The edge connectivity, also called the line connectivity, of a graph 
with at least two vertices
is the minimum number 
of edges whose deletion 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. The edge connectivity
of the singleton graph is taken to be 0.
Let 
be the vertex connectivity of a graph 
and 
its minimum vertex
degree. Then
 |
(Whitney 1932; Harary 1994, p. 43).
Connected bridgeless graphs with at least two vertices 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"].
Zhou and Zhang (2026) give the bound 
for a finite connected simple graph
with graph diameter at least 3, where 
is its edge connectivity, 
its minimum vertex
degree, and 
the minimum Lin-Lu-Yau curvature over its
edges. For graph diameter
2, they give the bound 
.
