A connected subgraph of a graph to which no vertex can be added and it still be connected. Formal Definition: Given a graph G=(V, E), a subgraph S=(V', E') is a maximally connected component if

• S is connected, and
• for all vertices u such that u∈ V and u∉ V' there is no vertex v∈ V' for which (u, v)∈ E.