Categorical attribute based centrality: E–I and G–F centrality

In a paper examining informal networks and organizational crisis, Krackhardt and Stern (1988) proposed a measure assessing the extent to which relations in a network were internal to a group as opposed to external. They called their measure the E–I index. The measure is now in wide use and is implemented in standard network packages such as UCINET ( Borgatti et al., 2002). The measure is based on a partition-based degree centrality measure and as such can be extended to other centrality measures and group level data. We explore extensions to closeness, betweenness and eigenvector centrality, and show how to apply the technique to sets of subgroups that do not form a partition. In addition, the extension to betweenness suggests a linkage to the Gould and Fernandez brokerage measures, which we explore.     

Group betweenness and co-betweenness: Inter-related notions of coalition centrality

Vertex betweenness centrality is a metric that seeks to quantify a sense of the importance of a vertex in a network in terms of its ‘control’ on the flow of information along geodesic paths throughout the network. Two natural ways to extend vertex betweenness centrality to sets of vertices are (i) in terms of geodesic paths that pass through at least one of the vertices in the set, and (ii) in terms of geodesic paths that pass through all vertices in the set. The former was introduced by Everett and Borgatti [Everett, M., Borgatti, S., 1999. The centrality of groups and classes. Journal of Mathematical Sociology 23 (3), 181–201], and called group betweenness centrality. The latter, which we call co-betweenness centrality here, has not been considered formally in the literature until now, to the best of our knowledge. In this paper, we show that these two notions of centrality are in fact intimately related and, furthermore, that this relationship may be exploited to obtain deeper insight into both. In particular, we provide an expansion for group betweenness in terms of increasingly higher orders of co-betweenness, in a manner analogous to the Taylor series expansion of a mathematical function in calculus. We then demonstrate the utility of this expansion by using it to construct analytic lower and upper bounds for group betweenness that involve only simple combinations of (i) the betweenness of individual vertices in the group, and (ii) the co-betweenness of pairs of these vertices. Accordingly, we argue that the latter quantity, i.e., pairwise co-betweenness, is itself a fundamental quantity of some independent interest, and we present a computationally efficient algorithm for its calculation, which extends the algorithm of Brandes [Brandes, U., 2001. A faster algorithm for betweenness centrality. Journal of Mathematical Sociology 25, 163] in a natural manner. Applications are provided throughout, using a handful of different communication networks, which serve to illustrate the way in which our mathematical contributions allow for insight to be gained into the interaction of network structure, coalitions, and information flow in social networks.     

The social networks of academic performance in a student context of poverty in Mexico

Purpose: To describe the structure of the social network of junior high school students from a low socioeconomic status and assess the association between centrality measurements and academic performance. In the centrality positions (eigenvector, closeness, degree, and betweenness), the female gender and “only study” were significant predictors of high academic performance. The density of the student social network was presented by homophilic associations that hint at the existence of subcultures at school.     

Egocentric and sociocentric measures of network centrality

Egocentric centrality measures (for data on a node’s first-order zone) parallel to Freeman’s [Social Networks 1 (1979) 215] centrality measures for complete (sociocentric) network data are considered. Degree-based centrality is in principle identical for egocentric and sociocentric network data. A closeness measure is uninformative for egocentric data, since all geodesic distances from ego to other nodes in the first-order zone are 1 by definition. The extent to which egocentric and sociocentric versions of Freeman’s betweenness centrality measure correspond is explored empirically. Across seventeen diverse networks, that correspondence is found to be relatively close—though variations in egocentric network composition do lead to some notable differences in egocentric and sociocentric betweennness. The findings suggest that research design has a relatively modest impact on assessing the relative betweenness of nodes, and that a betweenness measure based on egocentric network data could be a reliable substitute for Freeman’s betweenness measure when it is not practical to collect complete network data. However, differences in the research methods used in sociocentric and egocentric studies could lead to additional differences in the respective betweenness centrality measures.     

