Learn how to read gravity visualizations

The Reconstruction of a Hierarchical Organization

Hierachies are a typical example of a real life structure in the social sciences. Consider for example a traditional organization as it is shown below.

Tree structures are a very efficient way to link a large number of people with a minimal number of ties.

But this type of structure also has a disadvantage: the overall organization falls apart into disconnected subsystems if any of its links fails.

information typically available from observations ..

The information that is usually available from empirical observations is a list of pairs: that B communicates with A, C communicates with A , etc . Under favorable conditions a researcher investigating an unknown organization would succeed in identifying all communication channels. How can we reconstruct the original image from these data ?

Before we proceed it is useful to look at some of the structural properties of the nodes which can be derived from the observations. An important characterstic is the centrality of the nodes.

Centrality can focus on various aspects of a structure: If we let the number of direct links each node is engaged in determine the size of the spheres, we are guided to the most active members of the organization. Note the illusion: the size of the spheres does not correspond to their mass but is only used to guide our eyes to nodes with many links!

The Reconstruction Process

a first attempt

the iteration phase ...

applying forces ...

The director A has moved almost to the center, whereas B and C are in the middle of their subordinates. D E and F as well as G , H and I have moved close to their two-person workgroups: the less central actors of the system are located in the periphery whereas the central actors are located in the core of the system.

If you are still worried about the small irregularities of the last visualization, you should have a closer look at the gravity iterations which will provide a deeper insight into the applied procedures.

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Lothar Krempel, MPI für Gesellschaftsforschung, Lothringerstr.78, 50677 Köln, Germany
email: krempel@mpi-fg-koeln.mpg.de