BFS and DFS can be achieved in O(|V| + |E|). I understand the proof but it seems a bit lengthy. Can I argue O(|V| + |E|) in a very simply way? e.g. checking each edge at most once? Also what does O(|V| + |E|) imply?I know Dijstrka algorithm and many other algorithm is somewhat like BFS. Does it imply automatically they can be run in |V| + |E| is the lower bound? 
What simple arguments and insights can I observe that running both BFS and DFS can be achieved in O(|V| + |E|)?
graphs;algorithm analysis;runtime analysis;graph traversal