Aligning research and practice: The role of academic-community partnerships for improving measurement and process

ObjectiveCommunity programs addressing social determinants of health are growing in prominence and are increasingly expected to provide metrics of success. Our objective is to assess the role of an academic-community partnership for a community health worker program targeting social and medical needs, and determine factors impacting its effectiveness.MethodsWe draw on a 4.5-year partnership that includes both quantitative and qualitative data collection and analysis. Quantitative data collection mechanisms evolved as a result of the partnership. Qualitative interviews were conducted with community health workers and leadership.ResultsTo align medical and social support services in a sustainable and measurable manner, our academic-community partnership found that creating and maintaining a mutually beneficial space through small wins enabled us to then address larger problems and needs. Ongoing self-study and process evaluation allowed quick adjustments. Unique partnership elements such as having consistent funding and flexible timelines and objectives were essential.ConclusionsWhen integrating health and social services, academic-community partnerships create pathways for bidirectional learning than can quickly turn research into practice and support sustainability, especially when based on incrementally built trust and a history of small wins.     

The institutional antecedent to firms’ interorganizational network portfolios: Evidence from China

Although the amount of research on interorganizational networks has increased significantly in recent years, few studies have examined the antecedents to interorganizational network portfolios—organizations’ configuration of their relationship networks with other organizations. To address this gap, this study examines how firms’ interorganizational network portfolios vary across three types of ownership structures (i.e., state-owned, private, and multinational enterprises) in China. Cluster analysis of the data on 212 leading firms operating in China revealed two types of network portfolios firms maintain. Specifically, firms maintaining robust cross-sector portfolios had more extensive networks with organizations in the nonprofit and public sectors than firms maintaining limited cross-sector portfolios. Moreover, regression results suggested that firms across different ownership structures had distinct numbers and types of organizational partners, particularly nongovernmental organization (NGO) partners. Theoretical and practical implications are derived from the findings.     

Betweenness computation in the single graph representation of hypergraphs

Many real-world social networks are hypergraphs because they either explicitly support membership in groups or implicitly include communities. We present the HyperBC algorithm that exactly computes betweenness centrality (or BC) in hypergraphs. The forward phase of HyperBC and the backpropagation phase are specifically tailored for BC computation on hypergraphs. In addition, we present an efficient method for pruning networks through the notion of “non-bridging” vertices. We experimentally evaluate our algorithm on a variety of real and artificial networks and show that it significantly speeds up the computation of BC on both real and artificial hypergraphs, while at the same time, being very memory efficient.     

Reliability of measures of centrality and prominence

This paper evaluates the reliability of measures of centrality and prominence of social networks among high school students. The authors present and discuss results from eight experiments. Four types of social support: (1) instrumental support, (2) informational support, (3) social companionship, and (4) emotional support—were measured three times within each class. Four measurement scales: (1) binary, (2) categorical, (3) categorical with labels and (4) line production—were applied. Reliability of in- and out-degree, in- and out-closeness, betweenness and flow betweenness was estimated by the Pearson correlation coefficient. Meta analysis of factors affecting the test-retest reliability of measures of centrality and prominence was done by multiple classification analysis. Results show that,

• -Global measures (considering direct and indirect choices) are more sensitive to measurement errors than local measures (considering only direct choices).
• -In-measures are more stable than out-measures.
• -Among types of social support, emotional support gives the least stable measures of centrality and prominence, whereas social companionship gives the most stable results.
• -The reliability of centrality and prominence measures is higher when the network is denser.

