Was messen Zentralitätsindizes?

Brandes, Ulrik; Kosub, Sven; Nick, Bobo

doi:10.1007/978-3-531-93464-8_3

Cited by 7 publications

(8 citation statements)

References 21 publications

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“…The score of y after adding x → y can only increase because the set of paths coming into y now contains new elements. 19 If the constant vector 1 is replaced by a preference vector v in the definition, it is necessary that x have nonzero score before the addition for score monotonicity to hold. y x z Figure 2: A counterexample showing that SALSA fails to satisfy the score-monotonicity axiom.…”

Section: Score Monotonicitymentioning

confidence: 99%

Axioms for Centrality

Boldi

Vigna

2014

Internet Mathematics

388

322

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Given a social network, which of its nodes are more central? This question has been asked many times in sociology, psychology and computer science, and a whole plethora of centrality measures (a.k.a. centrality indices, or rankings) were proposed to account for the importance of the nodes of a network. In this paper, we try to provide a mathematically sound survey of the most important classic centrality measures known from the literature and propose an axiomatic approach to establish whether they are actually doing what they have been designed for. Our axioms suggest some simple, basic properties that a centrality measure should exhibit.Surprisingly, only a new simple measure based on distances, harmonic centrality, turns out to satisfy all axioms; essentially, harmonic centrality is a correction to Bavelas's classic closeness centrality [5] designed to take unreachable nodes into account in a natural way.As a sanity check, we examine in turn each measure under the lens of information retrieval, leveraging state-of-the-art knowledge in the discipline to measure the effectiveness of the various indices in locating web pages that are relevant to a query. While there are some examples of such comparisons in the literature, here for the first time we also take into consideration centrality measures based on distances, such as closeness, in an information-retrieval setting. The results closely match the data we gathered using our axiomatic approach.Our results suggest that centrality measures based on distances, which in the last years have been neglected in information retrieval in favor of spectral centrality measures, do provide high-quality signals; moreover, harmonic centrality pops up as an excellent general-purpose centrality index for arbitrary directed graphs.

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Section: Score Monotonicitymentioning

confidence: 99%

Axioms for Centrality

Boldi

Vigna

2014

Internet Mathematics

388

322

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“…Betweenness centrality is thus used here as a ‘filter’ metric since it combines one-sided dependence with node importance (see Appendix 1 for algorithmic expressions). More concretely, betweenness combines a reflection of the degree to which the whole network is dependent on a specific agent for its cohesion as well as by summing values of all relevant geodesics and thus remaining a core centrality metric (Brandes et al , 2012). Betweenness, therefore, is employed here to identify all actors that potentially play an exceptional role in relational space.…”

Section: A Network Approach In Decoupling Brokeragementioning

confidence: 99%

Exceptional or just well connected? Political entrepreneurs and brokers in policy making

Christopoulos

Ingold

2014

Eur. Pol. Sci. Rev.

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Policy brokers and policy entrepreneurs are assumed to have a decisive impact on policy outcomes. Their access to social and political resources is contingent on their influence on other agents. In social network analysis (SNA), entrepreneurs are often closely associated with brokers, because both are agents presumed to benefit from bridging structural holes; for example, gaining advantage through occupying a strategic position in relational space. Our aim here is twofold. First, to conceptually and operationally differentiate policy brokers from policy entrepreneurs premised on assumptions in the policy-process literature; and second, via SNA, to use the output of core algorithms in a cross-sectional analysis of political brokerage and political entrepreneurship. We attempt to simplify the use of graph algebra in answering questions relevant to policy analysis by placing each algorithm within its theoretical context. In the methodology employed, we first identify actors and graph their relations of influence within a specific policy event; then we select the most central actors; and compare their rank in a series of statistics that capture different aspects of their network advantage. We examine betweenness centrality, positive and negative Bonacich power, Burt's effective size and constraint and honest brokerage as paradigmatic. We employ two case studies to demonstrate the advantages and limitations of each algorithm for differentiating between brokers and entrepreneurs: one on Swiss climate policy and one on EU competition and transport policy.

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“…Beyond the obvious caveats to generalisation offered in other parts of this article, it is important to point out that each of these findings merits further research attention. Brokerage here is associated with a crude proxy of brokerage, betweenness centrality, which entails both medial and radial features (see Brandes et al, 2012). More sophisticated measures of brokerage such as honest brokerage or Burt’s structural hole measures (see Christopoulos and Ingold, 2015) hold the promise of a more accurate picture of privileged network positions to perceived leadership.…”

Section: Discussionmentioning

confidence: 99%

The impact of social networks on leadership behaviour

Christopoulos

2016

Methodological Innovations

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Dominant streams in leadership literature conceptualise it either as a role within sociopolitical structure or as a behavioural predisposition of agents. Leadership roles are determined by decisional power, most typically related to the hierarchical and structural position of agents within sociopolitical networks. Limitations in attaining meaningful predictions of leader potential can be related to the separation of leadership as an agency attribute from leaders as structurally embedded agents. Social network analysis allows for the contingent examination of both. In this article, a number of hypotheses are tested via an empirical case study where interaction and affiliation networks across multiple decision experiments are coupled with attribute and psychometric data of the actors. In this quasi-experimental setting, leadership emergence is studied among four groups of undergraduate students faced with a decision choice in an iterative political simulation game. Findings suggest that in egalitarian political systems, centrality in social networks is directly associated with political success, while in political systems imbued with power inequalities successful actors are idiocentric brokers. Methodologically, this study frames role simulation games as quasi-experimental tests. Group interactions can be controlled, but vitally also incorporated in studies of perceptions, behaviours and group outcomes. The use of attitudinal micro-surveys, psychometric tests, observation and relational surveys is combined for a comprehensive mapping of group dynamics suited to questions of agency. In conclusion, there are a number of insights offered on deploying these methods in tandem and the challenges inherent in such a research design.

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Was messen Zentralitätsindizes?

Cited by 7 publications

References 21 publications

Axioms for Centrality

Axioms for Centrality

Exceptional or just well connected? Political entrepreneurs and brokers in policy making

The impact of social networks on leadership behaviour

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