sentences:  Neighbourhood (graph theory)
  
  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 subgraph of "G" induced by all vertices adjacent to "v", i.e., the graph composed of the vertices adjacent to "v" and all edges connecting vertices adjacent to "v".