  We propose a biologically motivated quantity, twinness, to evaluate local
similarity between nodes in a network. The twinness of a pair of nodes is the
number of connected, labeled subgraphs of size n in which the two nodes possess
identical neighbours. The graph animal algorithm is used to estimate twinness
for each pair of nodes (for subgraph sizes n=4 to n=12) in four different
protein interaction networks (PINs). These include an Escherichia coli PIN and
three Saccharomyces cerevisiae PINs -- each obtained using state-of-the-art
high throughput methods. In almost all cases, the average twinness of node
pairs is vastly higher than expected from a null model obtained by switching
links. For all n, we observe a difference in the ratio of type A twins (which
are unlinked pairs) to type B twins (which are linked pairs) distinguishing the
prokaryote E. coli from the eukaryote S. cerevisiae. Interaction similarity is
expected due to gene duplication, and whole genome duplication paralogues in S.
cerevisiae have been reported to co-cluster into the same complexes. Indeed, we
find that these paralogous proteins are over-represented as twins compared to
pairs chosen at random. These results indicate that twinness can detect
ancestral relationships from currently available PIN data.
