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.     

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.     

Network models for social selection processes

We present network models for social selection processes, based on the p¹ class of models. Social selection occurs when individuals form social relationships on the basis of certain characteristics they possess. Similarity is a common hypothesis for selection processes, but one that is usually framed dyadically. Structural balance approaches move beyond dyadic conceptualizations and require more sophisticated modeling. The two-block chain graph approach of p¹ social influence models is adapted to allow individual attribute variables to be predictors of network ties. Using a range of dependence assumptions, we present a hierarchy of increasingly complex selection models, including models for continuous attribute measures, which in their simplest form may be assumed to be linear. The models have scope, however, for more complex functional formulations so that more specific hypotheses may be investigated by postulating a particular functional form. Our empirical examples illustrate how dyadic selection may be transmuted into structural effects, and how the absence of dyadic selection may still mask a subtle higher order selection effect as individuals “position” themselves within a wider social environment. In conclusion, we discuss the links between social influence and social selection models.     

Tangible transnational links in the houses of Italian immigrants in Melbourne

The transnational immigrant home is understood analytically, in an extensive literature, as a mobile construct that is not necessarily confined in its application to a single locale or building. The home has significant symbolic meaning for transnationals, as well as referring to their places of residence. In this study, however, we explore the physical structure of the transnational immigrant home and its materiality – the house. We examine two distinct types of homes of Italian immigrants in Melbourne – their past houses in Italy and their current houses in Melbourne. We argue that these houses form tangible links within Italian–Australian social space, and are parts of a network that constructs this transnational space. It is necessary to consider the actual materiality of such houses in order to extend the common understanding of ‘home’, seeing it not only as an abstract idea but also as a specifically located tangible structure and an active participant in the formation of transnational social spaces.     

An agent-based random-utility-maximization model to generate social networks with transitivity in geographic space

Stochastic actor-based approaches receive increasing interest in the generation of social networks for simulation in time and space. Existing models however cannot be readily integrated in agent-based models that assume random-utility-maximizing behavior of agents. We propose an agent-based model to generate social networks explicitly in geographic space which is formulated in the random-utility-maximizing (RUM) framework. The proposed model consists of a friendship formation mechanism and a component to simulate social encounters in a population. We show how transitivity can be incorporated in both components and how the model can be estimated based on data of personal networks using likelihood estimation. In an application to the Swiss context, we demonstrate the estimation and ability of the model to reproduce relevant characteristics of networks, such as geographic proximity, attribute similarity (homophily), size of personal networks (degree distribution) and clustering (transitivity). We conclude that the proposed social-network model fits seamlessly in existing large-scale micro-simulation systems which assume RUM behavior of agents.     

Social creativity as a function of agent cognition and network properties: A computer model

Inventions – concepts, devices, procedures – are often created by networks of interacting agents in which the agents can be individuals (as in a scientific discipline) or they can themselves be collectives (as in firms interacting in a market). Different collectives create and invent at different rates. It is plausible that the rate of invention is jointly determined by properties of the agents (e.g., their cognitive capacity) and by properties of the network of interactions (e.g., the density of the communication links), but little is known about such two-level interactions. We present an agent-based model of social creativity in which the individual agent captures key features of the human cognitive architecture derived from cognitive psychology, and the interactions are modeled by agents exchanging partial results of their symbolic processing of task information. We investigated the effect of agent and network properties on rates of invention and diffusion in the network via systematic parameter variations. Simulation runs show, among other results, that (a) the simulation exhibits network effects, i.e., the model captures the beneficial effect of collaboration; (b) the density of connections produces diminishing returns in term of the benefits on the invention rate; and (c) limits on the cognitive capacity of the individual agents have the counterintuitive consequence of focusing their efforts. Limitations and relations to other computer simulation models of creative collectives are discussed.     

