237833-network-science

Consider an adjacency matrix A A , such that A i j = 1  if there is an edge from vertex  j  to vertex  i ,   A_{ij} = 1 \text{ if there is an edge from vertex } j \text{ to vertex } A i j = 0  otherwise . Select the correct alternative: a) If the graph is undirected, A = A T A = A^T . b) If the graph is directed, the main diagonal is always equal to 1. c) If the graph is undirected, the main diagonal is always equal to 0. d) If the graph is directed, A A is invertible. e) None of the above Original idea by: João Vitor Baptista Moreira

After running a DFS algorithm in a directed graph, the following table represents the start and end time of each node. Node Start time End time A 1 10 B 8 9 C 2 7 D 3 4 E 5 6   Select the correct alternative about the edges:   a) The edge A -> C is a backward edge b) The edge D -> E is a forward edge c) The edge B -> C is a cross edge d) The edge E-> D is a forward edge e) None of the above Original idea by: João Vitor