I'm new to networkx and actually a bit confused on how to efficiently find the n-degree neighborhood of a node. The n-degree neighborhood of a node v_i is the set of nodes exactly n hops away from v_i. Given a specified n, I need find the n-degree neighborhood for each node in the graph/network.
Suppose I have the following graph and I want to find the n=1 neighborhood of node v1. That would be v2 and v3. Next suppose I want to find the n=2 neighborhood of node v1, then that would be v4.
import networkx as nx G = nx.Graph() G.add_edges_from([('v1','v2'),('v2','v4'),('v1','v3')]) def neighborhood(G, node, n): path_lengths = nx.single_source_dijkstra_path_length(G, node) return [node for node, length in path_lengths.iteritems() if length == n] print(neighborhood(G, 'v1', 1)) # ['v2', 'v3'] print(neighborhood(G, 'v1', 2)) # ['v4'] The most efficient way to find the n-neighbors of a given node is to use Depth first search: http://en.wikipedia.org/wiki/Depth-first_search. The function below returns the neighbors of start for all distances. However, if you need to find the n-neighbors for all nodes, using this function for all nodes would not be the most efficient solution. Instead, one could use this function just for a start-node in each connected component, and compute the n-neighbors for the other nodes relative to the starts, but that would be quite more complicated.
import networkx as nx def n_neighbor(G, start): # {distance : [list of nodes at that distance]} distance_nodes = {} # nodes at distance 1 from the currently visited ones next_shell = G.neighbors(start) # set of all visited nodes visited=set() visited.add(start) # how fare we are from start distance = 0 # until we run out of nodes while len(next_shell) > 0: # this will be the next shell shell_after_this = [] # update distance distance += 1 distance_nodes[distance] = [] # update visited and distance_nodes for node in next_shell: visited.add(node) distance_nodes[distance].append(node) # compute shell_after_this for node in next_shell: # add neighbors to shell_after_this # if they have not been visited already for neighbor in G.neighbors(node): if neighbor not in visited: shell_after_this.append(neighbor) # we repeat with the new_shell next_shell = set(shell_after_this) return distance_nodes # example G=nx.Graph() G.add_edge(1,2) G.add_edge(1,3) G.add_edge(2,3) G.add_edge(2,4) G.add_edge(3,5) G.add_edge(5,17) G.add_edge(2,6) print n_neighbor(G, 1) When you perform a Breadth First Search on a graph, starting at a root node r - the nodes are considered in increasing distance from r.
Thus, you just need to track the level of the nodes as you perform a BFS, see http://en.wikipedia.org/wiki/Level_structure for a more thorough discussion.