A graph may have several

strongly connected components, and it may be the case that there are paths linking a vertex from one to a vertex from the other.

To handle state expansion problem, because loops and similar structures can generate millions of paths, CFG is converted into the maximal

strongly connected components. Satisfiability modulo theories with proof based learning engine algorithm is the last step of this approach.

A Web-based social network, on the other hand, considers many complex structures like cycles, nested cycles,

strongly connected components etc.

Using graph analysis methods to derive cliques or

strongly connected components from graph representations of site structure may make it possible to develop a set of patterns that reflect good site management.

A b-balanced cut in a graph G = (V, E) is a cut that partitions the graph into connected components (

strongly connected components in the directed case), each of which contains at most (1 - b) [multiplied by] n vertices, where n = |V|.

(We do this only if some vertex n at level l has one or more incoming backedges whose source is not dominated by n.) This requires processing the subgraph of the (collapsed) flowgraph consisting of all vertices at a level greater than or equal to the current level l (that is, the set of vertices [[union].sub.j [is less than or equal to] l] [V.sub.j]) to identify its

strongly connected components (SCCs).

Graph theory [1] defines the cyclomatic number of a graph with n nodes, e edges, and p

strongly connected components as e - 1 + p, which represents the number of fundamental cycles of the graph.

In this section, we apply our results to the study of new polynomial invariants of directed graphs, or digraphs, based on studying the

strongly connected components. A

strongly connected component of a digraph [??] is a maximal subgraph [??], such that, for every pair of distinct vertices u and v, there is a directed path from u to [upsilon].

In general, one can consider

strongly connected components of T(A).

In the first level, the structural properties of a graph are studied and

strongly connected components are fused to reduce the original graph to a DAG.

We deal with this problem by contracting

strongly connected components of the graph induced by zero-length arcs.

Its vertices are the

strongly connected components [C.sub.1], ...