Social network data are prone to errors regardless their source. This paper focuses on missing data due to actor non-response in valued networks. If actors refuse to provide information, all values for outgoing ties are missing. Partially observed incoming ties to non-respondents and all other patterns for ties between members of the network can be used to impute missing outgoing ties. Many centrality measures are used to determine the most prominent actors inside the network. Using treatments for actor non-response enables us to estimate better the centrality scores of all actors regarding their popularity or prominence. Simulations using initial known blockmodel structures based on three most frequently occurring macro-network structures: cohesive subgroups, core-periphery models, and hierarchical structures were used to evaluate the relative merits of the treatments for non-response. The results indicate that the amount of non-respondents, the type of underlying macro-structure, and the employed treatment have an impact on centrality scores. Regardless of the underlying network structure, the median of the 3-nearest neighbors based on incoming ties performs the best. The adequacy (or not) of the other non-response treatments is contingent on the network macro-structure.

Where do new markets come from? I construct a network model in which national markets are nodes and flows of recorded music between them are links and conduct a longitudinal analysis of the global pattern of trade in the period 1976–2010. I hypothesize that new export markets are developed through a process of transitive closure in the network of international trade. When two countries' markets experience the same social influences, it brings them close enough together for new homophilous ties to be formed. The implication is that consumption of foreign products helps, not hurts, home-market producers develop overseas markets, but only in those countries that have a history of consuming the same foreign products that were consumed in the home market. Selling in a market changes what is valued in that market, and new market formation is a consequence of having social influences in common.

Network centrality has been addressed for more than 30 years; however, few studies provided statistical tests for verifying this network characteristic. By applying the idea of focus test in spatial analysis, we propose a statistical method to test the centrality of a network. We consider not only the degree of node, but also give weights on other nodes with different lengths of the shortest paths, which are called “distances” in networks. According to the density of distance based on the hidden variable model and the property of the multinomial distribution, a test statistic called “focus centrality” is provided to evaluate a network centrality. Besides the theoretical construction, we verify that the proposed method is feasible and effective in the simulation studies. Further, two empirical network data are studied as demonstrations.

R-MAT (for Recursive MATrix) is a simple, widely used model for generating graphs with a power law degree distribution, a small diameter, and communitys structure. It is particularly attractive for generating very large graphs because edges can be generated independently by an arbitrary number of processors. However, current R-MAT generators need time logarithmic in the number of nodes for generating an edge— constant time for generating one bit at a time for node IDs of the connected nodes. We achieve constant time per edge by precomputing pieces of node IDs of logarithmic length. Using an alias table data structure, these pieces can then be sampled in constant time. This simple technique leads to practical improvements by an order of magnitude. This further pushes the limits of attainable graph size and makes generation overhead negligible in most situations.

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.

Models of network evolution are based on the implicit assumption that network growth is continuous, uniform, and steady. Using the data collected from a large online-blogging platform, we show that the addition and removal of network ties by users do not occur sporadically at isolated nodes spread all over the network, as assumed by the vast majority of stochastic network models, but rather occur in brief bursts of intense local activity.

These bursts of network growth and attrition (addition and removal of network ties) are highly localized around focal nodes. Such network changes coincide with nearly instantaneous densification of the ties between the affected nodes, resulting in an increase of local clustering. Furthermore, we find that these network changes are tightly coupled to the dynamics of individual attributes, particularly the increase in homology between neighboring nodes (homophily) within the scope of the burst. Coincidence of the localized network change with the increase in homophily suggests a strong coupling between the selection and influence processes that lead to simultaneous elevation of assortativity and clustering.

Shared memberships, social statuses, beliefs, and places can facilitate the formation of social ties. Two-mode projections provide a method for transforming two-mode data on individuals’ memberships in such groups into a one-mode network of their possible social ties. In this paper, I explore the opposite process: how social ties can facilitate the formation of groups, and how a two-mode network can be generated from a one-mode network. Drawing on theories of team formation, club joining, and organization recruitment, I propose three models that describe how such groups might emerge from the relationships in a social network. I show that these models can be used to generate two-mode networks that have characteristics commonly observed in empirical two-mode social networks and that they encode features of the one-mode networks from which they were generated. I conclude by discussing these models’ limitations and future directions for theory and methods concerning group formation.

