how to get neighbor nodes?

Question

I'm working on reproduce of Ripple Walk Sampler. This is an algorithm to extract subgraph from target graph.

Here we have to set s and r as parameters. s is the size of subgraph and r is an expansion ratio, which means the ration of nodes in neighbor set to be sampled in current step.

For subgraph Gk, it is initialized with a random node vs, then expands along the connections among nodes.

After multiple steps of expansion, the subgraph with a size of s will be returned. During each expansion, the neighbor set contains the potential nodes to be sampled.

Then r of the nodes in neighbor set will be added into the current subgraph.

Here is the original pseudo code and the example of Sampling process.

And here is my attempt:

import random
import networkx as nx
import numpy as np

m = np.matrix([
    [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 
    [1, 0, 0, 0, 0, 1, 0, 0, 0, 0], 
    [0, 1, 0, 0, 0, 0, 0, 0, 0, 0], 
    [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 
    [0, 0, 0, 1, 0, 0, 0, 0, 0, 0], 
    [0, 0, 0, 0, 1, 0, 1, 1, 0, 0], 
    [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 
    [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 
    [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], 
    [0, 0, 0, 0, 0, 0, 0, 1, 0, 0]])
G = nx.from_numpy_matrix(m) #target graph
r = 0.5 #expansion ratio
S = 4 #subgraph size

Gk = nx.DiGraph() #initialize subgraph
Vk = [] #initialize nodes
vs = random.randint(0, G.size()) #randomly select the initial node from G
Gk.add_node(vs) #add vs to Gk

while len(Vk) < S:
    #get neighbor nodes set of Vk
    NS = [n for n in G.neighbors(vs)]
    print(NS)
    #randomly select r of nodes in NS, add them into the Vk
    for nodes in NS:
        if random.random() < r:
            Vk.append(nodes)

I'm struggling with the logic of line 4 in pseudo code, the part of getting neighbor set of Vk. I know this code is wrong but how should I implement this part?

Can someone help me to fix this? Any suggestions/advices would be appreciated.

Answer 1

Here you go:

import networkx as nx
import numpy as np
import matplotlib.pyplot as plt

def RPS(G, r=0.5, S=4):
    # designed for undirected graph
    #initialize subgraph
    Gk = nx.Graph()
    #initialize nodes 
    Vk = [] 
    #randomly select the initial node from G
    vs = np.random.randint(0, G.size()) 
    print(vs)
    #add vs to Gk
    Gk.add_node(vs) 
    Vk.append(vs)

    while len(Vk) < S:
        #get neighbor nodes set of Vk (step 4) (Also appending j just for the purpose of adding edge)
        NS = [(n, j) for j in Vk for n in G.neighbors(j) if n not in Vk]
        # randomly select r of nodes in NS, add them into the Vk
        for node, j in NS:
            if np.random.uniform() < r:
                Vk.append(node)
                Gk.add_edge(j, node)
                if len(Vk) == S:
                    break
    return Gk

if __name__ == '__main__':
    # "Undirected" graph adjacency matrix
    m = np.matrix([
        [0, 1, 0, 0, 0, 0, 0, 0, 0, 0], 
        [1, 0, 1, 0, 0, 1, 0, 0, 0, 0], 
        [0, 1, 0, 0, 0, 0, 0, 0, 0, 0], 
        [0, 0, 0, 0, 1, 0, 0, 0, 0, 0], 
        [0, 0, 0, 1, 0, 1, 0, 0, 0, 0], 
        [0, 1, 0, 0, 1, 0, 1, 1, 0, 0], 
        [0, 0, 0, 0, 0, 1, 0, 0, 0, 0], 
        [0, 0, 0, 0, 0, 1, 0, 0, 1, 1], 
        [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], 
        [0, 0, 0, 0, 0, 0, 0, 1, 0, 0]])

    # G = nx.from_numpy_matrix(m, create_using=nx.MultiDiGraph())
    G =  nx.from_numpy_matrix(m)
    #expansion ratio
    r  = 0.5
    #subgraph size
    S  = 4

    Gk = RPS(G, r, S)

    # VISUALIZATION
    pos = nx.spring_layout(G)
    nx.draw_networkx_nodes(G, pos)
    nx.draw_networkx_nodes(G, pos, nodelist=list(Gk.nodes()), node_color='r')
    nx.draw_networkx_labels(G, pos)
    nx.draw_networkx_edges(G, pos, edge_color='b', width=0.5)
    nx.draw_networkx_edges(G, pos, edgelist=list(Gk.edges()), edge_color='g', width=1)

    plt.axis('off')
    plt.show() 

Sample result:

(r = 0.5, S = 4, red - subgraph, blue - target graph)