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**NETWORK > REGIONS > COMPONENTS > VALUED GRAPHS **

**PURPOSE **Identify the weak components corresponding to each cut-off value of a weighted graph.

**DESCRIPTION **In a valued graph, the set of dichotomized graphs corresponding to each possible weight form a nested sequence of graphs. The weak components of each of these would also be nested and can be combined to form an hierarchical clustering of weak components. Once two nodes have been placed in the same weak component of a dichotomized graph for a particular cut-off value they remain in the same weak component for all smaller cut-off values for similarity type measures and larger cut-off values for distance type measures. This procedure produces a hierarchical clustering based on these facts.

**PARAMETERS Input valued network**

** **Name of file containing valued digraph. Data type: Valued graph.

**Operation**(Default = GT-greater than)

Select greater than or greater than and equal to for similarity data and less than or less than or equal to for distance type data.

** Output Dataset **(Default = 'hicomp')

Name of dataset to contain the partition indicator matrix. Each column of this matrix gives the component to which each actor was assigned in a given level. The columns are labeled by the corresponding cut-off value. A value of k in a column labeled x and row j means that actor j was in component k at cut-off value x.

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**LOG FILE **Hierarchical clustering diagram of the components. The columns are rearranged and labeled. A '·' in row label i column label j means that vertex j was not in a weak component with any other vertex (i.e. it was an isolate) using a cut-off value of i. An 'X' indicates that vertex j was in a non-trivial weak component with all vertices on the same row as j which can be found by tracing across that row without encountering a space.

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**TIMING **O(N^4) actually N^2 times the number of different values

**COMMENTS **None

**REFERENCES **None