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NETWORK > EGO NETWORKS > BROKERAGE


PURPOSE Calculates the brokerage measures proposed by Gould & Fernandez (1989). 

DESCRIPTION Given (a) a graph, and (b) a partition of nodes, this procedure calculates measures of five kinds of brokerage. Brokerage occurs when, in a triad of nodes A, B and C, A has a tie to B, and B has a tie to C, but A has no tie to C. That is, A needs B to reach C, and B is therefore a broker. When A, B, and C may belong to different groups, 5 kinds of brokerage are possible. The five kinds are named using terminology from social roles. In the description below, the notation G(x) is used to indicate the group that node x belongs to. Important:  It is assumed that a-->b-->c. For example, a (the source node) gives information to b (the broker), who gives information to c (the destination node). 
  
Coordinator. Counts the number of times b is a broker and G(a) = G(b) = G(c), that is, all three nodes belong to the same group.

Consultant.  Counts the number of times b is a broker and G(a) = G(c), but G(b)¹ G(a); that is, the broker belongs to one group, and the other two belong to a different group. 

Gatekeeper.  Counts the number of times b is a broker and G(a) ¹ G(b) and G(b) = G(c), that is, the source node belongs to a different group. 

Representative.  Counts the number of times b is a broker and G(a) = G(b) and G(c) ¹ G(b). That is, the destination node belongs to a different group. 

Liaison.  Counts the number of times b is a broker and G(a) ¹ G(b) ¹ G(c). That is, each node belongs to a different group.

When b is not the only intermediary between a and c, it is possible to give b only partial credit. That is, if there are two paths of length two between a and c, one of which involves b, we can choose to give b only 1/2 point instead of a full point. This is an option in the program.

The routine calculates these measures for each node in the network, and also the total of the five.  

The program also computes the expected values of each brokerage measure given the number of groups and the size of each group. That is, the expected values under the assumption that brokerage is independent of the group status of nodes. A final output divides the observed brokerage values by these expected scores. 

PARAMETERS Input dataset:
Name of file containing network to be analyzed. Data type: Digraph

Partition vector:
The name of an UCINET dataset that contains a partition of the actors. To partition the data matrix into groups specify a vector by giving the dataset name, a dimension (either row or column) and an integer value. For example, to use the second row of a dataset called ATTRIB, enter "ATTRIB ROW 2". The program will then read the second row of ATTRIB and use that information to define the groups. All actors with identical values on the criterion vector (i.e. the second row of attrib) will be placed in the same group.


Method: (default = 'unweighted')
Choices are 'unweighted' and 'weighted'. Unweighted directs the program to simply count up the number of times that a given node b is in a brokering position, regardless of how many other nodes are serving the same function with the same pair of endpoints a and c. Weighted directs the program to give partial scores in inverse proportion to the number of alternatives. 
 
(Output) Un-normalized Brokerage
Name of the file containing the raw count of scores for each type of brokerage.

(Output) Normalized Brokerage
Name of file containing brokerage scores divided by the expected values.
 

LOG FILE A table giving the brokerage scores for each node for the five broker types together with the total score.
For each node a table giving the number of times the node acts as a broker between the groups. Hence the i,j th entry in the table for node k gives the number of times k acts as a broker (of any kind) from group i to group j.
 
A table giving the brokerage scores divided by the expected values. 

A table giving the expected values. 

TIMING O(n^3).

COMMENTS None 

REFERENCE Gould, J. and Fernandez, J. 1989. Structures of mediation: A formal approach to brokerage in transaction networks. Sociological Methodology :89-126.