Find the number of edges in the largest connected component of a graph

First establish whether largest means the component with most vertices or most edges, because those can differ. Run BFS or DFS from every unvisited vertex, marking nodes globally so each belongs to one component. For an undirected adjacency list, sum degrees of vertices encountered in that component and divide by two, since each edge appears from both endpoints. For a directed graph, count outgoing edges directly, and clarify whether connectivity means weak or strong connectivity. If the graph arrives as an edge list, increment a component edge counter when processing each input edge whose endpoints are within the discovered component, or use degree accounting after traversal. Test isolated vertices, self-loops, parallel edges, disconnected components, and equal-size ties. Building and traversing adjacency lists is O(V+E) time and O(V+E) space. Avoid counting adjacency entries as edges without accounting for graph direction.