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pythonnetworkx

second-order neighbors of a node in a graph

I have the following graph and the function to find second-order neighbors of a node in the graph:

import networkx as nx  

G = nx.Graph()  
G.add_edge('1','2',weight=673)  
G.add_edge('2','4',weight=201)  
G.add_edge('4','1',weight=20)  
G.add_edge('2','3',weight=96)  
G.add_edge('3','4',weight=44)  
G.add_edge('6','3',weight=7)  
G.add_edge('6','4',weight=96)  
G.add_edge('5','6',weight=10)  
G.add_edge('7','6',weight=10)  
G.add_edge('8','6',weight=10)  

def neighbors_r2(node):  
    subgraph = nx.ego_graph(G,str(int(node)),center=False,radius=2)  
    return list(subgraph.nodes())  

print(f"second order neighbors are: {neighbors_r2(6)}.")

Graph G plot

My problem is that the result must be ['1', '2', '3', '4'], but the result of the code is ['1', '2', '4', '3', '5', '7', '8']. I understood the reason is because that ego_graph includes all neighbors of distance<=radius (here node). How can I change the function so that only returns nodes with second-order neighbors?

Solution

  • You can use a set comprehension and Graph.neighbors:

    def second_order_neighbors(G, node):
    return set(x for n in G.neighbors(node) for x in G.neighbors(n))-{node}

second_order_neighbors(G, '6')

    Output: {'1', '2', '3', '4'}