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NETWORKS > CENTRALITY > REACH CENTRALITY

PURPOSE Counts the number of nodes each node can reach in k or less steps. For k = 1, this is equivalent to degree centrality. For directed networks, both in-reach and out-reach are calculated. The routine also caculates weighted distance reach centrality for each vertex..

DESCRIPTION The input is a binary network. The output is a node by distance matrix X in which xij indicates the proportion of nodes that node i can reach in j or fewer steps.  In a connected network, each row will eventually reach 1 (100%). The routine first calculates the weighted distance reach centrality of each node. That is the sum of the number of actors that can be reached in k steps divided by k, this is the same as reciprocal distance closeness plus one.

In addition, the routine calculates some descriptive statistics based on these measures.

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

Output reach centrality: (Default = 'ReachCentrality')
Name of file which will contain distance weigthted reach and normalized distance weigthed reacfor each node. If the data is directed both in and out reach centrality scores are calcilated.

Ouput node-by-dist mat:
Output file that will contain the node by distance matrix described in the log file below.

LOG FILE
The distance weighted reach and normalized distance weighted reach centrality scores for each node. Both in and out scores are reported for directed data. Some descriptive statistics for the set of measures.
A table that gives the proportion of nodes reached by each node at each level of distance. The proportion is expressed as a value from zero to one. A value of x in row i column j means that 100x% of nodes are reachable from i in a path of length j or less. For directed data values for those that can be reached from the node and those that can reach the target node are reported.

TIMING O(N^2).

COMMENTS When searching for key individuals who are well positioned to reach many people in a few number of steps, this measure provides a natural metric for assessing each node.

REFERENCES