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.     

Modelling the evolution of a bipartite network—Peer referral in interlocking directorates

A central part of relational ties between social actors is constituted by shared affiliations and events. The action of joint participation reinforces personal ties between social actors as well as mutually shared values and norms that in turn perpetuate the patterns of social action that define groups. Therefore the study of bipartite networks is central to social science. Furthermore, the dynamics of these processes suggests that bipartite networks should not be considered static structures but rather be studied over time. In order to model the evolution of bipartite networks empirically we introduce a class of models and a Bayesian inference scheme that extends previous stochastic actor-oriented models for unimodal graphs. Contemporary research on interlocking directorates provides an area of research in which it seems reasonable to apply the model. Specifically, we address the question of how tie formation, i.e. director recruitment, contributes to the structural properties of the interlocking directorate network. For boards of directors on the Stockholm stock exchange we propose that a prolific mechanism in tie formation is that of peer referral. The results indicate that such a mechanism is present, generating multiple interlocks between boards.     

Being close: The quality of social relationships in a local organic cereal and bread network in Lower Austria

Experience of the drawbacks of a globalised and industrialised food system has generated interest in localised food systems. Local food networks are regarded as more sustainable food provision systems since they are assumed to have high levels of social embeddedness and relations of regard. This paper explores the social relations between food actors and how ‘local’ and ‘organic’ are expressed by detailing how actors describe qualities of their intra-network relationships, how they understand ‘local’ and how they are connected within the food system. A study from the province of Lower Austria in Austria, where organic cereals and bread are produced and marketed, serves to illuminate these issues. Actors agreed that geographical closeness contributed to the social closeness they experienced and that social relationships were a strong reason for being in the network. However, the meaning of ‘local’ was elastic depending on where inputs and consumers could be found. Furthermore, despite strong commitment to organic production methods and the local market, actors faced constraints that made them hybrids between organic and conventional, and between locally focused and globally dependent. Thus, the binary thinking along the local-global and organic-conventional divide does not hold. While it is important to not make a causal link between high quality of social relationships and local food networks, the case described here indicates the possibility of such a link.     

Influentials,novelty, and social contagion : The viral power of average friends,close communities,and old news

What is the effect of (1) popular individuals, and (2) community structures on the retransmission of socially contagious behavior? We examine a community of Twitter users over a five month period, operationalizing social contagion as ‘retweeting’, and social structure as the count of subgraphs (small patterns of ties and nodes) between users in the follower/following network.     

Popularity breeds contempt: The evolution of reputational dislike relations and friendships in high school

In this study, we examined the dynamics of the perception of “dislike” ties (reputational dislike) among adolescents within the contexts of friendship, perceived popularity, substance use, and Facebook use. Survey data were collected from a longitudinal sample of 238 adolescents from the 11th and 12th grades in one California high school. We estimated stochastic actor-based network dynamic models, using reports of reputational dislike, friendships, and perceived popularity, to identify factors associated with the maintenance and generation reputational dislike ties. The results showed that high-status adolescents and more frequent Facebook users tended to become perceived as or stay disliked by their peers over time. There was a tendency for friendships to promote the creation and maintenance of reputational disliking but not vice versa. Adolescents tended to perceive others as disliked when their friends also perceived them as disliked. There was no evidence that either cigarette smoking or drinking alcohol affected reputational dislike dynamics. This study highlights the important role that the hierarchical peer system, online peer context, and friendships play in driving information diffusion of negative peer relations among adolescents.     

Partitioning signed social networks

Structural balance theory has proven useful for delineating the blockmodel structure of signed social networks. Even so, most of the observed signed networks are not perfectly balanced. One possibility for this is that in examining the dynamics underlying the generation of signed social networks, insufficient attention has been given to other processes and features of signed networks. These include: actors who have positive ties to pairs of actors linked by a negative relation or who belong to two mutually hostile subgroups; some actors that are viewed positively across the network despite the presence of negative ties and subsets of actors with negative ties towards each other. We suggest that instead viewing these situations as violations of structural balance, they can be seen as belonging to other relevant processes we call mediation, differential popularity and internal subgroup hostility. Formalizing these ideas leads to the relaxed structural balance blockmodel as a proper generalization of structural balance blockmodels. Some formal properties concerning the relation between these two models are presented along with the properties of the fitting method proposed for the new blockmodel type. The new method is applied to four empirical data sets where improved fits with more nuanced interpretations are obtained.     