Collaboration networks provide a method for examining the highly heterogeneous structure of collaborative communities. However, we still have limited theoretical understanding of how individual heterogeneity relates to network heterogeneity. The model presented here provides a framework linking an individual's skill set to her position in the collaboration network, and the distribution of skills in the population to the structure of the collaboration network as a whole. This model suggests that there is a non-trivial relationship between skills and network position: individuals with a useful combination of skills will have a disproportionate number of links in the network. Indeed, in some cases, an individual's degree is non-monotonic in the number of skills she has—an individual with very few skills may outperform an individual with many. Special cases of the model suggest that the degree distribution of the network will be skewed, even when the distribution of skills is uniform in the population. The degree distribution becomes more skewed as problems become more difficult, leading to a community dominated by a few high-degree superstars. This has striking implications for labor market outcomes in industries where production is largely the result of collaborative effort.

Identification of influential nodes is an important step in understanding and controlling the dynamics of information, traffic, and spreading processes in networks. As a result, a number of centrality measures have been proposed and used across different application domains. At the heart of many of these measures lies an assumption describing the manner in which traffic (of information, social actors, particles, etc.) flows through the network. For example, some measures only count shortest paths while others consider random walks. This paper considers a spreading process in which a resource necessary for transit is partially consumed along the way while being refilled at special nodes on the network. Examples include fuel consumption of vehicles together with refueling stations, information loss during dissemination with error-correcting nodes, and consumption of ammunition of military troops while moving. We propose generalizations of the well-known measures of betweenness, random-walk betweenness, and Katz centralities to take such a spreading process with consumable resources into account. In order to validate the results, experiments on real-world networks are carried out by developing simulations based on well-known models such as Susceptible-Infected-Recovered and congestion with respect to particle hopping from vehicular flow theory. The simulation-based models are shown to be highly correlated with the proposed centrality measures.

Reproducibility: Our code and experiments are available at https://github.com/hmwesigwa/soc_centrality

Random multigraphs with fixed degrees are obtained by the configuration model or by so called random stub matching. New combinatorial results are given for the global probability distribution of edge multiplicities and its marginal local distributions of loops and edges. The number of multigraphs on triads is determined for arbitrary degrees, and aggregated triads are shown to be useful for analyzing regular and almost regular multigraphs. Relationships between entropy and complexity are given and numerically illustrated for multigraphs with different number of vertices and specified average and variance for the degrees.

Numerous works have been proposed to generate random graphs preserving the same properties as real-life large-scale networks. However, many real networks are better represented by hypergraphs. Few models for generating random hypergraphs exist, and also, just a few models allow to both preserve a power-law degree distribution and a high modularity indicating the presence of communities. We present a dynamic preferential attachment hypergraph model which features partition into communities. We prove that its degree distribution follows a power-law, and we give theoretical lower bounds for its modularity. We compare its characteristics with a real-life co-authorship network and show that our model achieves good performances. We believe that our hypergraph model will be an interesting tool that may be used in many research domains in order to reflect better real-life phenomena.

Dynamic Network Actor Models (DyNAMs) assume that an observed sequence of relational events is the outcome of an actor-oriented decision process consisting of two decision levels. The first level represents the time until an actor initiates the next relational event, modeled by an exponential distribution with an actor-specific activity rate. The second level describes the choice of the receiver of the event, modeled by a conditional multinomial logit model. The DyNAM assumes that the parameters are constant over the actors and the context. This homogeneity assumption, albeit statistically and computationally convenient, is difficult to justify, e.g., in the presence of unobserved differences between actors or contexts. In this paper, we extend DyNAMs by including random-effects parameters that vary across actors or contexts and allow controlling for unknown sources of heterogeneity. We illustrate the model by analyzing relational events among the users of an online community of aspiring and professional digital and graphic designers.

There is empirical evidence suggesting that a person's family, friends, or social ties influence who a person votes for. Sokhey & McClurg (2012) find that as political disagreement in a person's social network increases, then a person is less likely to vote correctly. We develop a model where voters have different favorite policies and wish to vote correctly for the candidate whose favorite policy is closest to their own. Voters have beliefs about each candidate's favorite policy which may or may not be correct. Voters update their beliefs about political candidates based on who their conservative and liberal social ties are supporting. We find that if everyone's social network consists only of those most like themselves, then the conditions needed for correct voting to be stable are fairly weak; thus political agreement in one's social network facilitates correct voting. We also give conditions under which correct voting is stable for networks exhibiting homophily and for networks exhibiting random social interactions.

