Pro-systems network analysis

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Pro-Systems Network Analysis. A project of Douglas R. White and Andrej Mrvar to create a multilevel version of Pajek in which clicking a node gives options to zoom in to a network within this node (e.g., a nation, corporation etc) or zoom out to a view of either the emergent units or neighborhoods for this node within this network or shift to another network in which this node is embedded.

Pro-generative systems also generalize genealogical or combinatorial descent of entities, e.g., countries, parties or cohesive groups that split or unite, etc.

There is the possibility of having "designed networks or entities" i.e., Jeff Johnson's (Open University) type of hypernetworks at certain levels.


Douglas R. White, Andrej Mrvar

(proposal outline for JoSS article with links in url)


We generalize the P-systems approach (Harary and White 2001) to kinship networks (P- as in P-graph for parental ties), in which networks are embedded in the nodes of higher-order networks, to a more general approach to network analysis. In the Pro-systems network approach Pro- is for progenerative ties, that is, the possibility of a subset of ties that trace the temporal priorities or generative origin and histories of nodes at each level of the analysis.


Accompanying the mathematical model of progenerative networks is a multi-level visualization system proposal and illustration (intended) for implementation in the Pajek program for large network analysis. Levels of expansion/contraction are coded numerically and a new type of relation gives pairs of levels and how they are related, e.g., 1 2 1 (Relation:1, 1 expands to 2) ≡ 1 2 2 (Relation:2, 1 contracts to 2). The units (1, 2 in this case) are either partitions or hierarchies. Partitions are numbered and colored: clicking a node colored by a partition expands or contracts according to the color, with a menu to move up or down in a hierarchy of networks:

Up: View relations among these types of nodes (click node a given color)
Collapse to this color and its neighbors
(-1=this color only 0=all 1= first only, 2=first and second, ..., 99=all connected)
Down: View relations among nodes of this color
Expand this color and its neighbors
(-1=this color only 0=all 1= first only, 2=first and second, ..., 99=all connected)

Hierarchies are numbered and are colored from largest to smallest in size. For a bicomponent hierarchy each set has at least one unique element. Hence any set can be clicked. The size of that set determines the sizes and colors of the nodes that can be clicked.

K-components are computed only for if their k-cores are within a limited range of sizes and depths that make computation feasible (possibly by R export and reimport). For a k-component sets are stacked, and only the largest node for such a set will be sized according to the highest k for that stack of k-components, so that each set of stacked k-components will have a clickable node to expand or contract, and that node will have a partition color.


Pajek analytics available at every level, and cohesive blocking occurs in some Up-operations. Exports to R and other network software.


The exemplary Pro-system is a kinship network, with multiple network representations: the Puck Ore-graph, the P-graph, and the Bipartite P-graph. Clicking a node in any of these formats will generate menu choices:

Up (as above)
Kinship (1=Ore, 2=P-graph, 3=Bipartite)
Other ( )

Other possibilities

Clicking a P-graph node:
Down includes the graph of a family
Up includes the lineage (1=male 2=female 3=both [3 colors, male, female, both])

Extensions of Herb Simon's graphs

Michael E. Gorman and Christy Nilsen 1994 Mapping or Graphing the Discovery Process

See also

(none of this looks relevant as yet although Latour did have clickable graphs for his science studies where the click zooms in on a region of the graph. Havent found an online link as yet)