations of the effectiveness of seeding (network targeting) strategies under different social conditions. Three main results emerge from our simulations. First, failure to consider homophily creates significant overestimation of the effectiveness of seeding strategies, casting doubt on conclusions drawn by simulation studies that do not model homophily. Second, seeding is constrained by the small fraction of potential influencers that exist in the network. We find that seeding more than 0.2% of the population is wasteful because the gain from their adoption is lower than the gain from their natural adoption (without seeding). Third, seeding is more effective in the presence of greater social influence. Stronger peer influence creates a greater than additive effect when combined with seeding. Our findings call into question some conventional wisdom about these strategies and suggest that their overall effectiveness may be overestimated.

In empirical studies of friendship networks, participants are typically asked, in interviews or questionnaires, to identify some or all of their close friends, resulting in a directed network in which friendships can, and often do, run in only one direction between a pair of individuals. Here we analyze a large collection of such networks representing friendships among students at US high and junior-high schools and show that the pattern of unreciprocated friendships is far from random. In every network, without exception, we find that there exists a ranking of participants, from low to high, such that almost all unreciprocated friendships consist of a lower ranked individual claiming friendship with a higher ranked one. We present a maximum-likelihood method for deducing such rankings from observed network data and conjecture that the rankings produced reflect a measure of social status. We note in particular that reciprocated and unreciprocated friendships obey different statistics, suggesting different formation processes, and that rankings are correlated with other characteristics of the participants that are traditionally associated with status, such as age and overall popularity as measured by total number of friends.

A measure of relative importance of network effects in the stochastic actor-oriented model (SAOM) is proposed. The SAOM is a parametric model for statistical inference in longitudinal social networks. The complexity of the model makes the interpretation of inferred results difficult. So far, the focus is on significance tests while the relative importance of effects is usually ignored. Indeed, there is no established measure to determine the relative importance of an effect in a SAOM. We introduce such a measure based on the influence effects have on decisions of individual actors in the network. We demonstrate its utility on empirical data by analyzing an evolving friendship network of university freshmen.

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.

Homeless men are frequently unsheltered and isolated, disconnected from supportive organizations and individuals. However, little research has investigated these men's social networks. We investigate the structure and composition of homeless men's social networks, vis-a-vis short- and long-term homelessness with a sample of men drawn randomly from meal lines on Skid Row in Los Angeles. Men continuously homeless for the past six months display networks composed of riskier members when compared to men intermittently homeless during that time. Men who report chronic, long-term homelessness display greater social network fragmentation when compared to non-chronically homeless men. While intermittent homelessness affects network composition in ways that may be addressable with existing interventions, chronic homelessness fragments networks, which may be more difficult to address with those interventions. These findings have implications for access to social support from network members which, in turn, impacts the resources homeless men require from other sources such as the government or non-governmental organizations.

Self-identification with peer crowds (jocks, popular kids, druggies, etc.) has an important influence on adolescent substance use behavior. However, little is known about the impact of the shared nature of crowd identification on different stages of adolescent drinking behavior, or the way crowd identification interacts with participation in school-sponsored sports activities. This study examines drinking influences from (1) peers with shared crowd identities, and (2) peers who jointly participate in organized sports at their school (activity members). This study introduces a new network analytic approach that can disentangle the effects of crowd identification and sports participation on individual behavior. Using survey data from adolescents in five high schools in a predominantly Hispanic/Latino district (N = 1,707), this paper examines the association between social influences and each stage of drinking behavior (intention to drink, lifetime, past-month, and binge drinking) by conducting an ordinal regression analysis. The results show that both shared identities and joint participation were associated with all stages of drinking, controlling for friends' influence. Additionally, shared identification overlapped with joint participation was associated with more frequent drinking. Related policy implications are discussed.

We study the diffusion of an idea, a product, a disease, a cultural fad, or a technology among agents in a social network that exhibits segregation or homophily (the tendency of agents to associate with others similar to themselves). Individuals are distinguished by their types—e.g., race, gender, age, wealth, religion, profession—which, together with biased interaction patterns, induce heterogeneous rates of adoption or infection. We identify the conditions under which a behavior or disease diffuses and becomes persistent in the population. These conditions relate to the level of homophily in a society and the underlying proclivities of various types for adoption or infection. In particular, we show that homophily can facilitate diffusion from a small initial seed of adopters.

This paper analyzes the relationship between unexplained racial/ethnic wage differentials on the one hand and social network segregation, as measured by inbreeding homophily, on the other. Our analysis is based on both the US and Estonian surveys, supplemented with the Estonian telephone communication data. In the case of Estonia we consider the regional variation in economic performance of the Russian minority, and in the US case we consider the regional variation in black--white differentials. Our analysis finds a strong relationship between the size of the wage differential and network segregation: Regions with more segregated social networks exhibit larger unexplained wage gaps.

