Applied network sampling

In principle, network sampling is an attractive method for estimating density and degree for large populations. This paper, based on the first extensive application of network sampling, reports some of the problems that may often arise in sampling and reaching respondents. The network sample or samples may be based on a list imperfectly reflecting the target population, the samples may be drawn nonrandomly from the list, and response may be nonrandom. We suggest and illustrate strategies for coping with each of these problems.     

Estimating point centrality using different network sampling techniques

The paper outlines the methodological choices that analysts must make when sampling social networks and assesses the impact of different sampling techniques on the estimation of network parameters. Using data from Galaskiewicz's (1919) study of Towertown and River City, the results show the extent to which sampling percentage, the number of trials/estimates, sampling procedure, and network size and density affect the ability of researchers to estimate the point centrality of organizations in networks of information and money transactions.     

Random sampling of alters from networks: A promising direction in egocentric network research

The social network perspective has great potential for advancing knowledge of social mechanisms in many fields. However, collecting egocentric (i.e., personal) network data is costly and places a heavy burden on respondents. This is especially true of the task used to elicit information on ties between network members (i.e., alter-alter ties or density matrix), which grows exponentially in length as network size increases. While most existing national surveys circumvent this problem by capping the number of network members that can be named, this strategy has major limitations. Here, we apply random sampling of network members to reduce cost, respondent burden, and error in network studies. We examine the effectiveness and reliability of random sampling in simulated and real-world egocentric network data. We find that in estimating sample/population means of network measures, randomly selecting a small number of network members produces only minor errors, regardless of true network size. For studies that use network measures in regressions, randomly selecting the mean number of network members (e.g., randomly selecting 10 alters when mean network size is 10) is enough to recover estimates of network measures that correlate close to 1 with those of the full sample. We conclude with recommendations for best practices that will make this versatile but resource intensive methodology accessible to a wider group of researchers without sacrificing data quality.     

Social network analysis with respondent-driven sampling data: A study of racial integration on campus

This paper presents respondent-driven sampling (RDS) as a viable method of sampling and analyzing social networks with survey data. RDS is a network based sampling and analysis method that provides a middle ground compliment to ego-centric and saturated methods of social network analysis. The method provides survey data, similar to ego-centric approaches, on individuals who are connected by behaviorally documented ties, allowing for macro-level analysis of network structure, similar to that supported by saturated approaches. Using racial interaction of university undergraduates as an empirical example, the paper examines whether and to what extent racial diversity at the institutional level is reflected as racial integration at the interpersonal level by testing hypotheses regarding the quantity and quality of cross-race friendships. The primary goal of this article, however, is to introduce RDS to the network community and to stimulate further research toward the goal of expanding the analytical capacity of RDS. Advantages, limitations, and areas for future research to network analysis using RDS are discussed.     

Assessing the performance of the bootstrap in simulated assemblage networks

Archaeologists are increasingly interested in networks constructed from site assemblage data, in which weighted network ties reflect sites’ assemblage similarity. Equivalent networks would arise in other scientific fields where actors’ similarity is assessed by comparing distributions of observed counts, so the assemblages studied here can represent other kinds of distributions in other domains. One concern with such work is that sampling variability in the assemblage network and, in turn, sampling variability in measures calculated from the network must be recognized in any comprehensive analysis. In this study, we investigated the use of the bootstrap as a means of estimating sampling variability in measures of assemblage networks. We evaluated the performance of the bootstrap in simulated assemblage networks, using a probability structure based on the actual distribution of sherds of ceramic wares in a region with 25 archaeological sites. Results indicated that the bootstrap was successful in estimating the true sampling variability of eigenvector centrality for the 25 sites. This held both for centrality scores and for centrality ranks, as well as the ratio of first to second eigenvalues of the network (similarity) matrix. Findings encourage the use of the bootstrap as a tool in analyses of network data derived from counts.     

