Figure 8 (a) gives an example illustrating the behavior of the shortest path search when the vertical distance between any two vertices are all less than T p for the vertices { v1, v2, v3, v4, v5, v6}.
A graph without loops and with at most one edge between any two vertices is called a simple graph.
A distance labeling scheme is a distributed data-structure designed to answer queries about distance between any two vertices of a graph G.
The data-structure consists in a label L x,G) assigned to each vertex x of G such that the distance dG x,y) between any two vertices x and y can be estimated as a function f(L x,G),L y,G)).
By constructing internally disjoint paths between any two vertices in the enhanced hypercube, for n≥3 and 2≤k≤n we prove that Dω Qn,k)= dω(Qn,k)= d(Qn,k) for 1≤ω
The diameter diam (G) of G is the maximum distance between any two vertices of G.
Newman defined a modularity measurement based on the probability of the link between any two vertices.
Adding an internal edge between any two vertices increases the number of loops by precisely one.
A graph G is connected if there is a path between any two vertices.
A graph G is called connected if there is a path between any two vertices.
