数据挖掘KDD领域-CELF已成为一种经典的社会网络影响最大化发现算法，用于改进贪心算法的效率(提升700%)。获得KDD 2019的经典论文奖，作者：Jure Leskovec，论文：Cost-effective Outbreak Detection in Networks（2007）。

CELF算法是基于影响力具有子模性特征提出的，即所有节点的影响力随着种子节点集合中节点数目增加在减弱，具有单调递减性。

 

import matplotlib.pyplot as plt
from random import uniform, seed
import numpy as np
import time
from igraph import *

def IC(g,S,p=0.5,mc=1000):
    """
    Input:  graph object, set of seed nodes, propagation probability
            and the number of Monte-Carlo simulations
    Output: average number of nodes influenced by the seed nodes
    """
    
    # Loop over the Monte-Carlo Simulations
    spread = []
    for i in range(mc):
        
        # Simulate propagation process      
        new_active, A = S[:], S[:]
        while new_active:

            # For each newly active node, find its neighbors that become activated
            new_ones = []
            for node in new_active:
                
                # Determine neighbors that become infected
                np.random.seed(i)
                success = np.random.uniform(0,1,len(g.neighbors(node,mode="out"))) < p
                new_ones += list(np.extract(success, g.neighbors(node,mode="out")))

            new_active = list(set(new_ones) - set(A))
            
            # Add newly activated nodes to the set of activated nodes
            A += new_active
            
        spread.append(len(A))
        
    return(np.mean(spread))

def celf(g,k,p=0.1,mc=1000):  
    """
    Input:  graph object, number of seed nodes
    Output: optimal seed set, resulting spread, time for each iteration
    """
      
    # --------------------
    # Find the first node with greedy algorithm
    # --------------------
    
    # Calculate the first iteration sorted list
    start_time = time.time() 
    marg_gain = [IC(g,[node],p,mc) for node in range(g.vcount())]

    # Create the sorted list of nodes and their marginal gain 
    Q = sorted(zip(range(g.vcount()),marg_gain), key=lambda x: x[1],reverse=True)

    # Select the first node and remove from candidate list
    S, spread, SPREAD = [Q[0][0]], Q[0][1], [Q[0][1]]
    Q, LOOKUPS, timelapse = Q[1:], [g.vcount()], [time.time()-start_time]
    
    # --------------------
    # Find the next k-1 nodes using the list-sorting procedure
    # --------------------
    
    for _ in range(k-1):    

        check, node_lookup = False, 0
        
        while not check:
            
            # Count the number of times the spread is computed
            node_lookup += 1
            
            # Recalculate spread of top node
            current = Q[0][0]
            
            # Evaluate the spread function and store the marginal gain in the list
            Q[0] = (current,IC(g,S+[current],p,mc) - spread)

            # Re-sort the list
            Q = sorted(Q, key = lambda x: x[1], reverse = True)

            # Check if previous top node stayed on top after the sort
            check = (Q[0][0] == current)

        # Select the next node
        spread += Q[0][1]
        S.append(Q[0][0])
        SPREAD.append(spread)
        LOOKUPS.append(node_lookup)
        timelapse.append(time.time() - start_time)

        # Remove the selected node from the list
        Q = Q[1:]

    return(S,SPREAD,timelapse,LOOKUPS)

# Create simple network with 0 and 1 as the influential nodes
source = [0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,2,3,4,5]
target = [2,3,4,5,6,7,8,9,2,3,4,5,6,7,8,9,6,7,8,9]

g = Graph(directed=True)
g.add_vertices(range(10))
g.add_edges(zip(source,target))

# Plot graph
g.vs["label"], g.es["color"], g.vs["color"] = range(10), "#B3CDE3", "#FBB4AE"
plot(g,bbox = (200,200),margin = 20,layout = g.layout("kk"))

# Run algorithms
celf_output   = celf(g,2,p = 0.2,mc = 1000)

# Print results
print("celf output:   " + str(celf_output[0]))

 

运行结果：celf output: [0, 1]

 代码来源：https://hautahi.com/im_greedycelf