You are given a weakly connected directed weighted graph — connected when the edge directions are ignored — and asked whether it contains a negative cycle anywhere— not just one reachable from some particular vertex.

Which approach settles it in O(|V| · |E|) time?

Consider a directed, weighted graph G with |V| vertices and |E| edges. What is the worst-case time complexity of finding the edge of largest weight, if G is implemented using an adjacency matrix?

Consider a directed, weighted graph G with |V| vertices and |E| edges. What is the worst-case time complexity of running a Depth-First Search (DFS) on G, if G is implemented using an unsorted adjacency list?

Consider a directed, weighted graph G with |V| vertices and |E| edges. What is the worst-case time complexity of finding the vertex with the greatest number of edges, counting incoming and outgoing together, if G is implemented using an unsorted adjacency list?

Consider a directed, weighted graph G with |V| vertices and |E| edges. What is the worst-case time complexity of running a Breadth-First Search (BFS) on G, if G is implemented using an adjacency matrix?

Consider a directed, weighted graph G with |V| vertices and |E| edges. What is the worst-case time complexity of running a Depth-First Search (DFS) on G, if G is implemented using an adjacency matrix?

Consider a directed, weighted graph G with |V| vertices and |E| edges. What is the worst-case time complexity of listing all the outgoing edges of the vertex that has the most outgoing edges, if G is implemented using an adjacency matrix?