     

Some unique properties of eigenvector centrality

Eigenvectors, and the related centrality measure Bonacich's c(β), have advantages over graph-theoretic measures like degree, betweenness, and closeness centrality: they can be used in signed and valued graphs and the beta parameter in c(β) permits the calculation of power measures for a wider variety of types of exchange. Degree, betweenness, and closeness centralities are defined only for classically simple graphs—those with strictly binary relations between vertices. Looking only at these classical graphs, where eigenvectors and graph–theoretic measures are competitors, eigenvector centrality is designed to be distinctively different from mere degree centrality when there are some high degree positions connected to many low degree others or some low degree positions are connected to a few high degree others. Therefore, it will not be distinctively different from degree when positions are all equal in degree (regular graphs) or in core-periphery structures in which high degree positions tend to be connected to each other.     

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.     

Centrality in affiliation networks

This paper discusses the conceptualization, measurement, and interpretation of centrality in affiliation networks. Although centrality is a well-studied topic in social network analysis, and is one of the most widely used properties for studying affiliation networks, virtually all discussions of centrality and centralization have concerned themselves with one-mode networks. Bonacich's work on simultaneous group and individual centralities is a notable exception (Social Networks, 1991, 13, 155–168). I begin by outlining the distinctive features of affiliation networks and describe four motivations for centrality indices in affiliation networks. I then consider properties of some existing centrality indices for affiliation networks, including the relationship between centralities for actors and events in these networks, and present a new conceptualization of centrality that builds on the formal properties of affiliation networks and captures important theoretical insights about the positions of actors and events in these networks. These centralities are then illustrated on Galaskiewicz's data on club and board memberships of a sample of corporate executive officers (Social Organization of an Urban Grants Economy. New York: Academic Press, 1985). The conclusion to this paper discusses strengths and weaknesses of centrality indices when applied to affiliation networks.     

Embedding time in positions: Temporal measures of centrality for social network analysis

Digital data enable researchers to obtain fine-grained temporal information about social interactions. However, positional measures used in social network analysis (e.g., degree centrality, reachability, betweenness) are not well suited to these time-stamped interaction data because they ignore sequence and time of interactions. While new temporal measures have been developed, they consider time and sequence separately. Building on formal algebra, we propose three temporal equivalents to positional network measures that incorporate time and sequence. We demonstrate how these temporal equivalents can be applied to an empirical context and compare the results with their static counterparts. We show that, compared to their temporal counterparts, static measures applied to interaction networks obscure meaningful differences in the way in which individuals accumulate alters over time, conceal potential disconnections in the network by overestimating reachability, and bias the distribution of betweenness centrality, which can affect the identification of key individuals in the network.     

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

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

Geodesic based centrality: Unifying the local and the global

A variety of node-level centrality measures, including purely structural measures (such as degree and closeness centrality) and measures incorporating characteristics of actors (such as the Blau's measure of heterogeneity) have been developed to measure a person's access to resources held by others. Each of these node-level measures can be placed on a continuum depending on whether they focus only on ego's direct contacts (e.g. degree centrality and Blau's measure of heterogeneity), or whether they also incorporate connections to others at longer distances in the network (e.g. closeness centrality or betweenness centrality). In this paper we propose generalized measures, where a tuning parameter δ regulates the relative impact of resources held by more close versus more distant others. We first show how, when a specific δ is chosen degree-centrality and reciprocal closeness centrality are two specific instances of this more general measure. We then demonstrate how a similar approach can be applied to node-level measures that incorporate attributes. When more or less weight is given to other nodes at longer distances with specific characteristics, a generalized measure of resource-richness and a generalized measure for diversity among one's connections can be obtained (following Blau's measure of heterogeneity). Finally, we show how this approach can also be applied to betweenness centrality to focus on more local (ego) betweenness or global (Freeman) betweenness. The importance of the choice of δ is illustrated on some classic network datasets.     

The structure of global centrality measures

The aim of this article is to identify and analyse the logic and structure of centrality measures applied to social networks. On the basis of the article by Borgatti and Everett, identifying the latent functions of centrality, we first use a survey of personal networks with 450 cases to perform an empirical study of the differences and correspondences between degree, closeness and betweenness centrality in personal networks. Then, we examine the correspondences between the three global indicators in each type of centrality: the maximum value, the mean value and the hierarchy or centralization. The results provide a better understanding of the centrality indicators of networks and the reality that they express in an empirical context.     

