12th Applied Statistics 2015
International Conference
September 20 - 23, 2015
Ribno (Bled), Slovenia

Past conferences:

2013 2012 2011 2010  2009
2008 2007 2006 2005  2004
 before 2004


  Important dates

  Acceptance note
     July 1
  Reduced early
  payment fee
     July 15



A Few Notes on Centrality and Flow

Stephen P. Borgatti
 University of Kentucky, USA

Centrality is often described as measuring the “importance” of a node in a network.  Dozens of measures have been proposed in the literature, most of which can be characterized quite directly in terms of a node’s involvement in the walk structure of a network (e.g., the average distance from the node to all other nodes; the number of walks of all lengths emanating from a node, weighted inversely by their length). Under a general rubric of social capital, measures of centrality are often used to predict node outcomes, such as career success. Unfortunately, almost none of these measures are explicitly derived from any kind of model of what is happening in the network and how these processes lead to the outcome state of each node. It is true that it has been shown that some centrality measures implicitly contain (or are consistent with) underlying models of network flows. For example, the formula for betweenness centrality yields precisely the expected values of the number of times that a token flowing through the network will reach a given node, given that the token takes only shortest paths, can only be in one place at one time, and chooses randomly between equally short paths. The problem is, this implicit model virtually never makes sense in the empirical settings where these measures are employed. For example, in the management field, we commonly study flows of information among members of an organization. Yet information does not travel only along shortest paths. Indeed, information does not try to get anywhere in particular, and no mind is guiding it, through intermediaries, to a specific target. It also does not so much “move” from node to node as “copy” – i.e., it can be in more than place at a time. There are several other models that are implicit in the set of extant centrality measures, but it is safe to say that they too are inappropriate for the vast majority of empirical settings social scientists wish to model. The objective of this paper is to explore new measures that are based on more plausible flow processes.  
 Applied Statistics 2015      http://conferences.nib.si/AS2015                                e-mail: info.AS@nib.si