Figure: A System of Organizational Systems
The case of interest here is a system of three organizational systems for which a complete matrix of interlocks between their advisory bodies has been reconstructed on the basis of available documents.
The specific missions of the subsystems as they are laid down in their organizational charters are basic research, implementation of large-scale projects and applied research. There is an ongoing political discussion about whether the overall design facilitates an efficient transfer of basic knowledge to more applied levels and industry.
are numerous opinions on how and whether such a system can be adequately governed and its overall efficiency enhanced, and while these opinions draw on an almost infinite number of causes and explanations, knowledge about the system's actual structure and its actual patterns of coordination are sparse and hidden in many dispersed documents.
Without our going into detail, it seems worthwhile to simply describe the system as a whole on the basis of the more or less institutionalized relations in and between its components. This will eventually allow us to locate coherent boundary spanning subsystems. Such a finding could prove quite useful for the organizations when they want to articulate their situation vis-a-vis one of several commissions which are installed for setting priorities for the entire system and for redistributing money between the subsystems.
The network data of the total system can be expected to reflect part of the inner structure of each of the systems, while the intersystem domain can be expected to reflect partly relations between the top levels of the subsystems and partly the disciplinary coordination between members of different subsystems working in similar substantive domains.
Choosing among the various alternatives for visualizing this dataset, we have decided not to start from the systems perspective and decompose the total system using the empirical network information, but to contrast the empirical data with the more commonly understood institutional layout as it corresponds to the formal charters of the subsystems.
This has lead us to assign each of the subsystems to different but equal-sized shapes, based on the common a priori understanding and formalized design. The shapes themselves are organized to form a regular pattern. By doing this, we have constrained the solution for the total system in various ways: a member of subsystem A may only be placed on one of the permissable locations of shape A, the same holding true for members of the other a priori sets B, C and D.
The algorithm itself exploits the full matrix describing the
entire system. In order to optimize for the degree of
centrality a member of A, B .. C has in the entire system, it tries to
place the most central elements first. The
centrality of each actor reflects its
embeddedness into the local subsystem as well as its links into the global
system. The solution will show that position in the target space
which minimizes both the internal and external relations 
.
The result is found
in Figure 
. It exhibits a considerable amount of ordered information:
nodes with no intersystem orientation are moved to the nonadjacent
locations of each shape: the entire system's periphery. Players in the
intersystem domain are oriented toward their main partners in the
other shapes. Furthermore, organizations with access to more than one
of the neighbouring systems are placed in between.
Figure: An organizational system and its interface to industry
While we find the overall result to be more impressive than we had
hoped for, and while it has proven to be useful for our purposes, Figure
also exhibits areas in which the placement of elements
has not be carried out in such a way that the location of each single
element is always best: an indicator of a too-rigorously constrained
solution space. Depending on the degree of outward orientation in the
subsystems, it happens that organizations are moved towards the
periphery despite being players in the intersystem domain. These
misplacements are errors that result from a solution space which
does not provide enough positions on the adjacent side of
the shape. Nevertheless, even these errors are controlled to the
degree that such elements differ in their (ranks) of centrality,
which the proposed algorithm makes up for.
A strategy to enhance a solution in terms of fit (to avoid
misplacements as they occur in Figure at the bottom left circle)
is to enlarge the
degrees of freedom in the design space. This can be done by increasing
the number of permissable locations in each of the shapes.
If there are 10 nodes in subset A, the algorithm may now choose
among 15 equally spaced positions to
locate each single element for its minimal overall distance in the target shape for A .
The results of such a modification can be seen in the next example.
Figure tries to visualize the three organizational
systems of the previous example and their interface with the 25 most
important industrial partners (having more than one link into the
system). These industrial partners can be expected to have some
effect on the coordination which occurs in the total system's
outcome.
The number of (equally spaced) positions available on each shape has been increased by 50 percent, while in the previous example there were exactly as many positions in the solution space as there were elements in each of the systems.
As we have no information on the dependencies among the industrial actors (the relations available are only the relations to each of the three organizational systems (a rectangular matrix), we have chosen a larger circle to constrain the placement of the industrial partners, surrounding the internal system.
As Figure shows, all of the industrial partners crowd
the southern hemisphere of the outer circle, while the north is
unpopulated: all industries linked to the inner top
circle B have also ties with either A or C.
At the same time, the placement of the organizations in the inner circles is very informative: while the members in the inner top circle B crowd the southern locations only, most of the elements in the lower right circle A have moved north: both (A and B) seem to build the inner core of the total system, while almost all members of C, the lower left circle, have moved west i.e. are almost exclusively linked to industrial partners.
Interesting phenomena can be detected for A and C, the two lower circles of the inner system. There are three nodes in the north east region of C which are connected to the inner core, while the top-level organization of C takes an intermediate location north-northwest: an appropriate place for organizations having a balanced ratio of ties to the inner core as well as to industrial organizations. For A, the lower right circle, we find only one single node to be placed in the south east section, indicating that this organization is linked to more industrial partners than to research organizations.
Focusing on the western sphere of A, we find a large node (having many ties) in the south west without direct links to the adjacent members of C. In this case, the short intersystem distance in the model space is not based on direct access but on the structural equivalence of the south east of C and west of A: nodes are placed close to each other when there is an overlap in their ties to third partners (industrial actors holding seats in both organizational systems) even if there are no direct links.
Looking at the most important industrial actors, whose importance can be read from the size of their nodes (symbolizing the number of links they have into the inner systems), we find the important ones to have access to the inner core. Without our a priori contraints of the the region of minimal distances for these would have been somewhere in between the inner circles, the adequate location for potential intermediaries between the inner circles. On the other hand, our constrained solution contains interesting information, too. As the distance to the center of the entire system is equal from all locations of the outer circle, the 'best' of the available locations for industrial actors which have access to the center is the one in which they can get closest to most of the research organizations in which they hold seats. The actual solution is therefore informative regarding the main orientation of these actors.
Characterizing the total system on the basis of its ties among boards of directors and advisory committees, we find an inner core which is almost exlusively formed by members of A and C (the upper and lower right circles) with only few intermediaries of B (the lower left system) attached. While this could indicate that there is too little transfer into the lower left system, we observe at the same time that the most important industrial actors which we have forced by design to the outer periphery, have links to the inner core, and are thus at the same time intermediaries between the inner core and the lower left.