Networks and geography: Modelling community network structures as the outcome of both spatial and network processes

This paper focuses on how to extend the exponential random graph models to take into account the geographical embeddedness of individuals in modelling social networks. We develop a hierarchical set of nested models for spatially embedded social networks, in which, following Butts (2002), an interaction function between tie probability and Euclidean distance between nodes is introduced. The models are illustrated by an empirical example from a study of the role of social networks in understanding spatial clustering in unemployment in Australia. The analysis suggests that a spatial effect cannot solely explain the emergence of organised network structure and it is necessary to include both spatial and endogenous network effects in the model.     

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.     

Neighborhood–Based Models For Social Networks

We argue that social networks can be modeled as the outcome of processes that occur in overlapping local regions of the network, termed local social neighborhoods. Each neighborhood is conceived as a possible site of interaction and corresponds to a subset of possible network ties. In this paper, we discuss hypotheses about the form of these neighborhoods, and we present two new and theoretically plausible ways in which neighborhood–based models for networks can be constructed. In the first, we introduce the notion of a setting structure, a directly hypothesized (or observed) set of exogenous constraints on possible neighborhood forms. In the second, we propose higher–order neighborhoods that are generated, in part, by the outcome of interactive network processes themselves. Applications of both approaches to model construction are presented, and the developments are considered within a general conceptual framework of locale for social networks. We show how assumptions about neighborhoods can be cast within a hierarchy of increasingly complex models; these models represent a progressively greater capacity for network processes to "reach" across a network through long cycles or semipaths. We argue that this class of models holds new promise for the development of empirically plausible models for networks and network–based processes.     

Trust and partner selection in social networks: An experimentally grounded model

This article investigates the importance of the endogenous selection of partners for trust and cooperation in market exchange situations, where there is information asymmetry between investors and trustees. We created an experimental-data driven agent-based model where the endogenous link between interaction outcome and social structure formation was examined starting from heterogeneous agent behaviour. By testing various social structure configurations, we showed that dynamic networks lead to more cooperation when agents can create more links and reduce exploitation opportunities by free riders. Furthermore, we found that the endogenous network formation was more important for cooperation than the type of network. Our results cast serious doubt about the static view of network structures on cooperation and can provide new insights into market efficiency.     

Corporate competition: A self-organized network

A substantial number of studies have extended the work on universal properties in physical systems to complex networks in social, biological, and technological systems. In this paper, we present a complex networks perspective on interfirm organizational networks by mapping, analyzing and modeling the spatial structure of a large interfirm competition network across a variety of sectors and industries within the United States. We propose two micro-dynamic models that are able to reproduce empirically observed characteristics of competition networks as a natural outcome of a minimal set of general mechanisms governing the formation of competition networks. Both models, which utilize different approaches yet apply common principles to network formation give comparable results. There is an asymmetry between companies that are considered competitors, and companies that consider others as their competitors. All companies only consider a small number of other companies as competitors; however, there are a few companies that are considered as competitors by many others. Geographically, the density of corporate headquarters strongly correlates with local population density, and the probability two firms are competitors declines with geographic distance. We construct these properties by growing a corporate network with competitive links using random incorporations modulated by population density and geographic distance. Our new analysis, methodology and empirical results are relevant to various phenomena of social and market behavior, and have implications to research fields such as economic geography, economic sociology, and regional economic development.     

Exponential random graph models for multilevel networks

Modern multilevel analysis, whereby outcomes of individuals within groups take into account group membership, has been accompanied by impressive theoretical development (e.g. Kozlowski and Klein, 2000) and sophisticated methodology (e.g. Snijders and Bosker, 2012). But typically the approach assumes that links between groups are non-existent, and interdependence among the individuals derives solely from common group membership. It is not plausible that such groups have no internal structure nor they have no links between each other. Networks provide a more complex representation of interdependence. Drawing on a small but crucial body of existing work, we present a general formulation of a multilevel network structure. We extend exponential random graph models (ERGMs) to multilevel networks, and investigate the properties of the proposed models using simulations which show that even very simple meso effects can create structure at one or both levels. We use an empirical example of a collaboration network about French cancer research elites and their affiliations (0125 and 0120) to demonstrate that a full understanding of the network structure requires the cross-level parameters. We see these as the first steps in a full elaboration for general multilevel network analysis using ERGMs.     

