Statistical Validation with K-Values

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The statistical validation is done by considering the p-values for each linked node pair in the adjacency network, assuming their neighbors in the bipartite network are randomly distributed. The FDR and Bonferroni correction for multiple test comparison are used to correct the p-value in order to take into account the fact that the null random hypothesis is tested for all the links of the adjacency network and not just once.

The details of the methodology are presented in the following paper:

M. Tumminello, S. Miccichè, F. Lillo, J. Piilo, R. N. Mantegna, Statistically validated networks in bipartite complex systems, PLoS ONE, 6 (3), e17994, (2011)

In order to generate the the network projected on one set, this version of the code considers subsets of the other set having degree k. For further details please refer to the Bacteria/COG bipartite system in the cited paper.


This program takes a bi-partite network in Pajek format (for an example please see below) and a boundary value that indicates how many nodes, counting from the first, belong to the first set (the boundary value is 5393 in the considered example). The remaining nodes are assumed to belong to the second set.

Sample network: (5393 nodes in the first set.)

As output the program gives the following file:

  • FirstPartition_Adjacency-network
  • FirstPartition_Bonferroni-network
  • FirstPartition_FDR-network
  • SecondPartition_Adjacency-network
  • SecondPartition_Bonferroni-network
  • SecondPartition_FDR-network


Submit a bipartite network in Pajek .net format to statistically validate the associated projected networks.

Submit a Network

The source codes were written by Jan Varho. These web pages are maintained by Marco Cipolla.