# TADM2E 5.12

From Algorithm Wiki

Algorithm: BFS of each vertex v ∈ V, O(|V| * (|V| + |E|)) Saving adjacent vertexes to an adjacency matrix or adjacency list O(1) Extensions: BFS stops at a depth of 2 - Depth 1-adjacent v in the original graph - Depth 2-adjacent v in the graph square BFS uses the vertex statuses unopened, open, and processed - Open and processed vertexes are not added to the queue again Time complexity of the algorithm O (|V| * (|V| + |E|)) = O((|V|)^2 + |V * E|)) = O(|V * E|) - The number of edges does not grow slower than the number of vertexes - In a graph of 1 vertex, when adding 1 vertex, 1+ edge is added - In a complete graph of n vertices, the number of edges is determined by the Handshaking lemma - - For a complete directed graph |E| = n * (n - 1) edges - - For a complete not directed graph |E| = n * (n - 1) / 2 edges