Signed graphs

1. Definition of signed graphs
2. Balanced and partitionable signed graphs
3. Inconsistency (error) of given partition of vertices
4. Searching for optimal partitions using local optimisation

1. Searching for the best partitions in
   • sample66.net, sample2.net, sample9.net
   • Sampson monastery: sam_aff2.net, sam_aff3.net, sam_aff4.net

1. Find partitions of signed graph into 1, 2,…n clusters (where n is number of vertices in the signed graph). For each number of clusters write the total error and number of optimal partitions. Report the partition where the total error is the lowest. Data

2. Interpretation of results.

1. Doreian, P., Batagelj, V. in Ferligoj, A. (2005): Blockmodeling. New York: Cambridge University Press. chapter 7.
2. Kropivnik, S., and Mrvar, A. (1996): An analysis of the slovene parliamentary parties. In: Ferligoj, A., and Kramberger, A. (Eds.): Developments in Data Analysis, 12, FDV, Ljubljana, str. 209-218.