Youtor
What are kCliques Graph Theory
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What are k-cliques/n-cliques in graph theory? We'll be going over two common definitions of k-cliques in today's graph theory lesson! • Second definition: 3:23 • The first definition of k-clique is that a k-clique is a clique with k vertices. Recall that a clique of a graph G is a set, C, of vertices of G, such that every pair of distinct vertices in C is joined by an edge in G. Equivalently, every pair of distinct vertices in C have a distance of 1 between them. We often also use the word clique to refer to the subgraph induced by a set of vertices that are all adjacent to each other, this is a complete subgraph. The two definitions are used interchangeably much of the time, based on whether we want to talk about a subgraph or its vertex set. • The second definition of k-clique we discuss says that a k-clique of G is a set, C, of vertices of G, such that every pair of vertices in C have a distance between them that is less than or equal to k. Thus, a 1-clique is the normal type of clique we're familiar with. Additionally, by definition, any m-clique is also a k-clique for all k greater than or equal to m. • What is a Clique: • What is a Clique? | Graph Theory, Cli... • Maximum and Maximal Cliques: • Maximum and Maximal Cliques | Graph T... • What is a Maximal Clique: • What is a Maximal Clique? | Graph The... • What are k-Cores: • What is the K-Core of a Graph? | K-Co... • What are k-Clubs and k-Clans: • What are k-Clans and k-Clubs? | Graph... • What is a k-Plex: • What is a k-Plex? | Graph Theory • ◆ Donate on PayPal: https://www.paypal.me/wrathofmath • ◆ Support Wrath of Math on Patreon: / wrathofmathlessons • 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/0fRtu... • Vallow SoundCloud: / benwatts-3 • ******************************************************************** • +WRATH OF MATH+ • Follow Wrath of Math on... • ● Instagram: / wrathofmathedu • ● Facebook: / wrathofmath • ● Twitter: / wrathofmathedu • My Music Channel: / seanemusic
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