Triangles Closure

The graph links lead to pages listing the vertex pairs that are 2-hops apart in the first intersection operand and 1-hop apart (i.e., adjacent) in the second intersection operand. Intermediaries are also on these pages. An intermediary vertex z is one where in the first operand graph there exist edges xz and yz but not xy, and in the second operand graph the xy edge now exists. Thus, at least one triangle has been "closed" by adding the second intersection operand. The other two edges of these triangles can be found by examining the intermediaries (i.e., the third vertex in the triangle).

∪ (edge union)The union of the edges in the operand graphs.
∩ (edge intersection)The intersection of the edges in the operand graphs.
Hn(G)The vertex-pairs in graph G that are exactly n-hops apart (i.e. a new graph is formed).
A n-hop exists when the length of the shortest path between two vertices is equal to n.
Note that H1(G) = G.