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NETWORK > REGIONS > COMPONENTS>SIMPLE GRAPHS

PURPOSE Identify the components, of an undirected graph - and the weak or strong components of a directed graph and find the main component.

DESCRIPTION In an undirected graph two vertices are members of the same component if there is a path connecting them. In a directed graph two vertices are in the same weak component if their is a semi-path connecting them. Two vertices x and y are in the same strong component if there is a path connecting x to y and a path connecting y to x. The largest component is called the main component.The routine finds all the components (weak or strong) and creates UCINET files corresponding to the main component. In addition it reports Blau's measure of heterogeneity which is 1 minus the sum of the squares of the proportions of the size of each component, the normalized Blau score, the entropy (-Spln(p)), normalized entropy and the fragmentation (proportion of vertices that cannot reach each other).

PARAMETERS
Input dataset:
Name of file containing network data to be analyzed. Dat type: Directed graph.

Minimum Size to save: (Default = 3)
Size of smallest component which is to be saved in the component by actor incidence matrix specified below.

Kind of components: (Default = Strong)
For directed data specify whether Strong or Weak components are required. For undirected data either choice will yield the components.

Output sets: (Default = 'Components_Sets')
Name of file which will contain a component by actor incidence matrix. A 1 in row i column j means that node j is in component i. This file is not displayed in the LOG FILE.

Output Partition matrix: (Default = 'Components_Partition')
Name of file which will contain a partition vector. A j in the ith position means that node i is a member of component j. This file is not displayed in the LOG FILE.

Output Main Comp.Vec:(Default=InMainComp)
Name of file which contains an indicator vector where a 1 in row i indicates that i is a member of the main component and a 0 indicates that it is not a member. This file is not displayed in the LOG FILE.

LOG FILE Number of components found.
List of all nodes indicating which labeled component each node is in.
List of components greater than minimum size, labeled - each component is specified by the vertices it contains.
Blau heterogeneity, normalized heterogeneity, entropy, normalized entropy and fragmentation scores.

TIMING O(N^2).

COMMENTS None.

REFERENCES None.