Research note: The consequences of different methods for handling missing network data in stochastic actor based models

Although stochastic actor-based models (e.g., as implemented in the SIENA software program) are growing in popularity as a technique for estimating longitudinal network data, a relatively understudied issue is the consequence of missing network data for longitudinal analysis. We explore this issue in our research note by utilizing data from four schools in an existing dataset (the AddHealth dataset) over three time points, assessing the substantive consequences of using four different strategies for addressing missing network data. The results indicate that whereas some measures in such models are estimated relatively robustly regardless of the strategy chosen for addressing missing network data, some of the substantive conclusions will differ based on the missing data strategy chosen. These results have important implications for this burgeoning applied research area, implying that researchers should more carefully consider how they address missing data when estimating such models.     

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.     

Collective action and network change

Network models of collective action commonly assume fixed social networks in which ties influence participation through social rewards. This implies that only certain ties are beneficial from the view of individual actors. Accordingly, in this study we allow that actors strategically revise their relations. Moreover, in our model actors also take into account possible network consequences in their participation choices. To handle the interrelatedness of networks and participation, we introduce new equilibrium concepts. Our equilibrium analysis suggests that structures that tend to segregate contributors from free riders are stable, but costless network change only promotes all-or-nothing participation and complete networks.     

Stochastic blockmodels: First steps

A stochastic model is proposed for social networks in which the actors in a network are partitioned into subgroups called blocks. The model provides a stochastic generalization of the blockmodel. Estimation techniques are developed for the special case of a single relation social network, with blocks specified a priori. An extension of the model allows for tendencies toward reciprocation of ties beyond those explained by the partition. The extended model provides a one degree-of-freedom test of the model. A numerical example from the social network literature is used to illustrate the methods.     

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.     

To make and keep friends: The role of health status in adolescent network tie formation and persistence

Health status may shape network structure through network dynamics (tie formation and persistence) and direction (sent and received ties), net of typical network processes. We apply Separable Temporal Exponential Random Graph Models (STERGMs) to National Longitudinal Study of Adolescent to Adult Health survey data (n = 1779) to differentiate how health status shapes network sent and received tie formation and persistence. Results indicate that networks are shaped by withdrawal of adolescents experiencing poor health, highlighting the importance of separating distinct and directed processes of friendship formation and persistence when considering how health relates to adolescent social life.     

Network public goods with asymmetric information about cooperation preferences and network degree

We propose a game theoretical model of one-shot network public goods formalizing the ‘closure argument’ that cooperation is more frequent in denser groups or networks. Equilibrium analyses show that (i) an ‘inefficiency problem’ exists: players all preferring mutual cooperation need not all cooperate; (ii) in dyads, groups and networks with degree independence, first order stochastic dominance shifts of the distribution of cooperation preferences or the degree distribution (weakly) increases cooperation, and (iii) the latter result does not hold for networks with degree dependence. Hence the closure argument always holds in networks satisfying degree independence but not in other networks.     

Actors and networks as objects

This paper explores the application of two contemporary computational methods to the development of sociological theory. Specifically, we combine the methods of object-orientation with discrete event simulation. This approach has several advantages for constructing and evaluating dynamic social theories.In object-oriented program design, objects combine and integrate the traditional concepts of data structures and algorithms, the building blocks of structured programming. Algorithms associated with objects are called methods or member functions. Constructing social actors as objects involves defining both their data attributes and the methods associated with these attributes. We also treat a social network as a computational object. It has data types of nodes and ties. As an object, the network must also have methods that add and delete nodes and ties. Once a network exists, we can create other data types and methods that describe and analyze the network. For example, networks have in-degree and out-degree vectors, and measures of hierarchy. In principle, we can create attributes of networks for all of the structural measures we use to describe networks.We use actor and network objects in a discrete event simulation of a process of formation of dominance structures, exploring several dynamic variations of the underlying theoretical model.     

