A GALLERY OF SOCIAL STRUCTURES
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.
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The Tree Structure of a Social Organisation
Think of A as the president with
B and C as his directors.
Each director heads a department of three workgroups with
D, E, F and G, H, I as project leaders .
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!
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Nodesize illustrating the number of direct links
If we want to draw trees automatically we have to make use of
information which is available in the overall structure.
A simple method could be to count with how many
other actors each member of the organization is connected to.
The Reconstruction Process
a first attempt
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A random placement of the nodes
A first step toward reconstructing the overall structure
from the relational information is to assign all nodes randomly to a number
of points evenly spaced along a circle and draw/compute the lines which
link these nodes. This is the start configuration for the iteration phase.
the iteration phase ...
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A minimal line length solution
A procedure which minimizes the overall line length
for the total structure could yield this result.
Note the the lowest level members are already neighbours of their
workgroup leaders and that the only ambivalence of this solution is
caused by the placement of A, B and C.
applying forces ...
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A result of the gravity procedure
While the circle permutation has already brought some order into
total system we get more accurate information when we apply a force
model to the above solution.
All nodes of equal closeness are placed on concentric circles around the
center of gravity of the total system.
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
Nodesize illustrating centrality
A minimal line length solution