2. Consider the following adjacency matrix describing the edge relations for an undirected, unweighted graph: A 0 1 1 0 0 0 0 1 1 0 0 1 0 100 100 100 10 01101000 0 0 0 1 0 1 1 10 0 1 0 0 1 0 0 1 0 0 1 0 1 0 0 1 1 0 0 0 0 110 (1) (a) Construct the graph associated with this adjacency matrix. Please, label the nodes so that v1 corresponds to the first row, v2 corresponds to the second, etc. (b) Reconstruct this graph using breadth-first search (BFS) starting from node 1. (c) What is the distance between node 1 and node 14? (d) How many nodes are at a distance of 3 away from node 1? (e) Is this graph connected? Explain. (f) What is the density of this graph? (g) What is the average degree of this graph? (h) Is this graph a tree? Explain. (i) Is this a bipartite graph? Explain.