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.     

What makes a network go round? Exploring the structure of a strong component with exponential random graph models

A strong component is a subgraph in a directed network where, following the direction of ties, all nodes in the graph are reachable from one another. Mutual reachability implies that every node in the graph is theoretically able to send materials to and/or influence every other node suggesting that strong components are amongst the more egalitarian network structures. Despite this intriguing feature, they remain understudied. Using exponential random graph models (ERGM) for directed networks, we investigate the social and structural processes underlying the generation of strong components. We illustrate our argument using a network of 301 nodes and 703 personal lending ties from Renaissance Florence. ERGM shows that our strong component arises from triadic clustering alongside an absence of higher-order star structures. We contend that these processes produce a strong component with a hierarchical, rather than an egalitarian structure: while some nodes are deeply embedded in a dense network of exchange, the involvement of others is more tenuous. More generally, we argue that such tiered core-periphery strong components will predominate in networks where the social context creates conditions for an absence of preferential attachment alongside the presence of localized closure. Although disparate social processes can give rise to hierarchical strong components linked to these two structural mechanisms, in Florence they are associated with the presence of multiple dimensions of social status and the connectedness of participants across disparate network domains.     

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.     

Measurement error in network data: A re-classification

Research on measurement error in network data has typically focused on missing data. We embed missing data, which we term false negative nodes and edges, in a broader classification of error scenarios. This includes false positive nodes and edges and falsely aggregated and disaggregated nodes. We simulate these six measurement errors using an online social network and a publication citation network, reporting their effects on four node-level measures – degree centrality, clustering coefficient, network constraint, and eigenvector centrality. Our results suggest that in networks with more positively-skewed degree distributions and higher average clustering, these measures tend to be less resistant to most forms of measurement error. In addition, we argue that the sensitivity of a given measure to an error scenario depends on the idiosyncracies of the measure's calculation, thus revising the general claim from past research that the more ‘global’ a measure, the less resistant it is to measurement error. Finally, we anchor our discussion to commonly-used networks in past research that suffer from these different forms of measurement error and make recommendations for correction strategies.     

Dense core model for cohesive subgraph discovery

Discovery of cohesive subgraphs is an important issue in social network analysis. As representative cohesive subgraphs, pseudo cliques have been developed by relaxing the perfection of cliques. By enumerating pseudo clique subgraphs, we can find some structures of interest such as a star-like structure. However, a little more complicated structures such as a core/periphery structure is still hard to be found by them. Therefore, we propose a novel pseudo clique called ρ-dense core and show the connection with the other pseudo cliques. Moreover, we show that a set of ρ-dense core subgraphs gives an optimal solution in a graph partitioning problem. Several experiments on real-life networks demonstrated the effectiveness for cohesive subgraph discovery.     

Information communities: The network structure of communication

This study puts forward a variable clique overlap model for identifying information communities, or potentially overlapping subgroups of network actors among whom reinforced independent links ensure efficient communication. We posit that the average intensity of communication between related individuals in information communities is greater than in other areas of the network. Empirical tests show that the variable clique overlap model is indeed more effective in identifying groups of individuals that have strong internal relationships in communication networks relative to prior cohesive subgroup models; the pathways generated by such an arrangement of connections are particularly robust against disruptions of information transmission. Our findings extend the scope of network closure effects proposed by other researchers working with communication networks using social network methods and approaches, a tradition which emphasizes ties between organizations, groups, individuals, and the external environment.     

Social network structure and the trade-off between social utility and economic performance

We put forward a computational multi-agent model capturing the impact of social network structure on individuals’ social trust, willingness to cooperate, social utility and economic performance. Social network structure is modeled as four distinct social capital dimensions: degree, centrality, bridging and bonding social capital. Model setup draws from socio-economic theory and empirical findings based on our novel survey dataset. Results include aggregate-level comparative statics and individual-level correlations. We find, inter alia, that societies that either are better connected, exhibit a lower frequency of local cliques, or have a smaller share of family-based cliques, record relatively better aggregate economic performance. As long as family ties are sufficiently valuable, there is a trade-off between aggregate social utility and economic performance, and small world networks are then socially optimal. We also find that in dense networks and trustful societies, there is a trade-off between individual social utility and economic performance; otherwise both outcomes are positively correlated in the cross section.     

Evolutionary Process of Social Capital Formation through Community Currency Organizations: The Japanese Case

Community currency systems are said to influence the revival of communities by promoting either local economic growth or social capital accumulation. However, no empirical studies have examined the multiple competing mechanisms for providing social support through transactional networks among participants. The current study connects network structural concepts to theories of social capital, transaction costs, homophily, and resource dependency at multiple levels and evaluates transactional relationships for community rebuilding and local economic development. We examine the evolutionary process of dynamic networks among local residents or organization members with network configurations in one of the largest Japanese community currency systems, “Peanuts.” Using longitudinal network data over 12 years for approximately 1400 actors, we conclude that the evolution and achievement of transactional network dynamics and partner selections differ between the two groups of participants: individual members and organization members. We also provide practical implications for sustaining participants’ transactions and commitment.     

Modeling social influence through network autocorrelation: constructing the weight matrix

Many physical and social phenomena are embedded within networks of interdependencies, the so-called ‘context’ of these phenomena. In network analysis, this type of process is typically modeled as a network autocorrelation model. Parameter estimates and inferences based on autocorrelation models, hinge upon the chosen specification of weight matrix W, the elements of which represent the influence pattern present in the network. In this paper I discuss how social influence processes can be incorporated in the specification of W. Theories of social influence center around ‘communication’ and ‘comparison’; it is discussed how these can be operationalized in a network analysis context. Starting from that, a series of operationalizations of W is discussed. Finally, statistical tests are presented that allow an analyst to test various specifications against one another or pick the best fitting model from a set of models.     

An exploratory comparison of name generator content: Data from rural India

Since the 1970s sociologists have explored the best means for measuring social networks, although few name generator analyses have used sociocentric data or data from developing countries, partly because sociocentric studies in developing countries have been scant. Here, we analyze 12 different name generators used in a sociocentric network study conducted in 75 villages in rural Karnataka, India. Having unusual sociocentric data from a non-Western context allowed us to extend previous name generator research through the unique analyses of network structural measures, an extensive consideration of homophily, and investigation of status difference between egos and alters. We found that domestic interaction questions generated networks that were highly clustered and highly centralized. Similarity between respondents and their nominated contacts was strongest for gender, caste, and religion. We also found that domestic interaction name generators yielded the most homogeneous ties, while advice questions yielded the most heterogeneous. Participants were generally more likely to nominate those of higher social status, although certain questions, such as who participants talk to uncovered more egalitarian relationships, while other name generators elicited the names of social contacts distinctly higher or lower in status than the respondent. Some questions also seemed to uncover networks that were specific to the cultural context, suggesting that network researchers should balance local relevance with global generalizability when choosing name generators.     

Random and biased networks: simulations and approximations

Work by Rapoport and his colleagues in the 1950s and early 1960s developed the idea of biased/random nets as a theory of social network structure. It aims to explain variation in aggregate network patterns by appeal to differences in local properties affecting linkages between nodes and how these differences cascade to affect the overall structure of the total network. While the theory is set out mathematically and uses formal logic to analyze the general model, the complexity of the compound outcome makes exact theory impossible. Consequently, plausible approximations and approximation formulas are used to link up the local properties to global structure. Research reported in this paper attempts to check these approximations through simulation studies. Programs are developed which generate specific networks over a reasonably large (S=100) population consistent with certain parametric specifciations which govern (coal patterns of connection. Properties of these networks are then compared with those predicted from the approximation arguments in an effort to refine those arguments to the point at which they can be used with confidence in other theoretical inquiries, such as recent applications of biased net theory to Blau's influential ideas on the social structural determinants of relational patterns.     

