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Typical network data describe one or two sets of nodes and the relations among, respectively between the nodes. The data do not necessarily contain, however, any information about the nodes themselves.

A typical problem which is solved by many network techniques is to classify the nodes on the basis on their direct or indirect links or even more complex information such as similarities or distances.

Since an adjacency matrix is a matrix of 1-step distances, we can interpret it as a distance matrix describing the distances between two sets of nodes, where is the number of nodes in the row set and the number of nodes in the column set. All directly connected pairs have an entry of one and all unconnected pairs an entry of zero, indicating the absence of a relation.

There is no reason not to use other distance matrices, which usually contain richer information than the adjacency matrix of a graph: the reachability matrix as a graph-theoretic distance measure or even similarities or distances resulting from more complex operations.

Roger Shepard's (1972) taxonomy of principal datatypes as a basis for muldimensional scaling procedures provides the concepts necessary to distinguish the basic information from technical transformations applied to yield an empirical distance matrix, which allows a fitting algorithm to find an optimal solution for a given model space.

Lothar Krempel
Fri Mar 31 13:14:02 MET DST 1995