Connectivity, weak connectivity

the connectivity of the undirected graphs

The strongly connected components of the forward graph are in the direction graph G, if the two vertices vi,vj (VI>VJ) have a direction path from VI to VJ, and there is a direction path from VJ to VI, the two vertices are strongly connected (strongly connected). If there is strong connectivity to every two vertices of the graph G, the G is a strongly connected graph. A strongly connected sub-graph of a graph, called a strongly connected component (strongly connected components). The edges of the graph are unidirectional, so accessibility does not have transitivity: U can reach V, not v reaches U. However, if you and V can reach each other, then for any other junction W, the accessibility between W and U is the same as the accessibility between W and V. The "mutual reach" relationship is an equivalence relationship, so that all nodes can be divided into sets according to the relationship, the points within the same set can reach each other, the points in different sets are not mutually accessible, as shown in the following diagram:

Each set is called a strongly connected component of the undirected graph (strong Connected COMPONENT,SCC). If you consider a set as a point, then all of the SCC forms an SCC diagram:

Pass Component a maximal connected sub-graph of undirected graph G is called a connected component of G (or connected branch). The connected graph has only one connected component, that is itself, and the non-connected undirected graph has multiple connected components.
in undirected graphs, if there is a path from vertex v1 to vertex v2, the vertex v1 and v2 are connected. If any pair of vertices in the graph are connected, the graph is called a connected graph. The concept of strong connectivity and weak connectivity only exists in the undirected graph. An undirected graph g= (v,e) is connected, so the number of edges is greater than or equal to the number of vertices minus one: | e|>=| V|-1, and vice versa. If g= (V, E) is a forward graph, then it is necessary for a strongly connected graph to be the number of edges greater than or equal to the vertex: | e|>=| V|, and vice versa. undirected graphs without loops are connected when and only if it is a tree, that is equivalent to: | e|=| V|-1.
Strong connected graph in the direction graph, if for each pair of vertex v1 and v2, there is a path from V1 to V2 and from V2 to V1, this graph is called strong connected graph. In the direction graph g= (V, E), if for any of the two different vertices x and y in V, there is a path from X to Y and from Y to X, then the G is a strongly connected graph. Correspondingly, there is the concept of strong connected components. The strongly connected graph has only one strong connected component, which is itself, and the non-strongly connected undirected graph has multiple strong components.
Unidirectional connected graphs if there is a direction graph, for any node V1 and v2, there is at least one of the paths from V1 to V2 and v2 to V1, then the original is a one-way connected graph. The g=<v,e> is a forward graph, if u->v means that the graph G contains a simple path from u to V, then the graph G is a single connected graph. The relationship between strong connected graphs, connected graphs and unidirectional connected graphs is that the strongly connected graphs must be one-way connected, and the one-way connected graphs must be weak connected graphs.
The weakly connected graph replaces all the forward edges of the graph with the undirected edges, and the resulting graph is called the base diagram of the original. If the Jhoira of a forward graph is a connected graph, the graph is weakly connected.
all vertices in the primary pathway path are different. The primary pathway must be a simple pathway, but the reverse is not true.