https://www.bebr.ufl.edu/sites/default/files/Centrality%20in%20Social%20Networks.pdf

Centrality in social networks conceptual clarification

http://www.analytictech.com/borgatti/papers/borgatti%20-%20Centrality%20in%20valued%20graphs%20-%20A%20measure%20of%20betweenness%20based%20on%20network%20flow.pdf

Centrality in valued graphs: A measure of betweenness based on network flow

Rethinking centrality: Methods and examples☆

This paper presents a theoretical analysis of the structural determinants of power in exchange networks, along with research findings from laboratory experiments and a computer simulation of bargaining in network structures. Two theoretical traditions are dealt with: (1) point centrality in graph-theoretic representations of structure, as an approach to power distributions; and (2) powerdependence principles applied to exchange networks. Measures of centrality available in the literature have the advantage of being easily applied to large and complex networks. In contrast, powerdependence concepts were conceived for use in microsociology and are found to be cumbersome in the analysis of complex networks. But despite the relative difficulty of applying power-dependence theory to network structures, that approach generates hypotheses about power distributions which are confirmed at nearly every point in a laboratory experiment with five-person networks and at every point in a computer simulation of networks too large for laboratory study. In contrast, centrality measures applied to the type of networks studied fail to predict power distributions. Although centrality measures might predict power in some networks, their generality is limited. Toward resolution of the issues raised, this study offers two theoretical points: (1) a distinction between two different principles of "connection" in social networks suggests that current measures of centrality might predict power in one type of network but not in the other; and (2) it offers a first step toward a fusion of power-dependence theory and structural centrality in a way which might be general across networks of both types.

/pdf/the-distribution-of-power-in-exchange-networks-theory-and-1065h4e4vw.pdf

The Distribution of Power in Exchange Networks: Theory and Experimental Results

The application of the network approach to the urban case poses several questions in terms of how to deal with metric distances, what kind of graph representation to use, what kind of measures to investigate, how to deepen the correlation between measures of the structure of the network and measures of the dynamics on the network, what are the possible contributions from the GIS community. In this paper, the author considers six cases of urban street networks characterized by different patterns and historical roots. The authors propose a representation of the street networks based firstly on a primal graph, where intersections are turned into nodes and streets into edges. In a second step, a dual graph, where streets are nodes and intersections are edges, is constructed by means of a generalization model named Intersection Continuity Negotiation, which allows to acknowledge the continuity of streets over a plurality of edges. Finally, the authors address a comparative study of some structural properties of the dual graphs, seeking significant similarities among clusters of cases. A wide set of network analysis techniques are implemented over the dual graph: in particular the authors show that the absence of any clue of assortativity differentiates urban street networks from other non-geographic systems and that most of the considered networks have a broad degree distribution typical of scale-free networks and exhibit small-world properties as well.

/pdf/the-network-analysis-of-urban-streets-a-dual-approach-57sq5ufcpd.pdf

The network analysis of urban streets: A dual approach

.— The paper considers the concept of centrality in an undirected graph. A system of axioms and an index for centrality satisfying the axioms are presented. The index is based on the degrees of the vertices in a given undirected graph, and it will enlarge the class of comparable graphs with respect to a centrality measure.

Juhani Nieminen

Papers

On the centrality in a graph