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.     

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.

     

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.     

Egocentric,sociocentric, or dyadic?: Identifying the appropriate level of analysis in the study of organizational networks

This paper examines the use of individual, dyadic and system-level analyses in the study of relational data in organizational networks. We argue that dyadic analyses are particularly appropriate when the dependent variable is quantitative and/or involves multiple behaviors. We show that system-level analyses, by aggregating potentially significant information, provide a less grounded account of the relations across networks than do dyadic analyses. Using examples from a study of corporate political behavior, we contrast dyadic analyses with those at both the individual and system-levels. Variables measured in raw dyadic form consistently perform better in accounting for similarity of corporate political behavior than do variables measured by taking system-level properties into account. Our findings suggest that although individual and system-level analyses are useful in a number of situations, dyadic analyses are a flexible means to examine the effects of multiple networks at multiple levels.     

Eigenvector-like measures of centrality for asymmetric relations

Eigenvectors of adjacency matrices are useful as measures of centrality or of status. However, they are misapplied to asymmetric networks in which some positions are unchosen. For these networks, an alternative measure of centrality is suggested that equals an eigenvector when eigenvectors can be used and provides meaningfully comparable results when they cannot.     

A note on measures of similarity based on centrality

This note presents a measure of similarity between connected nodes in terms of centrality based on Euclidean distances, and compares it to ‘assortative mixing’ [Newman, M.E.J., 2002. Assortative mixing in networks. Physical Review Letters 89, 208701], which is based on Pearson correlation coefficient. This study suggests that the measure based on Euclidean distances may be more appropriate for relatively smaller (N < 500) and denser networks.     

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.     

On the robustness of centrality measures under conditions of imperfect data

An analysis is conducted on the robustness of measures of centrality in the face of random error in the network data. We use random networks of varying sizes and densities and subject them (separately) to four kinds of random error in varying amounts. The types of error are edge deletion, node deletion, edge addition, and node addition. The results show that the accuracy of centrality measures declines smoothly and predictably with the amount of error. This suggests that, for random networks and random error, we shall be able to construct confidence intervals around centrality scores. In addition, centrality measures were highly similar in their response to error. Dense networks were the most robust in the face of all kinds of error except edge deletion. For edge deletion, sparse networks were more accurately measured.     

Connecting for success: Egocentric network types among underrepresented minority students at college

This study investigates the egocentric networks of underrepresented minority students. Adjustment to college for underrepresented minority students often means balancing between the origin (i.e., low-status family) and host (i.e., academic) environments, requiring students to develop different coping strategies. The analysis included 124 Roma university students. We employed the contact diary method and the EgoNet program for mapping students’ egocentric networks. We explored classification among egocentric networks by cluster analysis based on the network proportion of the origin, fellow, and host groups. Three clusters were distinguished. The Host-based cluster proved to be the most advantageous, while the Balancing cluster appeared to be the most disadvantageous in terms of network resources, well-being, and trust. Partners’ ethnicity and educational attainment showed a strong connection with cluster membership. Our results highlight that small fellow communities can successfully interconnect the origin and host groups in students’ egocentric networks.     

Network centrality and social movement media coverage: A two-mode network analytic approach

This article examines the relationship between structural location (namely, degree centrality) and news media coverage. Our central hypothesis is that the network centrality of social movement actors is positively associated with the prevalence of actors being cited in the print news media. This paper uses two-mode data from a communication network of environmentalists in British Columbia, and examines the relationship between their structural location and the frequency by which they are cited in newsprint media with regard to particular frames (about forest conservation, environmental protest, and related issues). We asked a sample of social movement participants about their ties to a target list of relatively high profile actors (environmental activists). We turned the resulting network matrix into a bipartite graph that examined the relationships amongst the target actors vis a vis the respondents. Next we calculated point in-degree for the target actors. For the target actors we also have data from a representative sample of 957 print news articles about forestry and conservation of old growth forests in British Columbia. We compare the effects of network centrality of the target actor versus several attributes of the target actors (gender, level of radicalism, leadership status) on the amount of media coverage that each of the target actors receives. We find that network centrality is associated with media coverage controlling for actor attributes. We discuss theoretical implications of this research. Finally, we also discuss the methodological pros and cons of using a “target name roster” to construct two-mode data on social movement activists.     

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.     

Induced, endogenous and exogenous centrality

Centrality measures are based upon the structural position an actor has within the network. Induced centrality, sometimes called vitality measures, take graph invariants as an overall measure and derive vertex level measures by deleting individual nodes or edges and examining the overall change. By taking the sum of standard centrality measures as the graph invariant we can obtain measures which examine how much centrality an individual node contributes to the centrality of the other nodes in the network, we call this exogenous centrality. We look at exogenous measures of degree, closeness and betweenness.     

Egocentric contact networks in comparison: Taiwan and Hungary

This study compares the size and structure of egocentric networks in Taiwan and Hungary using a diary approach. Both countries have transformed from authoritarian regimes to democratic states, yet they differ in social, economic, and cultural institutions that may be common to the respective larger region where each is located. To sample the structure of each egocentric network, we extracted information from largely identical contact diaries collected in both countries, 51 from Taiwan and 138 from Hungary. After comparing sample characteristics, network size, and composition, we construct a Strength of Ties (SoT) index based on two objective and two subjective measures of ego-alter ties. We then use this index to analyze tie strength by the types of relationships. On average, the number of alters contacted in one week is much larger in Taiwan than in Hungary, and the gap remains unchanged after controlling for key socio-demographic background factors. Even though the four indicators that we use to construct the SoT index are distributed similarly among the respondents in both Taiwan and Hungary, the composite index pinpoints how the types of relationships play somewhat different roles across the nations. The findings imply that the tendency to maintain only the closest ties with kin and other close friends is linked to distrust in others, a possible ill effect lingering from the authoritarian past. The implication is partially supported by further analyses using the ISSP 2006 survey data. We address how our findings may contribute to the existing literature on the linkage between societal characteristics and interpersonal ties.     

Reinterpreting network measures for models of disease transmission

In the wake of AIDS and HIV, a better framework is needed to model the pattern of contacts between infectious and susceptible individuals. Several network measures have been defined elsewhere which quantify the distance between 2 nodes, and the centrality of a node, in a network. Stephenson and Zelen (S-Z), however, have recently presented a new measure based on statistical estimation theory and applied it to a network of AIDS cases. This paper shows that the closeness measure proposed by S-Z is equivalent to the effective conductance in an electrical network, fits the measure into the existing theory of percolation, and provides a more efficient algorithm for computing S-Z closeness. The S-Z methodology is compared with the closeness measures of maximal flow, first passage time, and random hitting time. Computational problems associated with the measure are discussed in a closing section.     

Sorting out centrality: An analysis of the performance of four centrality models in real and simulated networks

Although the concept of centrality has been well developed in the social networks literature, its empirical development has lagged somewhat. This paper moves a step in that direction by assessing the performance of four centrality models under a variety of known and controlled situations. It begins by examining the assumptions underlying each model, as well as its behavior in a community influence network. It then assesses the robustness and sensitivity of each model under conditions of random and systematic variation introduced into this network.     

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.     

Cluster analysis of multiplex networks: Defining composite network measures

Social relations are multiplex by nature: actors in a group are tied together by various types of relationships. To understand and explain group processes it is, therefore, important to study multiple social networks simultaneously in a given group. However, with multiplexity the complexity of data also increases. Although some multivariate network methods (e.g. Exponential Random Graph Models, Stochastic Actor-oriented Models) allow to jointly analyze multiple networks, modeling becomes complicated when it focuses on more than a few (2–4) network dimensions. In such cases, dimension reduction methods are called for to obtain a manageable set of variables. Drawing on existing statistical methods and measures, we propose a procedure to reduce the dimensions of multiplex network data measured in multiple groups. We achieve this by clustering the networks using their pairwise similarities, and constructing composite network measures as combinations of the networks in each resulting cluster. The procedure is demonstrated on a dataset of 21 interpersonal network dimensions in 18 Hungarian high-school classrooms. The results indicate that the network items organize into three well-interpretable clusters: positive, negative, and social role attributions. We show that the composite networks defined on these three relationship groups overlap but do not fully coincide with the network measures most often used in adolescent research, such as friendship and dislike.     

The restructuring process and economic centrality in capitalist agriculture

The purpose of the paper is to examine contemporary relations in agricultural production. The discussion focuses upon the internal and external processes modifying production relations on the farm and, in particular, the changing significance of farm-based sources of income and capital (economic centrality) to the farm business in the restructuring of agricultural capital. There are a variety of reasons why farm businesses are finding it increasingly necessary to diversify their sources of income, and in some cases capital generation, which relate to their internal family relations and external contacts. While obtaining alternative sources of income for farmers may be advocated for the purpose of reducing their marginalisation and low income problems, this may only be realisable for a minority. The complexities of farm businesses and their external relations with other forms of capital suggest the need for a construction of a typology which focuses on the economic centrality of the business to the farm family. The discussion here is divided into four sections. First, the main characteristics of the restructuring process in British agriculture are identified, leading to a discussion focusing on the transformation of the family farm. The concept of economic centrality is then discussed as an important characteristic of the restructuring process affecting British farming, and a typology of farm businesses established, based upon empirical evidence collected from London's Metropolitan Green Belt. This evidence forms part of a wider study of the changing structure of farm businesses in three areas of lowland England (East Bedfordshire, West Dorset and London's Green Belt) which links farm business change to changes in the farm landscape.