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What are Adjacent Vertices?
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This video explains what adjacent vertices are, the relation with other terms in graph theory and includes examples and an exercise to practice this. What are adjacent vertices?
DEFINITION
When is a vertex adjacent to another vertex? If the opposite endpoints of an edge are adjacent vertices, there is a common edge between these vertices.
The video shows examples of adjacent and non-adjacent vertices in undirected and directed graphs. Also, the video also contains an example to practice this.
HYPERGRAPHS
Most definitions of adjacent vertices refer to two vertices. This is because in most graphs, edges connect two vertices. But this is not always the case, in a so-called hypergraph an edge can have several endpoints.
MULTIGRAPH
A multigraph adds two elements to the simple graph, parallel edges and edges from a vertex to itself, a so-called loop. Can a vertex be adjacent to itself? Yes, at a vertex with a loop both endpoints are the same, the vertex 'sees' itself as an adjacent vertex.
NEIGHBORHOOD
The closed neighborhood of a vertex in a graph is the subgraph induced of all the vertices adjacent to this vertex including the vertex itself. The properties of a neighborhood are used in many graph definitions and algorithms. An example of the use of neighbor vertices is the vertex degree.
In an undirected graph the degree of a vertex is equal to the number of adjacent vertices, the neighborhood of a vertex.
OTHER RELATED CONCEPTS
Isolated vertex: when a vertex is not adjacent to other vertices.
Complete graph: if all vertices are adjacent to another, every possible edge is present.
Adjacent edges: Not only vertices can be adjacent in a graph. Also, edges can be adjacent. These edges share a common vertex. More common is the synonym incident edges for these.
Other: adjacency matrix and adjacency list.
TIMESTAMPS
0:00 Adjacent vertices
0:19 Definition adjacent vertices
0:29 Undirected graph
0:44 Directed graph
0:52 Hypergraph
1:08 Exercise
1:15 Multigraph
1:42 Isolated vertex
1:49 Complete graph
1:58 Adjacent edges or incident edges
2:12 Neighborhood
2:28 Vertex degree
2:40 Other related concepts
2:48 Summary
VIDEOS IN THIS SERIES 🎞️
ABOUT US
#startnetworkanalysistoday #symbio6
CONTRIBUTIONS
Music: Nico Staf - Walking in the Sky
DEFINITION
When is a vertex adjacent to another vertex? If the opposite endpoints of an edge are adjacent vertices, there is a common edge between these vertices.
The video shows examples of adjacent and non-adjacent vertices in undirected and directed graphs. Also, the video also contains an example to practice this.
HYPERGRAPHS
Most definitions of adjacent vertices refer to two vertices. This is because in most graphs, edges connect two vertices. But this is not always the case, in a so-called hypergraph an edge can have several endpoints.
MULTIGRAPH
A multigraph adds two elements to the simple graph, parallel edges and edges from a vertex to itself, a so-called loop. Can a vertex be adjacent to itself? Yes, at a vertex with a loop both endpoints are the same, the vertex 'sees' itself as an adjacent vertex.
NEIGHBORHOOD
The closed neighborhood of a vertex in a graph is the subgraph induced of all the vertices adjacent to this vertex including the vertex itself. The properties of a neighborhood are used in many graph definitions and algorithms. An example of the use of neighbor vertices is the vertex degree.
In an undirected graph the degree of a vertex is equal to the number of adjacent vertices, the neighborhood of a vertex.
OTHER RELATED CONCEPTS
Isolated vertex: when a vertex is not adjacent to other vertices.
Complete graph: if all vertices are adjacent to another, every possible edge is present.
Adjacent edges: Not only vertices can be adjacent in a graph. Also, edges can be adjacent. These edges share a common vertex. More common is the synonym incident edges for these.
Other: adjacency matrix and adjacency list.
TIMESTAMPS
0:00 Adjacent vertices
0:19 Definition adjacent vertices
0:29 Undirected graph
0:44 Directed graph
0:52 Hypergraph
1:08 Exercise
1:15 Multigraph
1:42 Isolated vertex
1:49 Complete graph
1:58 Adjacent edges or incident edges
2:12 Neighborhood
2:28 Vertex degree
2:40 Other related concepts
2:48 Summary
VIDEOS IN THIS SERIES 🎞️
ABOUT US
#startnetworkanalysistoday #symbio6
CONTRIBUTIONS
Music: Nico Staf - Walking in the Sky
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