Question: Question 1 Consider the following directed graph G(V, E): e4 V2 V3 e1 V1 e5 e3 e6 e2 e7 V4 V5 (1.1) Find the adjacenty

Question 1 Consider the following directed graph G(V, E): e4 V2 V3 e1 V1 e5 e3 e6 e2 e7 V4 V5 (1.1) Find the adjacenty matrix A, incidence matrix B, and C as the adjacenty matrix of the undirected version of the graph. (1.2) Show that B 1 =0, where 1 and 0 represent the all-ones and zero vectors, respectively. (1.3) Based on 1.2, find an eigenvalue and eigenvector of BB and BBT. (1.4) Let L = BB . Show that L = D - C, where D = diag(deg(v1), ..., deg(v5)). (1.5) Find det (L). (1.6) Show that all eigenvalues of L are nonnegative

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