Missing data in networks: exponential random graph (p1) models for networks with non-respondents

Survey studies of complete social networks often involve non-respondents, whereby certain people within the “boundary” of a network do not complete a sociometric questionnaire—either by their own choice or by the design of the study—yet are still nominated by other respondents as network partners. We develop exponential random graph (p¹) models for network data with non-respondents. We model respondents and non-respondents as two different types of nodes, distinguishing ties between respondents from ties that link respondents to non-respondents. Moreover, if we assume that the non-respondents are missing at random, we invoke homogeneity across certain network configurations to infer effects as applicable to the entire set of network actors. Using an example from a well-known network dataset, we show that treating a sizeable proportion of nodes as non-respondents may still result in estimates, and inferences about structural effects, consistent with those for the entire network.If, on the other hand, the principal research focus is on the respondent-only structure, with non-respondents clearly not missing at random, we incorporate the information about ties to non-respondents as exogenous. We illustrate this model with an example of a network within and between organizational departments. Because in this second class of models the number of non-respondents may be large, values of parameter estimates may not be directly comparable to those for models that exclude non-respondents. In the context of discussing recent technical developments in exponential random graph models, we present a heuristic method based on pseudo-likelihood estimation to infer whether certain structural effects may contribute substantially to the predictive capacity of a model, thereby enabling comparisons of important effects between models with differently sized node sets.     

The influence of friends on adolescents’ behavior problems at school: The role of ego,alter and dyadic characteristics

This paper deals with the influence of friends in class on adolescents’ problematic school behavior (i.e. inattention in class and not doing homework). We examine whether this influence is moderated by ego (i.e. the adolescent's indegree), alter (i.e. friends’ indegree) and dyadic characteristics (i.e. friendship reciprocity). Influence processes are analyzed with a stochastic actor-based model (SIENA), while controlling for friendship selection. Using a 4-wave panel dataset, we find that friends influence adolescents’ problematic school behavior. Adolescents with a higher indegree are less likely to be influenced. The influence of friends is not significantly moderated by friends’ indegree and friendship reciprocity.     

Critical phenomena in complex contagions

Why do some contagions “go viral” and others do not? Research on “small world” networks (Watts and Strogatz, 1998) shows how a very small number of long-range ties that bridge between clusters can allow contagions to spread almost as rapidly as on a random network of equal density. Recent research shows how long-range ties that accelerate the spread of information and disease can impede the spread of complex contagions—behaviors, beliefs and preferences that diffuse via contact with multiple adopters ( Centola and Macy, 2007). In confirming this result analytically and extending the analysis from small world to power law networks, we discovered that complex contagions require a critical mass of infected nodes that corresponds to a phase transition in the ability of the contagion to take advantage of the “shortcuts” created by long-range ties. We demonstrate how this critical mass is related to the dynamics of the contagion process and identify implications for modeling behaviors that spread via social influence, such as viral marketing and social movements.     

Equicentrality and network centralization: A micro–macro linkage

This paper investigates a linkage between micro- and macrostructures as an intrinsic property of social networks. In particular, it examines the linkage between equicentrality [Kang, S.M., 2007. A note on measures of similarity based on centrality. Social Networks 29, 137–142] as a conceptualization of a microstructural process (i.e., the likelihood of social actors to be connected with similarly central others) and network centralization as a macrostructural construct, and shows that they have a negative linear association. In other words, when actors are connected with similarly central alters (i.e., high equicentrality), the overall network centralization is low. Conversely, when highly central actors are connected with low-centrality actors (i.e., low equicentrality), the overall network centralization is high. The relationship between degree equicentrality and degree centralization is more significant in observed networks, especially those evolving over time, as compared to random networks. An application of this property is given by venture capital co-investment networks.     

Types of stable network structures based on exhaustive search

Based on the works of Doreian [Doreian, P., 2006. Actor network utilities and network evolution. Social Networks 28, 137–164] and Xie and Cui [Xie, F., Cui, W., 2008b. A note on the paper ‘cost range and the stable network structures’. Social Networks 30, 102–103], the paper applies exhaustive search and inductive approaches to analyze possible transitions among isomeric social networks with five vertices. A total of seven types of stable network structures are identified, which include the complete, star, chain, cycle, near-chain, near-cycle and null graphs. Then, a modified theorem for the equilibrium forms which corrects the previous work is presented.