A Collaborative Student Affairs and Faculty Health Assessment and Intervention Initiative

Abstract

The authors describe a collaborative partnership forged between faculty and student affairs staff to improve student health at a large urban university. They examine skills and reward structures of each constituency and the stages of the collaboration in the context of 2 theoretical models. A comprehensive data collection and dissemination process in the campus community provided goals for the initial stage of the partnership, leading to implementation of campus initiatives that use the reciprocal skills of each stakeholder. Outcomes of the collaboration included (1) a working relationship between faculty and student affairs staff, (2) increased dialogue with high-level administrators, (3) more coordinated campus efforts to decrease high-risk drinking, (4) use of outcome measures for implementing and evaluating health programs, and (5) an opportunity for interdisciplinary research. The authors offer suggestions for implementing the process on other campuses.     

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.     

“This is not a drill”: Activation of a student-led influenza vaccination point of dispensing

Objective: To describe activation of a Point of dispensing (POD) in response to an influenza outbreak, highlighting the use of a student-led model. Participants: Faculty, staff, and students of Harris College of Nursing and Health Sciences, Texas Christian University (TCU), as well as those located in its primary building. Methods: In response to an August 2017 influenza outbreak, a vaccination clinic was conducted for a target population through POD activation. The larger campus community was served through provision of additional doses by the Texas Christian University Health Center and the annual October student-led vaccination clinic. Results: Eleven additional cases were diagnosed after vaccinations began. Conclusions: One hundred percent of the targeted population was vaccinated (n = 824), with an additional 127 participants vaccinated (others working in the building where POD held also vaccinated). This was the first time POD activation had occurred on campus in response to an outbreak.     

Interorganizational network portfolios of nonprofit organizations: Implications for collaboration management

Increasingly, nonprofit organizations engage in interorganizational collaboration to address large‐scale social problems. Scholarship typically focuses on the characteristics of both within‐sector and cross‐sector partnerships of two collaborating organizations or all partnering organizations involved in a collaboration, but we know little about the patterns of interorganizational relationships that single nonprofit organizations maintain. This research draws upon surveys from 452 nonprofits and introduces nonprofit network portfolios, which we define as the number, integration, intensity, and duration of relationships that nonprofits purposefully develop with other organizations. Using 12 network measures, Ward cluster analysis revealed three distinct network portfolios: restricted within‐sector (n = 319, 70.58%), which included limited collaboration and prioritized within‐sector partnerships; robust within‐sector (n = 80, 17.70%), which included more nonprofit partnerships than restricted within‐sector portfolios; and cross‐sector (n = 53, 11.72%), which had a rich assemblage of integrative partnerships with nonprofits, businesses, and government agencies. Further, nonprofits that maintained each type of portfolio differed in their revenue and social mission, suggesting these factors are related to the types of collaboration that nonprofits maintain. This study makes contributions to existing research on interorganizational networks and cross‐sector collaboration and suggests practical and policy implications for nonprofit network management.     

Connecting a University to a Distant Neighborhood

Abstract

The willingness on the part of university participants to listen attentively to community representatives is of great importance to successful collaborations. This article presents three phases of a university-community partnership between the Macedonia neighborhood in High Point, North Carolina, and the Center for the Study of Social Issues (CSSI) at the University of North Carolina at Greensboro. Although no professional network and neighborhood contacts were in place prior to this collaboration, the partnership addressed community needs by obtaining federal grant funding and by listening to the residents' concerns. Staff, students, and faculty overcame the challenges of inexperience and the difficulty of working with a neighborhood that was not located near the university. In various phases, the partnership moved away from a technical assistance approach to a self-help model. By actively engaging neighborhood residents through the Community Outreach Partnership Center (COPC), a learning and adaptation process occurred that resulted in successful university-community collaboration.