• connectivity graph
- Points define Connectivity:
FIG $ G $ $ N $ having a point of, after removing any $ k-1 $ vertices $ (1 <= k <= N) $, resulting subgraph is still in communication,
After removal does not communicate $ K $ vertices, called G $ $ $ K $ is a connected graph, called $ K $ FIG connectivity of $ G $, denoted by $ K (G) $.
- Connectivity of edge definition:
Having sides $ N $ G $ $ in FIG, after removal of any $ k-1 $ edges $ (1 <= k <= N) $, resulting subgraph is still in communication,
After removal does not communicate $ K $ edges, called G $ $ $ K $ are connected graph, called $ K $ FIG connectivity of $ G $, denoted by $ K (G) $.
• connectivity with minimal cut
Since FIG point connectivity is to remove any $ k-1 $ a communication points, remove $ k $ points do not communicate, so is to remove a minimum of $ k $ caused none,
This is $ k $ point is that this minimum cut point set in FIG. Similarly connectivity minimum edge cut.
• Connectivity computing
- Specify the source and sink
Specify the source and sink is required to specify a particular point s to a another specific connectivity point t
1, edge connectivity (minimum cut)
• directed graph:
S is the source, t is the sink node to establish a network, each edge of the original remains in the network, a capacity of 1. Minimal Cut the network (i.e., maximum flow) is the original value of the communication side.
•Undirected graph:
FIG each edge (i, j) is split into <i, j> and <j, i> two sides, there are further processing in accordance with the method of FIG;
2, the point of communication (minimal cut point set)
• directed graph:
We need to split points. To establish a network, each point in the original $ I $ network split into $ i '$ and $ i' '$ represents the in and out points, there is an edge $ <i', i '' > $, capacity. 1
($ <S ', S' '> $ and $ <t', t '' > $ exception, not showing the capacity of positive infinity amputated). Each edge original $ <i, j> $ is the network side $ <i '', j ' > $,
capacity to positive infinity. To $ s' $ is the source point, $ t '' $ is the sink node seeking maximum flow, maximum flow value of the original is the point of communication.•Undirected graph:
FIG each edge $ (i, j) $ split into $ <i, j> $ and $ <j, i> $ two sides, there are further processing in accordance with the method of FIG.
- Do not specify the source and sink
Fixing a point source, sink enumerate other points, this time is to specify the source and the sink, taking the smallest minimum cut (or minimum cut set).