Question

For the following digraph D, find the incidence matrix B using the node set V = \{a, b, c, d, e\} and the arc set E = \{1,2,3,4,5,6\}. Compute $BB^T$ and find its relationship to the degree matrix and the adjacency matrix of the underlying graph of D.

          For the following digraph D, find the incidence matrix B using the node
set V = \{a, b, c, d, e\} and the arc set E = \{1,2,3,4,5,6\}. Compute $BB^T$ and
find its relationship to the degree matrix and the adjacency matrix of the
underlying graph of D.

$For the following digraph D, find the incidence matrix B using the node set V = {a, b, c, d, e} and the arc set E = {1,2,3,4,5,6}. Compute BB^T and find its relationship to the degree matrix and the adjacency matrix of the underlying graph of D.$

Added by Kelly C.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Karl Zipple

Step 1

The incidence matrix of a digraph D is a |V| x |E| matrix where each row represents a node and each column represents an arc. If arc e (column) is outgoing from node v (row), then the corresponding entry in the matrix is -1. If arc e is incoming to node v, then Show more…

Show all steps

Thanks for your feedback!

For the following digraph D, find the incidence matrix B using the node set V = {a,b,c,d,e} and the arc set E = {1,2,3,4,5,6}. Compute BBT and find its relationship to the degree matrix and the adjacency matrix ofthe underlying graph of D. b 3