Edge Connectivity

The edge connectivity, also called the line connectivity, of a graph is the minimum number of edges  whose deletion from a graph  disconnects . In other words, it is the size of a minimum edge cut. The edge connectivity of a disconnected graph is therefore 0, while that of a connected graph with a graph bridge is 1.

Let  be the vertex connectivity of a graph  and  its minimum degree, then for any graph,

(Whitney 1932, Harary 1994, p. 43).

Connected bridgeless graphs are 2-edge connected.

The edge connectivity of a graph can be determined in the Wolfram Language using EdgeConnectivity[g]. Precomputed edge connectivities for many named graphs can be obtained using GraphData[graph, "EdgeConnectivity"].

REFERENCES

Harary, F. Graph Theory. Reading, MA: Addison-Wesley, p. 43, 1994.

Skiena, S. Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica. Reading, MA: Addison-Wesley, pp. 177-178, 1990.

Whitney, H. "Congruent Graphs and the Connectivity of Graphs." Amer. J. Math. 54, 150-168, 1932.