Graph connectivity measures how well the nodes in a network are linked together and how resilient the structure is to disruptions. At its simplest level, a graph is connected if you can travel from any node to any other node by following a sequence of edges. Core Categories of Connectivity
Graphs are classified by how easily information or paths flow through them:
Undirected Connectivity: A basic framework where edges have no direction. The graph is either connected (one entire piece) or disconnected (divided into separate maximal connected subgraphs called components).
Strongly Connected (Directed): Applies to directed graphs (digraphs) where arrows dictate travel direction. It is strongly connected if a valid path exists in both directions between every single pair of nodes.
Weakly Connected (Directed): A directed graph that only becomes connected if you replace all directed arrows with regular, bidirectional edges. Measuring Network Resilience (k-Connectivity)
Beyond an “all-or-nothing” connected status, mathematicians measure how robust a network is by evaluating what it takes to break it apart.
[ Node A ] ——— [ Node B ] |/ | | / | | [ Node C ]–/ | | | [ Node D ] —————– [ Node E ]
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