Measuring knowledge and experience in two mode temporal networks

Two mode social network data consisting of actors attending events is a common type of social network data. For these kinds of data it is also common to have additional information about the timing or sequence of the events. We call data of this type two-mode temporal data. We explore the idea that actors attending events gain information from the event in two ways. Firstly the event itself may provide information or training; secondly, as co-attendees interact, they may pass on skills or information they have gleaned from other events. We propose a method of measuring these gains and demonstrate its usefulness using the classic Southern Women Data and a covert network dataset.     

A model for the multiplex dynamics of two-mode and one-mode networks,with an application to employment preference,friendship, and advice

We propose a new stochastic actor-oriented model for the co-evolution of two-mode and one-mode networks. The model posits that activities of a set of actors, represented in the two-mode network, co-evolve with exchanges and interactions between the actors, as represented in the one-mode network. The model assumes that the actors, not the activities, have agency.     

Logit Models for Affiliation Networks

Once confined to networks in which dyads could be reasonably assumed to be independent, the statistical analysis of network data has blossomed in recent years. New modeling and estimation strategies have made it possible to propose and evaluate very complex structures of dependency between and among ties in social networks. These advances have focused exclusively on one-mode networks—that is, networks of direct ties between actors. We generalize these models to affiliation networks, networks in which actors are tied to each other only indirectly through belonging to some group or event. We formulate models that allow us to study the (log) odds of an actor's belonging to an event (or an event including an actor) as a function of properties of the two-mode network of actors' memberships in events. We also provide illustrative analysis of some classic data sets on affiliation networks.     

Partitioning large signed two-mode networks: Problems and prospects

While a substantial amount of attention within social network analysis (SNA) has been given to the study of one-mode networks, there is an increasing consideration of two-mode networks. Recent research on signed networks resulted in the relaxed structural balance (RSB) approach and its subsequent extension to signed two-mode networks involving social actors and social objects. We extend this approach to large signed two-mode networks, and address the methodological issues that arise. We develop tools to partition these types of networks and compare them with other approaches using a recently collected dataset of United Nations General Assembly roll call votes. Although our primary purpose is methodological, we take the first step towards bridging Heider's structural balance theory with recent theorizing in international relations on soft balancing of power processes.     

A comparative study of social network models: Network evolution models and nodal attribute models

This paper reviews, classifies and compares recent models for social networks that have mainly been published within the physics-oriented complex networks literature. The models fall into two categories: those in which the addition of new links is dependent on the (typically local) network structure (network evolution models, NEMs), and those in which links are generated based only on nodal attributes (nodal attribute models, NAMs). An exponential random graph model (ERGM) with structural dependencies is included for comparison. We fit models from each of these categories to two empirical acquaintance networks with respect to basic network properties. We compare higher order structures in the resulting networks with those in the data, with the aim of determining which models produce the most realistic network structure with respect to degree distributions, assortativity, clustering spectra, geodesic path distributions, and community structure (subgroups with dense internal connections). We find that the nodal attribute models successfully produce assortative networks and very clear community structure. However, they generate unrealistic clustering spectra and peaked degree distributions that do not match empirical data on large social networks. On the other hand, many of the network evolution models produce degree distributions and clustering spectra that agree more closely with data. They also generate assortative networks and community structure, although often not to the same extent as in the data. The ERGM model, which turned out to be near-degenerate in the parameter region best fitting our data, produces the weakest community structure.     

Network cohesion and social support

This article analyses the effects of personal network cohesion on different types of social support using two dimensions of cohesion: network closure (defined as a tightly knit set of actors around the ego) and cliquishness (defined as the extent to which an actor is connected with a number of cohesive sub-sets of alters). Data were obtained from a personal networks’ survey conducted in Catalonia (Spain), which was completed by 441 adults and gathered information about exchange of social support in networks made of 30 alters. A multilevel analysis disentangles the effects on support of these two structural dimensions at the network-level from compositional effects at the network and tie-level. The results show that network closure does not play a relevant role in support once confounders at the network and tie levels are controlled for. However, cliquishness has a significant association with labor-related support and housing support, net of statistical controls. Implications of these results in network research are discussed.     

