Code base for graph theory work

Package designed for research into graphlets and graph complexity algorithms, should be general enough for anything beyond that.

graffal is intended to be used with white space delimited files. There are three types of file that will create a graph using this program:

1. An edge list,

   a b
   a c
   b e
   b h
   b c
   c g
   e h
   f g
   g h
   

   will produce the following graph:

   

2. An adjacency list,

   a b d
   b a c
   c b d
   d b c g
   e h
   f h g
   g d f
   h e i
   i h
   

   will produce the following graph:

   

   3. Or an adjacency matrix,

   * a b c d
   a 0 1 0 1
   b 1 0 1 0
   c 0 1 0 1
   d 1 0 1 0
   

   will produce the following graph:

   

Graffal can write these visualizations to file - the file name and extension type is up to the user. Default name is temp, default extension is .png. The file will be written to graffal/graffal_tests/.

Graphlets are connected induced subgraphs of a graph, each of which has been enumerated by researchers as below:

(Pržulj, 2007)

Given a "graff" object G, graffal can generate all n-node graphlets from G.
With this graffal can count the frequency of each graphlet occuring in G.

Alternatively, graffal can count how many graphlet automorphism orbits each node of G takes part in.

Measures to gauge the complexity of a graph are widespread and varied. Graffal implements the following measures of complexity:

• The Vertex Degree Information Measure

  Measure based on each nodes vertex degree.

• The Complexity B Measure

  Measure based on the proportion of vertex degree to inter-node distance row and column totals.

• The Graph Distance Complexity Measure

  Measure based on the weighted sum of vertex distance complexities of individual nodes.

• The Total Walk Count

  Measures the total number of all k-walks, k-1 walks, ... 1-walks.

The following measures gauge the complexity of a graph by using information derived from its graphlets.

• Graphlet Frequency Information

  Measure based on the frequency counts of the graphlets.

• Graphlet Orbit Distribution Information

  Measure based on the counts of nodes in all possible graphlet automorphism orbits.

• Local Node Complexity Measure

  Evaluates the complexity of a graph by measuring the complexity of each of it's nodes orbit diversity.