Hypernetwork sampling: Duality and differentiation among voluntary organizations

One of the recurrent problems in the study of social organization is that survey researchers are forced to study individuals, while they are often interested in hypotheses about organizations or systems of organizations. This paper offers some methods which allow survey researchers to address hypotheses about the relations generated among individuals by organizations, the organizations themselves, and the relations among organizations. Estimators are developed for the number and size distribution of organizations in communities, the density of relations among individuals generated by organizations, the number and density of interorganizational linkages, and the amount of membership overlap among organizations. This approach combines Granovetter's idea of network sampling with Breiger's notion of the duality of persons and groups to produce a quantitative approach to the study of voluntary organization. We provide an illustration of the methods we develop by testing two of Blau's structural hypotheses on data concerning voluntary organizations. The hypotheses that structural differentiation increases with system size and that this increase is at a decreasing rate are strongly supported. The paper closes with some suggestions for further elaborations of the hypernetwork approach.     

Bias decomposition and estimator performance in respondent-driven sampling

Respondent-Driven Sampling (RDS) is a method of network sampling that is used to sample hard-to-reach populations. The resultant sample is non-random, but different weighting methods can account for the over-sampling of (1) high-degree individuals and (2) homophilous groups that recruit members more effectively. While accounting for degree-bias is almost universally agreed upon, accounting for recruitment-bias has been debated as it can further increase estimate variance without substantially reducing bias. Simulation-based research has examined which weighting procedures perform best given underlying population network structures, group recruitment differences, and sampling processes. Yet, in the field, analysts do not have a priori knowledge of the network they are sampling. We show that the RDS sample data itself can determine whether a degree-based estimator is sufficient. Formulas derived from the decomposition of a ‘dual-component’ estimator can approximate the ‘recruitment component’ (RC) and ‘degree component’ (DC) of a sample’s bias. Simulations show that RC and DC values can predict the performance of different classes of estimators. Samples with extreme ‘RC’ values, a consequence of network homophily and differential recruitment, are better served by a classical estimator. The use of sample data to improve estimator selection is a promising innovation for RDS, as the population network features that should guide estimator selection are typically unknown.     

Estimating network properties from snowball sampled data

This article addresses the estimation of topological network parameters from data obtained with a snowball sampling design. An approximate expression for the probability of a vertex to be included in the sample is derived. Based on this sampling distribution, estimators for the mean degree, the degree correlation, and the clustering coefficient are proposed. The performance of these estimators and their sensitivity with respect to the response rate are validated through Monte Carlo simulations on several test networks. Our approach has no complex computational requirements and is straightforward to apply to real-world survey data. In a snowball sample design, each respondent is typically enquired only once. Different from the widely used estimator for Respondent-Driven Sampling (RDS), which assumes sampling with replacement, the proposed approach relies on sampling without replacement and is thus also applicable for large sample fractions. From the simulation experiments, we conclude that the estimation quality decreases with increasing variance of the network degree distribution. Yet, if the degree distribution is not to broad, our approach results in good estimates for the mean degree and the clustering coefficient, which, moreover, are almost independent from the response rate. The estimates for the degree correlation are of moderated quality.     

Triadic configurations in limited choice sociometric networks: Empirical and theoretical results

Previous research demonstrated that information contained in triad censuses from heterogeneous collections of social networks occupies a high dimensional space. Regions of this space, and locations of triad censuses within it, are largely defined by lower order network properties: network density and dyad distributions [Faust, K., 2006. Comparing social networks: size, density, and local structure. Metodološki Zvezki (Advances in Methodology and Statistics) 3 (2), 185–216; Faust, K., 2007. Very local structure in social networks. Sociological Methodology 37, 209–256]. The current paper extends comparative work on triad censuses by addressing three related issues. First, it determines and interprets the space occupied by triad censuses for 128 friendship networks gathered using a limited choice sociometric protocol. Second, it constructs a theoretical space for triad censuses expected given lower order graph properties and examines the dimensionality and shape of this space. Third, it brings together these lines of investigation to determine where the empirical triad censuses reside within the theoretical space. Results show that the empirical triad censuses are almost perfectly represented in one dimension (explaining 99% of the data) and that network density explains over 96% of the variance in locations on this dimension. In contrast, the theoretical space for triad censuses is at least four-dimensional, with distinctive regions defined by network density and dyad distributions. Within this theoretical space, the empirical triad censuses occupy a restricted region that closely tracks triad censuses expected given network density. Results differ markedly from prior findings that the space occupied by triad censuses from heterogeneous social networks is of high dimensionality. Results also reinforce observations about constraints that network size and density place on graph level indices.     

Linked Ego Networks: Improving estimate reliability and validity with respondent-driven sampling

Respondent-driven sampling (RDS) is currently widely used for the study of HIV/AIDS-related high risk populations. However, recent studies have shown that traditional RDS methods are likely to generate large variances and may be severely biased since the assumptions behind RDS are seldom fully met in real life. To improve estimation in RDS studies, we propose a new method to generate estimates with ego network data, which is collected by asking respondents about the composition of their personal networks, such as “what proportion of your friends are married?”. By simulations on an extracted real-world social network of gay men as well as on artificial networks with varying structural properties, we show that the precision of estimates for population characteristics is greatly improved. The proposed estimator shows superior advantages over traditional RDS estimators, and most importantly, the method exhibits strong robustness to the recruitment preference of respondents and degree reporting error, which commonly happen in RDS practice and may generate large estimate biases and errors for traditional RDS estimators. The positive results henceforth encourage researchers to collect ego network data for variables of interests by RDS, for both hard-to-access populations and general populations when random sampling is not applicable.     

Ties,sites and irregularities: pitfalls and benefits in using respondent-driven sampling for surveying a homeless population

Respondent-driven sampling (RDS) is a survey method for hidden populations and, as such, it offers a suitable approach for sampling the homeless. Surprisingly, the practical use of RDS in surveying homeless populations has only sporadically been described in the professional literature so far, and the specifics of using RDS for sampling this group have not been reflected in depth. The goal of the article is to investigate how three specific concerns, namely the transitional character of social ties among the homeless, problems with locating the interview site, and the irregular use of coupons, affect the sampling process. The findings of the article are based on experience using RDS for creating two independent samples of homeless persons in two Czech cities. Worries of poor referral effectiveness were disproved, but poor validity of the network size indicator, tendency towards irregular use of coupons, and negative effects arising from selecting service centres for the homeless as survey sites were confirmed.     

A note on strangers,friends and happiness

Using network data obtained in the 1985 General Social Survey, expressions of happiness are shown to increase with the size of a person's discussion network and decrease with the prevalence of strangers in the network. The density of especially close relations in the network has no direct effect on happiness. It is the negative impact of strangers rather than the positive impact of close relations that determines expressions of happiness. The network size and stranger effects remain strong even after respondent differences in socioeconomic status, age, sex, race, and domestic situation are held constant. However, it is clear that an almost certain route to strengthening the network measures to predict well-being lies in studying how happiness varies with the position of a spouse or other domestic partner in the respondent's network.     

The development of structure in random networks: an analysis of the effects of increasing network density on five measures of structure

The density of ingroup relations continues to be proposed as an indicator of structural cohesion. Network density is obviously a misleading indicator of structural cohesion when a group has subgroups; in such circumstances, the cohesion may be entirely internal to the subgroups. However, it is plausible that network density is a useful indicator of structural cohesion when it can be assumed that a group lacks subgroups. In order to analyze this possibility, I construct a set of random networks, increase the density of relations in these networks, and observe how the networks' structure develops in terms of five measures. The results show that low densities in large networks may be associated with more structural cohesion than higher densities in smaller networks; it is suggested that in field studies, attempts to control for network size will encounter problems of nonlinearity and heteroscedasticity. I conclude that network density is not a useful indicator of structure and that direct measurement of structure is to be preferred.     

Community understanding of respondent-driven sampling in a medical research setting in Uganda: importance for the use of RDS for public health research

Respondent-driven sampling (RDS) is a widely-used variant of snowball sampling. Respondents are selected not from a sampling frame, but from a social network of existing members of the sample. Incentives are provided for participation and for the recruitment of others. Ethical and methodological criticisms have been raised about RDS. In this study RDS was used to recruit male household heads in rural Uganda. We investigated community members' understanding and experience of the method, and explored how these may have affected the quality of the RDS survey data. Our findings suggest that because participants recruit participants, the use of RDS in medical research may result in increased difficulties in gaining informed consent, and data collected using RDS may be particularly susceptible to bias due to differences in the understanding of key concepts between researchers and members of the community.     