A network centrality bias: Central individuals in workplace networks have more supportive coworkers

Combining the results of two empirical studies, we investigate the role of alters’ motivation in explaining change in ego’s network position over time. People high in communal motives, who are prone to supportive and altruistic behavior in their interactions with others as a way to gain social acceptance, prefer to establish ties with co-workers occupying central positions in organizational social networks. This effect results in a systematic network centrality bias: The personal network of central individuals (individuals with many incoming ties from colleagues) is more likely to contain more supportive and altruistic people than the personal network of individuals who are less central (individuals with fewer incoming ties). This result opens the door to the possibility that the effects of centrality so frequently documented in empirical studies may be due, at least in part, to characteristics of the alters in an ego’s personal community, rather than to egos themselves. Our findings invite further empirical research on how alters’ motives affect the returns that people can reap from their personal networks in organizations.     

Analysing networks of networks

We consider data with multiple observations or reports on a network in the case when these networks themselves are connected through some form of network ties. We could take the example of a cognitive social structure where there is another type of tie connecting the actors that provide the reports; or the study of interpersonal spillover effects from one cultural domain to another facilitated by the social ties. Another example is when the individual semantic structures are represented as semantic networks of a group of actors and connected through these actors’ social ties to constitute knowledge of a social group. How to jointly represent the two types of networks is not trivial as the layers and not the nodes of the layers of the reported networks are coupled through a network on the reports. We propose to transform the different multiple networks using line graphs, where actors are affiliated with ties represented as nodes, and represent the totality of the different types of ties as a multilevel network. This affords studying the associations between the social network and the reports as well as the alignment of the reports to a criterion graph. We illustrate how the procedure can be applied to studying the social construction of knowledge in local flood management groups. Here we use multilevel exponential random graph models but the representation also lends itself to stochastic actor-oriented models, multilevel blockmodels, and any model capable of handling multilevel networks.     

Social Networks and Social Settings: Developing a Coevolutionary View

One way to think about social context is as a sample of alters. To understand individual action, therefore, it matters greatly where these alters may be coming from, and how they are connected. According to one vision, connections among alters induce local dependencies—emergent rules of social interaction that generate endogenously the observed network structure of social settings. Social selection is the decision of interest in this perspective. According to a second vision, social settings are collections of social foci—physical or symbolic locales where actors meet. Because alters are more likely to be drawn from focused sets, shared social foci are frequently considered as the main generators of network ties, and hence of setting structure. Affiliation to social foci is the decision of central interest in this second view. In this paper we show how stochastic actor–oriented models (SAOMs) originally derived for studying the dynamics of multiple networks may be adopted to represent and examine these interconnected systems of decisions (selection and affiliation) within a unified analytical framework. We illustrate the empirical value of the model in the context of a longitudinal sample of adolescent participating in the Glasgow Teenage Friends and Lifestyle Study. Social selection decisions are examined in the context of networks of friendship relations. The analysis treats musical genres as the main social foci of interest.     

The Emergence and Stability of Groups in Social Networks

An important puzzle in social network research is to explain how macro-level structures emerge from micro-level network processes. Explaining the emergence and stability of structural groups in social networks is particularly difficult for two reasons. First, because groups are characterized both by high connectedness within (group cohesion) and lack of connectedness between them (group boundaries). Second, because a large number of theoretical micro-level network processes contribute to their emergence. We argue that traditional social network theories that are concerned with the evolution of positive relations (forces of attraction) are not sufficient to explain the emergence of groups because they lack mechanisms explaining the emergence of group boundaries. Models that additionally account for the evolution of negative ties (forces of repulsion) may be better suited to explain the emergence and stability of groups. We build a theoretical model and illustrate its usefulness by fitting stochastic actor-oriented models (SAOMs) to empirical data of co-evolving networks of friendship and dislike among 479 secondary-school students. The SAOMs include a number of newly developed effects expressing the co-evolution between positive and negative ties. We then simulate networks from the estimated models to explore the micro-macro link. We find that a model that considers forces of attraction and repulsion simultaneously is better at explaining groups in social networks. In the long run, however, the empirically informed simulations generate networks that are too stylized to be realistic, raising further questions about model degeneracy and time heterogeneity of group processes.     

