Use this if you are using igraph from R
A vertex is a neighbor of another one (in other words, the two vertices are adjacent), if they are incident to the same edge.
neighbors(graph, v, mode = c("out", "in", "all", "total"))
graph | 
 The input graph.  | 
v | 
 The vertex of which the adjacent vertices are queried.  | 
mode | 
 Whether to query outgoing (‘out’), incoming (‘in’) edges, or both types (‘all’). This is ignored for undirected graphs.  | 
A vertex sequence containing the neighbors of the input vertex.
Other structural queries: 
[.igraph(),
[[.igraph(),
adjacent_vertices(),
are_adjacent(),
ends(),
get.edge.ids(),
gorder(),
gsize(),
head_of(),
incident_edges(),
incident(),
is_directed(),
tail_of()
g <- make_graph("Zachary")
n1 <- neighbors(g, 1)
n34 <- neighbors(g, 34)
intersection(n1, n34)