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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**