The redundancy of a system denotes the amount of duplicate components or mechanisms in it. For a network, especially one in which mass or information is being transferred from an origin to a destination, redundancy is related to the robustness of the system. Existing network measures of redundancy rely on local connectivity (e.g. clustering coefficients) or the existence of multiple paths. As in many systems there are functional dependencies between components and paths, a measure that not only characterizes the topology of a network, but also takes into account these functional dependencies, becomes most desirable.

We propose a network redundancy measure in a prototypical model that contains functionally dependent directed paths: a Boolean model of a signal transduction network. The functional dependencies are made explicit by using an expanded network and the concept of elementary signaling modes (ESMs). We define the redundancy of a Boolean signal transduction network as the maximum number of node-independent ESMs and develop a methodology for identifying all maximal node-independent ESM combinations. We apply our measure to a number of signal transduction network models and show that it successfully distills known properties of the systems and offers new functional insights. The concept can be easily extended to similar related forms, e.g. edge-independent ESMs.

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.

This paper provides an examination of inter-organizational collaboration in the UK research system. Data are collected on organizational collaboration on projects funded by four key UK research councils: Arts and Humanities Research Council, Economic and Social Research Council, Engineering and Physical Sciences Research Council, and Biotechnology and Biological Sciences Research Council. The organizational partnerships include both academic and nonacademic institutions. A collaboration network is created for each research council, and an exponential random graph model is applied to inform on the mechanisms underpinning collaborative tie formation on research council-funded projects. We find that in the sciences, collaborative patterns are much more hierarchical and concentrated in a small handful of actors compared to the social sciences and humanities projects. Institutions that are members of the elite Russell Group (a set of 24 high-ranking UK universities) are much more likely to be involved in collaborations across research councils.

The position people occupy in their social and professional networks is related to their social status and has strong effects on their access to social resources. While attainment of particular positions is driven by behavioral traits, many biological factors predispose individuals to certain behaviors and motivations. Prior work on exposure to fetal androgens (measured by second-to-fourth digit ratio, 2D:4D) shows that it correlates with behaviors and traits related to social status, which might make people more socially integrated. However, it also predicts certain anti-social behaviors and disorders associated with lower socialization. We explore whether 2D:4D correlates with network position later in life and find that individuals with low 2D:4D become more central in their social environment. Interestingly, low 2D:4D males are more likely to exhibit high betweenness centrality (they connect separated parts of the social structure), while low 2D:4D females are more likely to exhibit high in-degree centrality (more people name them as friends). These gender-specific differences are reinforced by transitivity (the likelihood that one's friends are also friends with one another): neighbors of low 2D:4D men tend not to know each other; the contrary is observed for low 2D:4D women. Our results suggest that biological predispositions influence the organization of human societies and that exposure to prenatal androgens influences different status seeking behaviors in men and women.

Respondent-driven sampling (RDS) is an increasingly popular chain-referral sampling method. Although it has proved effective at generating samples of hard to reach populations—meaning populations for which sampling frames are not available because they are hidden or socially stigmatized like sex workers or injecting drug users—quickly and cost-effectively, the ease of collecting the sample comes with a cost: bias or inefficiency in the estimates of population parameters (Gile & Handcock, 2010; Goel & Salganik, 2010). One way that RDS can produce inefficient estimates is if one or more of the recruitment chains gets stuck among members of a cohesive subpopulation, preventing the RDS sampling process from exploring other areas of the network. If that happens, members of the population subgroup recruit one another repeatedly, leading to an increase in sample size without increasing the diversity of the sample. This type of stickiness is particularly likely when hidden populations are stratified, and the stratified groups are organized into venues that provide opportunities to recruit other members of the same stratum. Female sex workers (FSW) in China, who are stratified into tiers of sex work that are correlated with marital status, age, and risk behaviors, are a prime example (Merli et al., 2014; Yamanis et al., 2013). Chinese FSW recruit clients from venues such as karaoke bars, massage parlors, or street corners. At larger venues, sex workers who participate in an RDS study might recruit other members of the same venue into the study at a higher rate than expected, leading to inefficient estimates. In short, the chain could get stuck in a venue.

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.

Writers for popular media frequently draw on insights known about social networks in developing their plotlines and character biographies (whether in books, television, movies, etc.). Perhaps most known to network analysts in this respect, Freeman (2000) presents a collection of network concepts represented in comic strips. These depictions often are consistent with the patterns network analysts observe in real-world empirical examples. For example, the long-running sitcom Friends exhibited strong homophily (McPherson et al., 2001) or assortative mixing on race and socioeconomic status among the main characters. Other times the violation of these typical patterns can serve to generate dramatic tension or a source of comedy. For example transitivity—or the tendency of one's friends to also become friends (Holland & Leinhardt, 1972)—is absent in the movie Hush where Jessica Lange's character plots to kill the daughter-in-law she does not like. P-O-X social balance (Heider, 1948) describes the tendency for friends to share common interests, which was violated to comedic effect in the Seinfeld episode where Jerry's character simply cannot accept his date's refusal to try a taste of the pie he finds delicious, bothering him for days and ultimately leading to his ending the relationship.

Measurement errors are omnipresent in network data. Most studies observe an erroneous network instead of the desired error-free network. It is well known that such errors can have a severe impact on network metrics, especially on centrality measures: a central node in the observed network might be less central in the underlying, error-free network. The robustness is a common concept to measure these effects. Studies have shown that the robustness primarily depends on the centrality measure, the type of error (e.g., missing edges or missing nodes), and the network topology (e.g., tree-like, core-periphery). Previous findings regarding the influence of network size on the robustness are, however, inconclusive. We present empirical evidence and analytical arguments indicating that there exist arbitrary large robust and non-robust networks and that the average degree is well suited to explain the robustness. We demonstrate that networks with a higher average degree are often more robust. For the degree centrality and Erdős–Rényi (ER) graphs, we present explicit formulas for the computation of the robustness, mainly based on the joint distribution of node degrees and degree changes which allow us to analyze the robustness for ER graphs with a constant average degree or increasing average degree.

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.

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.

The topic of anomaly detection in networks has attracted a lot of attention in recent years, especially with the rise of connected devices and social networks. Anomaly detection spans a wide range of applications, from detecting terrorist cells in counter-terrorism efforts to identifying unexpected mutations during ribonucleic acid transcription. Fittingly, numerous algorithmic techniques for anomaly detection have been introduced. However, to date, little work has been done to evaluate these algorithms from a statistical perspective. This work is aimed at addressing this gap in the literature by carrying out statistical evaluation of a suite of popular spectral methods for anomaly detection in networks. Our investigation on the statistical properties of these algorithms reveals several important and critical shortcomings that we make methodological improvements to address. Further, we carry out a performance evaluation of these algorithms using simulated networks and extend the methods from binary to count networks.

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.

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.