We can model this problem as a graph-theoretical one: First, an undirected graph G = (V, E) where V is the set of peptides P, and the edge set
E contains an edge [p.sub.i][p.sub.j] (or a loop at [p.sub.i], denoted by [p.sub.i][p.sub.i]) if and only if [p.sub.i] and [p.sub.j] interact.
A mathematical system G=(V,E) is called a graph, where a vertex set is V=V(G) and an edge set
The hosts gained the early territorial advantage and it was not long before the home fans were cheering the first score after an overlap on the right edge set
Clare clear to cross on his landmark appearance after eight minutes.
At the initial time, each edge in the core edge set
or border edge set
is only associated with an initial distance, without any interaction.
Consider molecular graph G having vertex set [V.sub.G] and edge set
The edge set
of P[D.sub.1] has following four partitions:
[for all][l.sub.i] [member of] [V.sub.l1], if there is [d.sub.j] [member of] [V.sub.d1] satisfying the fact that the association between [l.sub.i] and [d.sub.j] belongs to the set of newly collected 2048 lncRNA-disease associations, then we define that there is an edge between [l.sub.i] and [d.sub.j] in [G.sub.1], and by this way, we can obtain the edge set
[E.sub.1] of [G.sub.1].
Throughout this article, we assume G to be a connected graph, V (G) and E (G) are the vertex set and the edge set
, respectively, and [d.sub.v] denotes the degree of a vertex v.
Let G(V, E) be a graph with the vertex set V and the edge set
Throughout this paper, we always let G = (V(G),E(G)) be a simple molecular graph with the vertex set V(G) and the edge set
Here mesh network is modeled as a graph G = < [??],[??]> where the vertices set [??] represent mesh nodes and the edge set
[??] represents communication links in the network.
The combined effects of gravity and simply driving on a gravel road will tend to push material to the edges--plowing winter snow before the lane is frozen and with a cutting edge set
too close to the ground will significantly speed the process.