Graph Representation with an Adjacency Matrix | Graph Theory, Adjaceny Matrices

Wrath of Math
Wrath of Math
85 هزار بار بازدید - 6 سال پیش - How do we represent graphs
How do we represent graphs using adjacency matrices? That is the subject of today's graph theory lesson! We will take a graph and use an adjacency matrix to represent it! It is a most soulless, but at times useful, graph representation. An adjacency matrix has a row and a column for each vertex in the graph it represents. If the vertex represented by row i is adjacent to the vertex represented by column j, then the entry in the i-th row and j-th column is a 1, otherwise it is a 0. Thus, we can find the degree of a vertex by adding up all the entries in the row or column that represents it! If an adjacency matrix represents a simple graph, then it will have 0s along its diagonal since a vertex cannot be adjacent to itself (this is assuming you construct the matrix so that the vertices are represented by rows in the same order that they are in the columns). Also, if a graph is undirected, then the adjacency matrix that represents it will be symmetric (meaning it is symmetric across the diagonal). There are lots of cool things to notice about adjacency matrices, which cannot possibly be listed here or covered in one video, but everything here is elaborated on in the video lesson! I hope you find this video helpful, and be sure to ask any questions down in the comments! ******************************************************************** The outro music is by a favorite musician of mine named Vallow, who, upon my request, kindly gave me permission to use his music in my outros. I usually put my own music in the outros, but I love Vallow's music, and wanted to share it with those of you watching. Please check out all of his wonderful work. Vallow Bandcamp: https://vallow.bandcamp.com/ Vallow Spotify: https://open.spotify.com/artist/0fRtulS8R2Sr0nkRLJJ6eW Vallow SoundCloud: https://soundcloud.com/benwatts-3 ******************************************************************** +WRATH OF MATH+ ◆ Support Wrath of Math on Patreon: https://www.patreon.com/wrathofmathlessons Follow Wrath of Math on... ● Instagram: https://www.instagram.com/wrathofmathedu ● Facebook: https://www.facebook.com/WrathofMath ● Twitter: https://twitter.com/wrathofmathedu My Music Channel:
6 سال پیش در تاریخ 1397/10/17 منتشر شده است.
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