Schema via Structure? Personal Network Density and the Moral Evaluation of Infidelity

This article considers whether the density of a person's social network is related to his/her moral attitudes toward infidelity. Integrating recent sociological thinking on moral schemas with network theory's insights about deviance and structural independence, I employ data from a representative sample of American men aged 57–85. Findings indicate that men with the densest personal networks are least likely to condone infidelity. This association, moreover, was independent of men's education, their beliefs about religion and sex, and attitudes about their partners, among other factors. The findings imply an affinity between micro‐social structure and moral judgment, suggesting that network density can help constrain even the expression of moral attitudes.     

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.     

Bridging: Locating critical connectors in a network

This paper proposes several measures for bridging in networks derived from Granovetter's (1973) insight that links which reduce distances in a network are important structural bridges. Bridging is calculated by systematically deleting links and calculating the resultant changes in network cohesion (measured as the inverse average path length). The average change for each node's links provides an individual level measure of bridging. We also present a normalized version which controls for network size and a network-level bridging index. Bridging properties are demonstrated on hypothetical networks, empirical networks, and a set of 100 randomly generated networks to show how the bridging measure correlates with existing network measures such as degree, personal network density, constraint, closeness centrality, betweenness centrality, and vitality. Bridging and the accompanying methodology provide a family of new network measures useful for studying network structure, network dynamics, and network effects on substantive behavioral phenomenon.     

The evolution of structural resilience of global oil and gas resources trade network

This paper establishes anetwork resilience evaluation framework of the global oil and gas resourcetrade network in 2010, 2015 and 2020. The results are as follows: The links of the oil trade network present a gradually shrinking trend, and the gas tradenetwork presents a trend of close connection first and then reduced. In termsof network density, network centrality, network connectivity and network size, the structural resilience of the oil and gas resource trade network displays ashrinking trend, and the gas trade network is superior. Concerninginvulnerability and recovery, the resilience of the oil trade network issuperior to the natural gas trade network. In simulated attacks, the oil tradenetwork reveals a higher resilience towards intentional attacks, and the gastrade network shows a higher resilience towards random attacks. The Strait ofHormuz and the Strait of Malacca are critical chokepoints in the networks.     

Network structure and minimum degree

Social network researchers have long sought measures of network cohesion, Density has often been used for this purpose, despite its generally admitted deficiencies. An approach to network cohesion is proposed that is based on minimum degree and which produces a sequence of subgraphs of gradually increasing cohesion. The approach also associates with any network measures of local density which promise to be useful both in characterizing network structures and in comparing networks.     

Beyond interviewer effects in the standardized measurement of ego-centric networks

The effects which interviewers exert on the collection of ego-centric networks have recently come into the focus of methodological considerations. Studies consistently show that the size of networks varies depending on the interviewer. We would like to expand on this research strand by pointing to different aspects which have so far gone unremarked in the discussion. First, size is mainly analysed as a network measure which is influenced during data collection, while other common measures such as network density or composition have not received sufficient consideration. Second, large-scale surveys using face-to-face interviews usually allocate interviewers to a single sampling point. Differences between sampling points (locality effects) are attributed to interviewer effects. Hence, we disentangle the effects of the locality and interviewer. Third, the discussion on interviewer effects often follows an “actor-oriented” consideration of how data collection situations are structured by interviewers. Expanding this approach from a relational perspective, we consider the relationship between the interviewers and respondents and whether this relationship influences the collection of network data. To test our hypotheses about the influence of interviewers, the locality and the interviewer-respondent relationship on different network measures, we use data from the 2010 German General Social Survey (n = 2827 respondents, n = 220 interviewers). The multilevel analyses show that the relationship between the interviewer and the respondent is not very relevant. Furthermore, the analyses show that interviewers have an influence on the network size but not on measures of their composition. However, evidence on the prevalence of locality or interviewer effects is mixed. Finally, homophilous interviewer-respondent relationships have very little effect on network characteristics. We find evidence of training and fatigue effects on network size. However, much of the variation in network size caused by the interviewer still remains unexplained. We draw conclusions on how to organize interview situations in surveys.