Conditionally exponential random models for individual properties and network structures: Method and application

Exponential random models have been widely adopted as a general probabilistic framework for complex networks and recently extended to embrace broader statistical settings such as dynamic networks, valued networks or two-mode networks. Our aim is to provide a further step into the generalization of this class of models by considering sample spaces which involve both families of networks and nodal properties verifying combinatorial constraints. We propose a class of probabilistic models for the joint distribution of nodal properties (demographic and behavioral characteristics) and network structures (friendship and professional partnership). It results in a general and flexible modeling framework to account for homophily in social structures. We present a Bayesian estimation method based on the full characterization of their sample spaces by systems of linear constraints. This provides an exact simulation scheme to sample from the likelihood, based on linear programming techniques. After a detailed analysis of the proposed statistical methodology, we illustrate our approach with an empirical analysis of co-authorship of journal articles in the field of neuroscience between 2009 and 2013.     

Analyzing event stream dynamics in two-mode networks: An exploratory analysis of private communication in a question and answer community

Information about social networks can often be collected as event stream data. However, most methods in social network analysis are defined for static network snapshots or for panel data. We propose an actor oriented Markov process framework to analyze the structural dynamics in event streams. Estimated parameters are similar to what is known from exponential random graph models or stochastic actor oriented models as implemented in SIENA. We apply the methodology on a question and answer web community and show how the relevance of different kinds of one- and two-mode network structures can be tested using a new software.     

Structural holes and bridging in two-mode networks

Social networks are often structured in such a way that there are gaps, or “structural holes,” between regions. Some actors are in the position to bridge or span these gaps, giving rise to individual advantages relating to brokerage, gatekeeping, access to non-redundant contacts, and control over network flows. The most widely used measures of a given actor’s bridging potential gauge the extent to which that actor is directly connected to others who are otherwise not well connected to each other. Unfortunately, the measures that have been developed to identify structural holes cannot be adapted directly to two-mode networks, like individual-to-organization networks. In two-mode networks, direct contacts cannot be directly connected to each other by definition, making the calculation of redundancy, effective size, and constraint impossible with conventional one-mode methods. We therefore describe a new framework for the measurement of bridging in two-mode networks that hinges on the mathematical concept of the intersection of sets. An actor in a given node class (“ego”) has bridging potential to the extent that s/he is connected to actors in the opposite node class that have unique profiles of connections to actors in ego’s own node class. We review the relevant literature pertaining to structural holes in two-mode networks, and we compare our primary bridging measure (effective size) to measures of bridging that result when using one-mode projections of two-mode data. We demonstrate the results of applying our approach to empirical data on the organizational affiliations of elites in a large U.S. city.     

A latent space model for cognitive social structures data

This paper introduces a novel approach for modeling a set of directed, binary networks in the context of cognitive social structures (CSSs) data. We adopt a relativist approach in which no assumption is made about the existence of an underlying true network. More specifically, we rely on a generalized linear model that incorporates a bilinear structure to model transitivity effects within networks, and a hierarchical specification on the bilinear effects to borrow information across networks. This is a spatial model, in which the perception of each individual about the strength of the relationships can be explained by the perceived position of the actors (themselves and others) on a latent social space. A key goal of the model is to provide a mechanism to formally assess the agreement between each actors’ perception of their own social roles with that of the rest of the group. Our experiments with both real and simulated data show that the capabilities of our model are comparable with or, even superior to, other models for CSS data reported in the literature.     

Universal evolution patterns of degree assortativity in social networks

Degree assortativity characterizes the propensity for large-degree nodes to connect to other large-degree nodes and low-degree to low-degree. It is important to describe the forces forming the network and to predict the behavior of dynamic systems on the network. To understand the evolutionary dynamics of degree assortativity, we collect a variety of empirical temporal social networks, and find that there is a universal pattern that the degree assortativity increases at the beginning of evolution and then decreases to a long-lasting stable level. We develop a bidirectional selection model to re-construct the evolution dynamic. In our model, we assume each individual has a social status that—in analogy to Pareto’s wealth distribution —follows a power-law distribution. We assume the social status determines the probability of an interaction between two actors. By varying the ratio of link establishment from within the same status level to across different status levels, the simulated network can be tuned to be assortative or disassortative. This suggests that the rise-and-fall pattern of degree assortativity is a consequence of the different network-forming forces active at different mixing of status. Our simulations indicate that Pareto social status distribution in the population may drive the social evolution in a way of self-optimization to promote the social interaction among individuals and the status gap plays an important role for the assortativity of the social network.     