Jaccard-Spline index of structural proximity in contact networks

Network analysts are increasingly being called upon to apply their expertise to groups for which the only available or reliable data is a contact network. With no opportunity to gather additional data, the merits of such applications depend on empirical studies that validate the employment of structural constructs based on contact networks. Fortunately, we possess such studies in abundance. One of the strongest research traditions in social network analysis is the development of formal constructs that may be employed in analyses of networks. I suggest that greater insight into predictive success of network constructs may be acquired by addressing the following question: what features of the contact network in which a dyad is situated allow the prediction of other relations with an accuracy that validates the imputation of the latter given data on the former? In this article, I present findings on the structural contexts of dyads in contact networks and the relationship of these contexts with two fundamental forms of cohesive cognitive relations—accorded interpersonal influence and perceived interpersonal agreement. Based on these findings, I formalize a measure of structural proximity in contact networks with values that correspond to the conditional probabilities of these two forms of cohesive cognitive relations. The substantive settings of this analysis are policy groups with members who are embedded in contact structures based on regular interpersonal communication on policy issues and cognitive structures based on perceived interpersonal agreement and accorded interpersonal influence.     

The structure of educational research: The role of multivocality in promoting cohesion in an article interlock network

Researchers interested in the social and intellectual features of scholarly knowledge have emphasized the importance of small-scale, informally organized groups of people interested in the same or closely related research problems. The structure of these social networks, in large part, influences the way which research problems are identified, studied and transformed into policy. Building on popular concerns about the state of the educational research field, this study examines what its structure implies about the field's ability to integrate ideas and practices. Using data about which articles readers access from the online database of the Teachers College Record, one of the field's more popular journals, it is shown that the article interlock network exhibits a structure that fits parameters of both small-world and structurally cohesive models. Furthermore, this study unpacks the network's community structure to show that those articles that serve as the core through which much of the network is connected possess a multivocal identity; an ambiguous identity that appeals to multiple audiences simultaneously. Results are suggestive of mechanisms that could be used to promote greater cohesion across the network's distinct communities.     

Considering clustering measures: Third ties,means, and triplets

Measures that estimate the clustering coefficients of ego and overall social networks are important to social network studies. Existing measures differ in how they define and estimate triplet clustering with implications for how network theoretic properties are reflected. In this paper, we propose a novel definition of triplet clustering for weighted and undirected social networks that explicitly considers the relative strength of the tie connecting the two alters of the ego in the triplet. We argue that our proposed definition better reflects theorized effects of the important third tie in the social network literature. We also develop new methods for estimating triplet, local and global clustering. Three different types of mathematical means, i.e. arithmetic, geometric, and quadratic, are used to reflect alternative theoretical assumptions concerning the marginal effect of tie substitution.     

A study of sign adjustment in weighted signed networks

We analyse the adjustment of networks comprising of weighted positive (P) and negative (N) symmetric relations under the impact of various balancing rules. Five kinds of rules are studied: (1) a local minimal edge adjustment which is a special case of, (2) a local pressure based rule, (3) a local sign based rule, (4) a global rule and (5) rules varying on a local to global dimension. The convergence and convergent proportions of different 3-cycles and, thus the impact upon β(3) balance, under the different kinds of adjustment rule are studied both analytically and through simulation. The effects of network size (n), density (d) and the initial proportion of positive edges (α₀) upon the convergence of 3-cycles and, thus, balance and the eventual implications for the process of group formation are explored.     

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.     

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.     

Chronic illness and social network bridging in later life

Chronic disease has profound impacts on the structural features of individuals’ interpersonal connections such as bridging — ties to people who are otherwise poorly connected to each other. Prior research has documented competing arguments regarding the benefits of network bridging, but less is known about how chronic illness influences bridging and its underlying mechanisms. Using data on 1555 older adults from the National Social Life, Health, and Aging Project (NSHAP), I find that older adults diagnosed with chronic illness tend to have lower bridging potential in their networks, particularly between kin and non-kin members. They also report more frequent interactions with close ties but fewer neighbors, friends, and colleagues in their networks, which mediates the association between chronic illness and social network bridging. These findings illuminate both direct and indirect pathways through which chronic illness affects network bridging and highlight the context-specific implications for social networks in later life.