scispace - formally typeset
Open AccessJournal ArticleDOI

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

Linton C. Freeman, +2 more
- 01 Jun 1991 - 
- Vol. 13, Iss: 2, pp 141-154
Reads0
Chats0
TLDR
A new measure of centrality, C, is introduced, based on the concept of network flows, which is defined for both valued and non-valued graphs and applicable to a wider variety of network datasets.
About: 
This article is published in Social Networks.The article was published on 1991-06-01 and is currently open access. It has received 996 citations till now. The article focuses on the topics: Betweenness centrality & Random walk closeness centrality.

read more

Citations
More filters
Journal ArticleDOI

Centrality and network flow

Stephen P. Borgatti
- 01 Jan 2005 - 
TL;DR: A key claim made in this paper is that centrality measures can be regarded as generating expected values for certain kinds of node outcomes given implicit models of how traffic flows, and that this provides a new and useful way of thinking about centrality.
Journal ArticleDOI

Node centrality in weighted networks: Generalizing degree and shortest paths.

Tore Opsahl, +2 more
- 01 Jul 2010 - 
TL;DR: This paper proposes generalizations that combine tie strength and node centrality, and illustrates the benefits of this approach by applying one of them to Freeman’s EIES dataset.
Journal ArticleDOI

A measure of betweenness centrality based on random walks

Mark Newman
- 01 Jan 2005 - 
TL;DR: In this paper, the authors propose a measure of betweenness based on random walks, counting how often a node is traversed by a random walk between two other nodes, not just the shortest paths.
Journal ArticleDOI

Models of core/periphery structures

Stephen P. Borgatti, +1 more
- 01 Oct 2000 - 
TL;DR: This paper seeks to formalize the intuitive notion of a core/periphery structure and suggests algorithms for detecting this structure, along with statistical tests for testing a priori hypotheses.
Journal ArticleDOI

A Graph-theoretic perspective on centrality

Stephen P. Borgatti, +1 more
- 01 Oct 2006 - 
TL;DR: This paper develops a unified framework for the measurement of centrality and shows centrality to be intimately connected with the cohesive subgroup structure of a network.
References
More filters
Journal ArticleDOI

A Set of Measures of Centrality Based on Betweenness

Linton C. Freeman
TL;DR: A family of new measures of point and graph centrality based on early intuitions of Bavelas (1948) is introduced in this paper, which define centrality in terms of the degree to which a point falls on the shortest path between others and there fore has a potential for control of communication.
Journal ArticleDOI

Power and Centrality: A Family of Measures

Phillip Bonacich
- 01 Mar 1987 - 
TL;DR: In this article, the rank orderings by the four networks whose analysis forms the heart of this paper were analyzed and compared to the rank ordering by the three centrality measures, i.e., betweenness, nearness, and degree.
Book

Flows in networks

D. R. Ford, +1 more
TL;DR: Ford and Fulkerson as mentioned in this paper set the foundation for the study of network flow problems and developed powerful computational tools for solving and analyzing network flow models, and also furthered the understanding of linear programming.
Journal ArticleDOI

Flows in Networks.

Frank Harary, +2 more
- 01 Nov 1964 - 
TL;DR: The techniques presented by Ford and Fulkerson spurred the development of powerful computational tools for solving and analyzing network flow models, and also furthered the understanding of linear programming.
Journal ArticleDOI

A new status index derived from sociometric analysis.

Leo Katz
- 01 Mar 1953 - 
TL;DR: A new method of computation which takes into account who chooses as well as how many choose is presented, which introduces the concept of attenuation in influence transmitted through intermediaries.
Frequently Asked Questions (10)
Q1. What contributions have the authors mentioned in the paper "Centrality in valued graphs: a measure of betweenness based on network flow" ?

In this paper, Friedkin et al. introduced three new betweenness-based measures of centrality. 

A numeric value is associated with each edge in E by defining afunction, or mapping, C from the Cartesian product S X S to some subset of the non-negative integers. 

The flow-based measures of centrality can be applied to ordinary non-valued graphs by assigning all edges the uniform value of 1. 

If the authors think of the edges of the graph as channels of communication linking pairs of people, then the value of the connection linking two people determines the capacity of the channel linking them, or the maximum amount of information that can be passed between them. 

of course, if x and y are not adjacent, then the capacity of the channel linking them directly is zero, and there can be no direct flow from one to the other. 

It is called an i-j cut set because if the edges in E,, were “Cut,” or removed from the graph, x, would no longer be reachableFig. 

Whenever a graph contains no cycles, every pair of points in that graph is either (1) reachable by a single path, or (2) unreachable. 

Flow is constrained only by the channel capacities and by two additional conditions: (1) the flow out of x, must be equal the flow into x,, and (2) the flow out of each intermediate point on any indirect path connecting x, to x, must be equal to the flow into that point. 

When the capacities of all channels in a an acyclic valued graph are uniformly set at 1, the maximum flow between any reachable pair of points must be exactly 1. 

The consensus is that binary representations fail to capture any of the important variability in strength displayed in actual interpersonal relationships.