Dynamic exchange networks

Considering the theoretical and empirical untenability of static exchange networks, researchers have asked how exchange outcomes change when links are added or deleted. The present paper assesses the validity of seemingly sensible propositions concerning the effects of adding and deleting a link on (i) the payoffs of the actors in the link, (ii) the payoffs of actors in neighboring links and (iii) the variance of payoffs in the exchange network. The propositions were examined by applying expected value theory (EVT) to all 13,597 networks up to size 8. All propositions were falsified. Some falsifications of propositions could be attributed to EVTs prediction that actors use sub-optimal exchange relations. Since other well-known theories of exchange, like power-dependence theory and network exchange theory, also predict that actors use sub-optimal relations, these results are robust to selection of the theory of exchange.     

Exponential random graph models for little networks

Statistical models for social networks have enabled researchers to study complex social phenomena that give rise to observed patterns of relationships among social actors and to gain a rich understanding of the interdependent nature of social ties and actors. Much of this research has focused on social networks within medium to large social groups. To date, these advances in statistical models for social networks, and in particular, of Exponential-Family Random Graph Models (ERGMS), have rarely been applied to the study of small networks, despite small network data in teams, families, and personal networks being common in many fields. In this paper, we revisit the estimation of ERGMs for small networks and propose using exhaustive enumeration when possible. We developed an R package that implements the estimation of pooled ERGMs for small networks using Maximum Likelihood Estimation (MLE), called “ergmito”. Based on the results of an extensive simulation study to assess the properties of the MLE estimator, we conclude that there are several benefits of direct MLE estimation compared to approximate methods and that this creates opportunities for valuable methodological innovations that can be applied to modeling social networks with ERGMs.     

The structure of online social networks mirrors those in the offline world

We use data on frequencies of bi-directional posts to define edges (or relationships) in two Facebook datasets and a Twitter dataset and use these to create ego-centric social networks. We explore the internal structure of these networks to determine whether they have the same kind of layered structure as has been found in offline face-to-face networks (which have a distinctively scaled structure with successively inclusive layers at 5, 15, 50 and 150 alters). The two Facebook datasets are best described by a four-layer structure and the Twitter dataset by a five-layer structure. The absolute sizes of these layers and the mean frequencies of contact with alters within each layer match very closely the observed values from offline networks. In addition, all three datasets reveal the existence of an innermost network layer at ∼1.5 alters. Our analyses thus confirm the existence of the layered structure of ego-centric social networks with a very much larger sample (in total, >185,000 egos) than those previously used to describe them, as well as identifying the existence of an additional network layer whose existence was only hypothesised in offline social networks. In addition, our analyses indicate that online communities have very similar structural characteristics to offline face-to-face networks.     

Triadic closure in two-mode networks: Redefining the global and local clustering coefficients

As the vast majority of network measures are defined for one-mode networks, two-mode networks often have to be projected onto one-mode networks to be analyzed. A number of issues arise in this transformation process, especially when analyzing ties among nodes’ contacts. For example, the values attained by the global and local clustering coefficients on projected random two-mode networks deviate from the expected values in corresponding classical one-mode networks. Moreover, both the local clustering coefficient and constraint (structural holes) are inversely associated to nodes’ two-mode degree. To overcome these issues, this paper proposes redefinitions of the clustering coefficients for two-mode networks.     

The duality of firms and directors in board interlock networks: A relational event modeling approach

The long tradition of scholarly work on corporate interlocks has left us with competing theoretical frameworks on the causes of interlock networks. Board interlocks are studied either as means to overcome the resource dependence of corporations or as a group cohesion mechanism of business elites. This contrast is due to an empirical divide of the literature where either the firms or the individuals are considered as decision-making bodies. In systematically ignoring the agency of the other group of actors, these literatures suffer from both theoretical and empirical biases in understanding the drivers of new interlocks. In this paper, we employ a relational event modeling technique that allows us to overcome this problem. The analysis of board appointments in Denmark demonstrates how in fact both personal and corporate considerations simultaneously drive the evolution of the corporate networks. The study of the duality of actors is essential for understanding the causes and consequences of corporate networks across time and space.