运用si感染模型感染导入的'football.edge'数据集，输出打印节点感染状态和邻居，之后设置观测节点，利用定位源的反向传播初始时间的方差来定位，输出结果并将最终结果可视化

以下是利用SI感染模型感染'football.edge'数据集的Python代码：

import networkx as nx
import numpy as np
import random

# 读取数据集
G = nx.read_edgelist('football.edge')

# SI感染模型
def SI_model(G, beta):
    # 初始化节点状态
    nodes_status = {node: 'S' for node in G.nodes()}
    # 随机选择一个节点作为感染源
    source = random.choice(list(G.nodes()))
    nodes_status[source] = 'I'
    
    # 迭代更新节点状态
    while True:
        flag = True  # 判断是否还有节点可以感染
        for node in G.nodes():
            if nodes_status[node] == 'S':
                for neighbor in G.neighbors(node):
                    if nodes_status[neighbor] == 'I':
                        # 以概率beta感染该节点
                        if np.random.random() < beta:
                            nodes_status[node] = 'I'
                            flag = False
                            break
            if not flag:
                break
        if flag:
            break
            
    return nodes_status

# 运行SI模型并输出节点状态和邻居
beta = 0.2
nodes_status = SI_model(G, beta)
for node in G.nodes():
    print(f"Node {node} status: {nodes_status[node]}, neighbors: {list(G.neighbors(node))}")

设置观测节点并利用定位源的反向传播初始时间的方差来定位：

# 设置观测节点
observed_nodes = [1, 4, 13, 14, 17, 22, 25, 29, 31, 33]

# 利用定位源的反向传播算法定位
def reverse_propagation(observed_nodes, nodes_status, beta, max_iter=1000, tol=1e-6):
    # 初始化
    N = len(nodes_status)
    H = np.zeros((N, N))
    for i in range(N):
        for j in range(N):
            if i == j:
                H[i, j] = 1
            else:
                H[i, j] = -beta * int(j in G.neighbors(i))
    Y = np.zeros((N, N))
    for i in observed_nodes:
        Y[i, i] = 1
    t = np.zeros(N)
    
    # 反向传播
    for i in range(max_iter):
        t_new = np.dot(np.linalg.inv(H), Y - np.exp(-beta*t))
        if np.linalg.norm(t_new - t) < tol:
            break
        t = t_new
        
    return t

# 运行定位算法
t = reverse_propagation(observed_nodes, nodes_status, beta)

# 输出结果
print("Estimated infection time:")
for node in G.nodes():
    print(f"Node {node}: {t[node]}")

最后，将最终结果可视化：

import matplotlib.pyplot as plt

# 可视化定位结果
pos = nx.spring_layout(G)
node_color = [t[node] for node in G.nodes()]
nx.draw_networkx(G, pos, node_size=50, node_color=node_color, cmap=plt.cm.Reds)
plt.title("Infection time estimation")
plt.colorbar()
plt.show()