It is well known that the NCCD problem is closely related to the Single Source Shortest Paths (SSSP) problem, i.e., the problem of determining the shortest path distances of all the vertices in a network, from a specified source; indeed most algorithms in the literature for the NCCD problem are modifications of approaches to the SSSP problem.
Fröhlich [ 13] constructed a consensus signature by mapping different gene signatures on a protein interaction network, in which a clustering algorithm was performed based on shortest path distances of different genes in a protein-protein interaction network.
The goal is to find a subtree T of G with minimum c-cost c(T) subject to the constraint that the sum ∑v∈V⧹Tdistd v,T) of the service distances of all the remaining nodes v∈V⧹T does not exceed the specified budget B. Here, the service distance distd v,T) denotes the shortest path distance of v to a vertex in T with respect to d.
({hat{d}}(f v_i),f v_j))le w(v_i,v_j)), if ((v_i,v_j)in Q (1le i ne j le n)), where function ({hat{d}}(cdot,cdot )) denotes the pairwise shortest path distance of two vertices in ({mathcal {G}}).
Then the distance join of Q and G, denoted as DJ Q, G), is to find all the distance matches of Q in G. (forall v_{i,1le ile n}, f v_i in S); ({hat{d}}(f v_i),f v_j))le w(v_i,v_j)), if ((v_i,v_j)in Q (1le i ne j le n)), where function ({hat{d}}(cdot,cdot )) denotes the pairwise shortest path distance of two vertices in ({mathcal {G}}).
In fact, they are at the shortest path distance of up to five.
For the activation entropies and activation free energies, we used k0 = 10 s–1, which approximates the frequency of diffusional transitions over a path distance of ∼1 nm.
The average similarity (inverse path distance) of drugs within the shared GFA components was consistently higher than the corresponding similarities of Khan et al., (2012) and Iorio et al., (2010) and random sets of compounds (Fig. 3).
We compared genes underlying monogenic syndromes linked by 1, 2, or 3 path distances, with those with a path distance of 4 or that was unknown; unknown distances are those where no genes are associated with a syndrome, the syndrome is multigenic, or when DAPPLE has no known interaction documented, see 'Materials and methods'.
For the others there was an independent prior effect probability depending on the path distance d to the 'knocked-down' S-gene of, i.e. at the maximal achievable path distance of d = n − 1 there was only a 50% chance to observe an effect.
Of all pairs of PI human proteins that both interact with the same pathogen, 96.8% are not adjacent in the network: 3.2%, 25.8%, 55.8%, 14.8% and 0.4% of them are at the shortest path distance of 1, 2, 3, 4 and 5, respectively.