We assess the potential of network motif profiles to characterize ego-networks in much the same way that a bag-of-words strategy allows text documents to be compared in a vector space framework. This is potentially valuable as a generic strategy for comparing nodes in a network in terms of the network structure in which they are embedded. In this paper, we consider the computational challenges and model selection decisions involved in network motif profiling. We also present three case studies concerning the analysis of Wikipedia edit networks, YouTube spam campaigns, and peer-to-peer lending in the Prosper marketplace.

The human connectome has been widely studied over the past decade. A principal finding is that it can be decomposed into communities of densely interconnected brain regions. Past studies have often used single-scale modularity measures in order to infer the connectome's community structure, possibly overlooking interesting structure at other organizational scales. In this report, we used the partition stability framework, which defines communities in terms of a Markov process (random walk), to infer the connectome's multi-scale community structure. Comparing the community structure to observed resting-state functional connectivity revealed communities across a broad range of scales that were closely related to functional connectivity. This result suggests a mapping between communities in structural networks, models of influence-spreading and diffusion, and brain function. It further suggests that the spread of influence among brain regions may not be limited to a single characteristic scale.

This paper presents a variable neighborhood search (VNS) algorithm that is specially designed for the blockmodeling of two-mode binary network matrices in accordance with structural equivalence. Computational results for 768 synthetic test networks revealed that the VNS heuristic outperformed a relocation heuristic (RH) and a tabu search (TS) method for the same problem. Next, the three heuristics were applied to two-mode network data pertaining to the votes of member countries on resolutions in the United Nations General Assembly. A comparative analysis revealed that the VNS heuristic often provided slightly better criterion function values than RH and TS, and that these small differences in criterion function values could sometimes be associated with substantial differences in the actual partitions obtained. Overall, the results suggest that the VNS heuristic is a promising approach for blockmodeling of two-mode binary networks. Recommendations for extensions to stochastic blockmodeling applications are provided.

The study of covert networks is plagued by the fact that individuals conceal their attributes and associations. To address this problem, we develop a technology for eliciting this information from qualitative subject-matter experts to inform statistical social network analysis. We show how the information from the subjective probability distributions can be used as input to Bayesian hierarchical models for network data. In the spirit of “proof of concept,” the results of a test of the technology are reported. Our findings show that human subjects can use the elicitation tool effectively, supplying attribute and edge information to update a network indicative of a covert one.

The gravity model, long the empirical workhorse for modeling international trade, ignores network dependencies in bilateral trade data, instead assuming that dyadic trade is independent, conditional on a hierarchy of covariates over country, time, and dyad. We argue that there are theoretical as well as empirical reasons to expect network dependencies in international trade. Consequently, standard gravity models are empirically inadequate. We combine a gravity model specification with “latent space” networks to develop a dynamic mixture model for real-valued directed graphs. The model simultaneously incorporates network dependencies in both trade incidence and trade volumes. We estimate this model using bilateral trade data from 1990 to 2008. The model substantially outperforms standard accounts in terms of both in- and out-of-sample predictive heuristics. We illustrate the model's usefulness by tracking trading propensities between the USA and China.

Degree distribution is a fundamental property of networks. While mean degree provides a standard measure of scale, there are several commonly used shape measures. Widespread use of a single shape measure would enable comparisons between networks and facilitate investigations about the relationship between degree distribution properties and other network features. This paper describes five candidate measures of heterogeneity and recommends the Gini coefficient. It has theoretical advantages over many of the previously proposed measures, is meaningful for the broad range of distribution shapes seen in different types of networks, and has several accessible interpretations. While this paper focuses on degree, the distribution of other node-based network properties could also be described with Gini coefficients.

We discuss our outreach efforts to introduce school students to network science and explain why researchers who study networks should be involved in such outreach activities. We provide overviews of modules that we have designed for these efforts, comment on our successes and failures, and illustrate the potentially enormous impact of such outreach efforts.

To find out, we measure co-voting similarity networks in the US Senate and trace individual careers over time. Standard network visualization tools fail on dense highly clustered networks, so we used two aggregation strategies to clarify positional mobility over time. First, clusters of Senators who often vote the same way capture coalitions, and allow us to measure polarization quantitatively through modularity (Newman, 2006; Waugh et al., 2009; Poole, 2012). Second, we use role-based blockmodels (White et al., 1976) to identify role positions, identifying sets of Senators with highly similar tie patterns. Our partitioning threshold for roles is stringent, generating many roles occupied by single Senators. This combination allows us to identify movement between positions over time (specifically, we used the Kernighan–Lin improvement of a Louvain method greedy partitioning algorithm for modularity [Blondel et al., 2008], and CONCOR with an internal similarity threshold for roles; see Supplementary materials for details).