What are Graph Powers? [Graph Theory Tutorial]

[@VitalSine]

Let me know if you can think of any other interesting properties of graph powers in the comments 👍

[@sabinomuniz5542]

Explained it so simply. Much thanks!

[@VitalSine]

Thank you, I'm glad the video was helpful!

[@rosetta-stxned]

puts it so simply. thanks

[@VitalSine]

You're welcome, glad you liked the video :)

[@VitalSine]

0:00 Definition of Graph Power 6:00 Example 1 7:39 Diameter and Graph Powers

[@marianaaa24]

this video is a life SAVER thank you!!!

[@VitalSine]

I'm glad it was helpful!

[@darrenfinch1935]

Very simple explanation thanks so much!

[@VitalSine]

You're very welcome 👍

[@yuezhouliu9278]

Nice video! Are there any properties that relate the adjacency matrices of G and its graph power G^k?

[@VitalSine]

Thank you! If A is the adjacency matrix of G, then the adjacency matrix of G^k can be found by changing all nonzero entries in A^k to 1.

[@YOURFRIENDMATHEMATICS]

Nice video.

[@VitalSine]

Thank you! Glad you liked it :)

[@rafaelarvexm.sancho9823]

Is it the same in getting the Adjacency matrix of A(G^k) in the power of adjacency matrix of G (A^k(G))? Thank you!

[@VitalSine]

Hello, I thought I had responded to this before but just saw that it was left without a reply, sorry about that. The adjacency matrix A(G^k) will be the adjacency matrix (A(G))^k, where all nonzero entries are replaced with 1s.

[@OracleOfSages]

How do you find G4? And I’m not talking about a relation with just straight bridges.

[@VitalSine]

Excellent question. One approach would be to take the sum of the first four powers of the adjacency matrix, A, of your graph. Let B = A^1 + A^2 + A^3 + A^4. Zero the diagonal entries. Then two vertices, i and k in G4 are adjacent if and only if B(i, k) is nonzero.