Is the average shortest path length of gene set a reflection of their biological relatedness?

When a set of genes are identified to be related to a disease, say through gene expression analysis, it is common to examine the average distance among their protein products in the human interactome as a measure of biological relatedness of these genes. The reasoning for this is that, genes associated with a disease would tend to be functionally related, and that functionally related genes would be closely connected to each other in the interactome. Typically, average shortest path length (ASPL) of disease genes (although referred to as genes in the context of disease-associations, the interactions are among protein-products of these genes) is compared to ASPL of randomly selected genes or to ASPL in a randomly permuted network. We examined whether the ASPL of a set of genes is indeed a good measure of biological relatedness or whether it is simply a characteristic of the degree distribution of those genes. We examined the ASPL of genes sets of some disease and pathway associations and compared them to ASPL of three types of randomly selected control sets: uniform selection, from entire proteome, degree-matched selection, and random permutation of the network. We found that disease associated genes and their degree-matched random genes have comparable ASPL. In other words, ASPL is a characteristic of the degree of the genes and the network topology, and not that of functional coherence.