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**NETWORK > COHESION > REACHABILITY**

**PURPOSE **Constructs a matrix of reachability values for every pair of nodes.

**DESCRIPTION **The reachability for a pair of nodes is the value of an optimum path.

The algorithm produces a value in row i, col j of a matrix if node j is reachable from node i and a blank otherwise.

This value can be any of the following:

The length of the shortest path.

The cost of the cheapest path, where the cost is the sum of all the values.

The strength of the strongest path, where the strength is the value of the weakest link.

The probability of the most 'probable' path, where the probability of a path is the product of the probabilities of its edges.

**PARAMETERS**

**Input dataset**

** **Name of file containing dataset to be analyzed. Data type: Valued graph.

**Type of Data: **(Default = ADJACENCY)

Choices are:

**Adjacency** - standard binary data, distance corresponds to graph theoretic geodesic.

**Strengths **- values indicate cost or lengths of links between nodes.Optimum is strongest path.

**Costs** - values indicate strengths, capacities or cost.Optimum is the cheapest cost.

**Probabilities** - values indicate probability of link and restricted to [0,1]. Optimum is most probable path.

**Output dataset:** (Default = 'Reachability')

Name of data file containing reachability matrix.

**LOG FILE **Matrix of reachability values between all pairs of nodes.

**TIMING **O(NLOGN)

**COMMENTS **None but see comments on

** ****NETWORK>COHESION>DISTANCE**

**REFERENCES** Doreian P (1974). 'On the connectivity of Social Networks'. Journal of Mathematical Sociology, 3, 245-258.