There are many different definitions of cohesive subgraphs in the literature, including maximal clique [19], k-core [20], k-truss [21], and maximal k-edge

connected subgraph [22].

Therefore, [T.sub.[gamma]](x) [for all]x [member of] N [B.sub.[gamma]] cannot be a T1ST which contradicts the fact that [T.sub.[gamma]](x) is a

connected subgraph of T2SG.

Correa, "The node-edge weighted 2-edge

connected subgraph problem: linear relaxation, facets and separation," Discrete Optimization, vol.

From a large amount of data analysis under three attack modes, we can see that nonscale networks maintained a similar network topology, and the scale of the largest

connected subgraph is approximately equal.

A component of graph G is defined as a

connected subgraph that is maximal.

Suppose the communication graph [G.sub.[sigma]] on subinterval [[t.sub.r,s], [t.sub.r,s+1]) has [n.sub.[sigma]] [greater than or equal to] 1

connected subgraphs [G.sup.i.sub.[sigma]], and each

connected subgraph [G.sup.i.sub.[sigma]] has [d.sup.i.sub.[sigma]] = [d.sup.i.sub.[sigma]F] + [d.sup.i.sub.[sigma]R] nodes, where [d.sup.i.sub.[sigma]F] [greater than or equal to] 1 represents the number of followers, [d.sup.i.sub.[sigma]R] [greater than or equal to] 1 represents the number of leaders, i = 1, 2, ..., [n.sub.[sigma]].

Then, based on the lexicographic order, gSpan uses the DFS strategy to efficiently mine frequently

connected subgraph patterns.

Keywords: vertex-colored graph,

connected subgraph, tropical subgraph, colorful subgraph, vertex-colored random graph.

We call R a trunk of F if R is a maximal

connected subgraph of F such that every colored vertex in R is a leaf of R.

The symmetric algebra [S.sub.R] (I (G)) is a integrity domain if and only if every

connected subgraph of G has either at most a cycle of odd length or no monomial walk.

More formally, a graph is a knight subgraph if it is an isomorphism of some

connected subgraph of the infinite knight's graph.

Because a graph is connected if every pair of vertices is connected by a path, a

connected subgraph of G represents a set of related rows and columns in M.