On centrality functions of a graph

Kishi, G.

doi:10.1007/3-540-10704-5_5

Cited by 4 publications

(2 citation statements)

References 2 publications

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“…Avoiding the difficulties and context-specific limitations of measurement theory, several authors have taken axiomatic approaches to characterize centrality indices (e.g. Kishi, 1981; Ruhnau, 2000; Sabidussi, 1966), and such characterizations may help selecting or ruling out indices for specific purposes. See Boldi and Vigna (2014) for a recent account with many references.…”

Section: Centralitymentioning

confidence: 99%

Network positions

Brandes

2016

Methodological Innovations

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A formal definition of position in networks is proposed. Based on the conceptualization of networks as data on intersecting dyads, it leads to integrated means of analysis for various kinds of relational and attribute data and to a simultaneous unification and generalization of a wide range of network-analytic methods. In fact, by defining network positions explicitly, various methods can be broken down into sequences of generic steps that are more amenable to substantive theorizing, integration of qualitative insight, and empirical validation.

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Section: Centralitymentioning

confidence: 99%

Network positions

Brandes

2016

Methodological Innovations

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“…This paper uses the following f ( v ) which is defined by setting $(t) = t, representative among centrality functions defined in Eq. (6) : ( 7 ) By the definition of g (u, V ) the value of f ( v ) represents the sum of flow quantities between v and other vertices. All the discussions below are made concerning this centrality function.…”

Section: Introductionmentioning

confidence: 99%

Synthesis of a flow network with a given centrality on each vertex

Takeuchi

Kishimoto

Kishi

1989

Electron Comm Jpn Pt III

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This paper considers the problem of constructing a flow network when the centrality at each vertex is given. Here, attention is given to a centrality function such that the centrality at a vertex under consideration is the sum of maximum flow values between it and all other vertices. It is a representative centrality function among those representing the centrality of each vertex in an undirected flow network in which edges have capacity. First, we introduce a necessary and sufficient condition wherein a given sequence is a centrality sequence for a flow network. Next, we present a procedure for determining a terminal capacity matrix of a flow network with a given centrality sequence. Furthermore, we determine a terminal capacity matrix of a flow network with a given centrality sequence such that the sum of edge capacity is minimum. From these discussions we can see that the problem of constructing a flow network when a centrality is given, can be reduced to the previously known problem of constructing a flow network when a terminal capacity matrix is given.

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