Neighbourhood (graph theory)
（重定向自Adjacent vertices）
![A graph consisting of 6 vertices and 7 edges](/Images/godic/202412/20/6n-graf.svg2458.png")
![In the octahedron graph, the neighbourhood of any vertex is a 4-cycle.](/Images/godic/202412/20/Octahedron_graph2458.png")
- For other meanings of neighbourhoods in mathematics, see Neighbourhood (mathematics). For non-mathematical neighbourhoods, see Neighbourhood (disambiguation).
In graph theory, an adjacent vertex of a vertex v in a graph is a vertex that is connected to v by an edge. The neighbourhood of a vertex v in a graph G is the induced subgraph of G consisting of all vertices adjacent to v. For example, the image shows a graph of 6 vertices and 7 edges. Vertex 5 is adjacent to vertices 1, 2, and 4 but it is not adjacent to 3 and 6. The neighbourhood of vertex 5 is the graph with three vertices, 1, 2, and 4, and one edge connecting vertices 1 and 2.