Connectivity (graph theory)
![This graph becomes disconnected when the right-most node in the gray area on the left is removed](/Images/godic/202501/06/Network_Community_Structure.svg5248.png")
![This graph becomes disconnected when the dashed edge is removed.](/Images/godic/202501/06/Sample-graph5248.jpg")
![With vertex 0 this graph is disconnected, the rest of the graph is connected.](/Images/godic/202501/06/UndirectedDegrees.svg5248.png")
In mathematics and computer science, connectivity is one of the basic concepts of graph theory: it asks for the minimum number of elements (nodes or edges) that need to be removed to disconnect the remaining nodes from each other. It is closely related to the theory of network flow problems. The connectivity of a graph is an important measure of its resilience as a network.