Footnotes

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Revised version of a presentation at the 3rd European Conference for Network Analysis, Muenchen, 1993. Thanks to Cynthia Lehmann for revising my english manuscript. More information about network visualization is available via Mosaic under following URL: http://www.mpi-fg-koeln.mgp.de/lk/netvis.html

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The size of the nodes in this and all following figures is proportional to the sum of both the in- and outdegree of a node. This characterizes a node by all direct activities it is engaged in and reflects the direct component of centrality.

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The two different rank-orders of centrality are listed in Table gif: for direct links the algorithm proceeds according to the rank-order given in the column 'Degree of Centrality', while for geodesics the rank-order given under 'Closeness' is used. As the reader can verify, the 'boundary spanners' have higher ranks (are more central) when geodesics are used.

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To prevent unwanted weights from entering into the optimization procedure, the algorithm locates each of the organizational shapes on a second circle, choosing the diameters of the larger circle to correspond to the diameters of the shapes representing the single systems.

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While Figure gif was one of the first results we achieved with our algorithm, there is also some further criticism because circles C and D seem to be interchanged. This results from using a square arrangement for the four circles. Because the diagonal whithin a square is longer than one of its sides, the overall distance for the total system could have been reduced by interchanging C and D. For an automatic solution, we would have to use a two-level strategy: first to assign each of the four a priori blocks to their best fitting shape, and then to rearrange the nodes in each of the subsystems in a second step.

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