The determinants of heroin flows in Europe: A latent space approach

This study utilises recent advances in statistical models for social networks to identify the factors shaping heroin trafficking in relation to European countries. First, it estimates the size of the heroin flows among a network of 61 countries, before subsequently using a latent space approach to model the presence of trafficking and the amount of heroin traded between any two given countries. Many networks, such as trade networks, are intrinsically weighted, and ignoring edge weights results in a loss of relevant information. Traditionally, the gravity model has been used to predict legal trade flows, assuming conditional independence among observations. More recently, latent space position models for social networks have been used to analyze legal trade among countries, and, mutatis mutandis, can be applied to the context of illegal trade to count both edge weights and conditional dependence among observations. These models allow for a better understanding of the generative processes and potential evolution of heroin trafficking routes. This study shows that geographical and social proximity provide fertile ground for the formation of heroin flows. Opportunities are also a driver of drug flows towards countries where regulation of corruption is weak.     

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.     

Theoretische und statistische Modellierung von Cross-Pressures in Kontextanalysen

Cross-pressures can be defined as individually perceived social pressure that results from heterogeneity in the social context, mainly due to conflicting social expectations of relevant social actors. In this paper we discuss the theoretical position of “cross-pressures” in the structural-individualist paradigm and present methods for modeling cross-pressures in multilevel regression models. We argue that cross pressures form a specific class of context effects, that is macro-micro links, and sketch a reconstruction as part of the problem of defining the social situation in the Model of Frame Selection. The theoretical model implies that empirical applications of the concept would ideally use multiplicative terms for the specification of cross-level interactions in multilevel models. Modeling random slopes and context fixed-effects the interaction can be identified empirically. As an example we analyze the relation between postmaterialism and environmental concern, moderated by national wealth using WVS data. Our results indicate that postmaterialism and environmental concern form an integrated value cluster in wealthy societies, but are separate constructs in poorer societies.     

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.     

Analytic strategies for longitudinal networks with missing data

Missing data are often problematic when analyzing complete longitudinal social network data. We review approaches for accommodating missing data when analyzing longitudinal network data with stochastic actor-based models. One common practice is to restrict analyses to participants observed at most or all time points, to achieve model convergence. We propose and evaluate an alternative, more inclusive approach to sub-setting and analyzing longitudinal network data, using data from a school friendship network observed at four waves (N = 694). Compared to standard practices, our approach retained more information from partially observed participants, generated a more representative analytic sample, and led to less biased model estimates for this case study. The implications and potential applications for longitudinal network analysis are discussed.     

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 network capital, economic mobility and poverty traps

This paper explores the role social network capital might play in facilitating poor agents?? escape from poverty traps. We model and simulate endogenous link formation among households heterogeneously endowed with both traditional and social network capital who make investment and technology choices over time in the absence of financial markets and faced with multiple production technologies featuring different fixed costs and returns. We show that social network capital can either complement or substitute for productive assets in facilitating some poor households?? escape from poverty. However, the voluntary nature of costly link formation also creates exclusionary mechanisms that impede some poor households?? use of social network capital. Through numerical simulation, we show that the ameliorative potential of social networks therefore depends fundamentally on the broader socio-economic wealth distribution in the economy, which determines the feasibility of social interactions and the net intertemporal benefits resulting from endogenous network formation. In some settings, targeted public transfers to the poor can crowd-in private resources by inducing new social links that the poor can exploit to escape from poverty.     

The role of network setting and gender in online content popularity

In this study, we explore the role of specific network structures that enhance social capital and assess the extent to which gender, social ties, and communication interaction relate to content popularity within online social networks (OSNs). Our results are based on an extensive OSN data set, containing over 100,000 members, connected by over 1.7 million links. The findings indicate that content popularity inference is more accurate when considering activity interaction among users and that network structures known as advantageous for amassing social capital in the offline environment are relevant online as well. We conclude by discussing how gender mediates the correlation between some network measures and the growth of users’ content popularity and provide a potential explanation for the emergence of gender differences.