Is it always beneficial to create a new relationship (have a new follower/friend) in a social network? This question can be formally stated as a property of the centrality measure that defines the importance of the actors of the network. Score monotonicity means that adding an arc increases the centrality score of the target of the arc; rank monotonicity means that adding an arc improves the importance of the target of the arc relatively to the remaining nodes. It is known that most centralities are both score and rank monotone on directed, strongly connected graphs. In this paper, we study the problem of score and rank monotonicity for classical centrality measures in the case of undirected networks: in this case, we require that score, or relative importance, improves at both endpoints of the new edge. We show that, surprisingly, the situation in the undirected case is very different, and in particular that closeness, harmonic centrality, betweenness, eigenvector centrality, Seeley’s index, Katz’s index, and PageRank are not rank monotone; betweenness and PageRank are not even score monotone. In other words, while it is always a good thing to get a new follower, it is not always beneficial to get a new friend.

The order of the authors in the published article is incorrect. The authors should appear as follows:

J. Schneider, B. Cornwell, A. Jonas, R. Behler, N. Lancki, B. Skaathun, L. E. Young, E. Morgan, S. Michaels, R. Duvoisin, A. S. Khanna, S. Friedman, P. Schumm, E. Laumann, for the uConnect Study Team

The authors regret the error.

In relational event networks, endogenous statistics are used to summarize the past activity between actors. Typically, it is assumed that past events have equal weight on the social interaction rate in the (near) future regardless of the time that has transpired since observing them. Generally, it is unrealistic to assume that recently past events affect the current event rate to an equal degree as long-past events. Alternatively one may consider using a prespecified decay function with a prespecified rate of decay. A problem then is that the chosen decay function could be misspecified yielding biased results and incorrect conclusions. In this paper, we introduce three parametric weight decay functions (exponential, linear, and one-step) that can be embedded in a relational event model. A statistical method is presented to decide which memory decay function and memory parameter best fit the observed sequence of events. We present simulation studies that show the presence of bias in the estimates of effects of the statistics whenever the decay, as well as the memory parameter, are not properly estimated, and the ability to test different memory models against each other using the Bayes factor. Finally, we apply the methodology to two empirical case studies.

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.

We study the incentives that agents have to invest in costly protection against cascading failures in networked systems. Applications include vaccination, computer security, and airport security. Agents are connected through a network and can fail either intrinsically or as a result of the failure of a subset of their neighbors. We characterize the equilibrium based on an agent's failure probability and derive conditions under which equilibrium strategies are monotone in degree (i.e. in how connected an agent is on the network). We show that different kinds of applications (e.g. vaccination, malware, airport/EU security) lead to very different equilibrium patterns of investments in protection, with important welfare and risk implications. Our equilibrium concept is flexible enough to allow for comparative statics in terms of network properties, and we show that it is also robust to the introduction of global externalities (e.g. price feedback, congestion).

Measures of bipartite network structure have recently gained attention from network scholars. However, there is currently no measure for identifying key players in two-mode networks. This article proposes measures for identifying key players in bipartite networks. It focuses on two measures: fragmentation and cohesion centrality. It extends the centrality measures to bipartite networks by considering (1) cohesion and fragmentation centrality within a one-mode projection, (2) cross-modal cohesion and fragmentation centrality, where a node in one mode is influential in the one-mode projection of the other mode, and (3) cohesion and fragmentation centrality across the entire bipartite structure. Empirical examples are provided for the Southern Women’s data and on the Ndrangheta mafia data.

In this paper, we study how the topology of the International Trade Network (ITN) changes in geographical space, and along time. We employ geographical distance between countries in the world to filter the links in the ITN, building a sequence of subnetworks, each one featuring trade links occurring at similar distance. We then test if the assortativity and clustering of ITN subnetworks changes as distance increases, and we find that this is indeed the case: distance strongly impacts, in a non-linear way, the topology of the ITN. We show that the ITN is disassortative at long distances, while it is assortative at short ones. Similarly, the main determinant of the overall high-ITN clustering level are triangular trade triples between geographically close countries. This means that trade partnership choices and trade patterns are highly differentiated over different distance ranges, even after controlling for the economic size and income per capita of trading partners, and it is persistent over time. This evidence has relevant implications for the non-linear evolution of globalization.