Graphs have many intersting properties not least from the perspective of spatial structure and complexity. Planar graphs arising from road and other transport networks can be analysed to identify load and asymmetries in a structure. It remains a challenge to ascribe a measure of complexity to an arbitrary graph.
The following two images were produced by my GraViz graph visualisation and algorith manipulation program. The first shows a K-Rune (See LOTR Appendices) with a shortest path indicated between two highlighted nodes. The second shows an approximation to the New Zealand roads network with Wellington connected via a shortest path to the tip of the North Island. Various properties of the graph(s) are shown in the panel on the left of the main rendering window.
The following two images show screendumps of the tool examining a
randomly generated graph of 100 nodes, connected to each other node
with probability 0.01. The graph has one major component - shown with
nodes of the same colour, and some smaller components. The second
screendump shows the table view of the same data, also generated by
the tool, and allows examination of statistics for individual clusters
or components in the data.
Some of our work on graph structure and network analysis is available in Technical Notes: