Pairing subgrapHs Using NetworK Environment Equivalence

Shared-edge ratio

The similarity of subgraph network context is given by the shared-edge ratio. The shared-edge ratio is simply the weighted proportion of highlighted edges that are shared between the two species.

For example, if we take w_i = 1 and w_e = 0.1 for the subgraph pair above:

The number of internal edges: N_i = 2

    shared N_i^shared = 2
    unshared N_i^unshared = 0

The number of external edges: N_e = 10

    shared N_e^shared = 4
    unshared N_e^unshared = 6

The weighted total number of edges is given by:

    N = w_i*N_i + w_e*N_e = 3.0

The weighted total number of shared edges is given by:

    N^shared = w_i*N_i^shared + w_e*N_e^shared = 2.4

The shared-edge ratio is then given by:

    S = N^shared/N = 0.8