網路彈性量化：從最小割到平均節點連通性

import networkx as nx
import matplotlib.pyplot as plt
import networkx.connectivity as nxcon # 導入 connectivity 模組

# --- 創建範例網路 
---
# 空手道網路
G_karate_demo = nx.karate_club_graph()
mr_hi_node = 0
john_a_node = 33

# 德國電網 (簡化，確保連通性)
G_electric_demo = nx.Graph()
for i in range(30):
    G_electric_demo.add_edge(i, i+1)
G_electric_demo.add_edge(0, 15)
G_electric_demo.add_edge(10, 25)
G_electric_demo.add_edge(20, 30)
G_electric_demo.add_edge(5, 25)
# 確保連通性
if not nx.is_connected(G_electric_demo):
    print("警告：電網網路不連通，已嘗試修復。")
    # 簡單修復：連接兩個最大的組件
    components = list(nx.connected_components(G_electric_demo))
    if len(components) > 1:
        for i in range(len(components[0])):
            for j in range(len(components[1])):
                 if G_electric_demo.number_of_edges() < G_electric_demo.number_of_nodes() * 2: # 避免過度稠密
                    G_electric_demo.add_edge(list(components[0])[i], list(components[1])[j])
                    break
            if G_electric_demo.number_of_edges() > G_electric_demo.number_of_nodes() * 2: break

# GÉANT 網路 (簡化，確保連通性)
G_internet_demo = nx.Graph()
for i in range(8):
    for j in range(i+1, 8):
        G_internet_demo.add_edge(i, j)
for i in range(8, 30):
    G_internet_demo.add_edge(i, i % 8)
    if i % 4 == 0:
        if i+10 < 30:
            G_internet_demo.add_edge(i, i+10)
        else:
            G_internet_demo.add_edge(i, 29)
# 確保連通性
if not nx.is_connected(G_internet_demo):
    print("警告：網際網路網路不連通，已嘗試修復。")
    components = list(nx.connected_components(G_internet_demo))
    if len(components) > 1:
        for i in range(len(components[0])):
            for j in range(len(components[1])):
                if G_internet_demo.number_of_edges() < G_internet_demo.number_of_nodes() * 2:
                    G_internet_demo.add_edge(list(components[0])[i], list(components[1])[j])
                    break
            if G_internet_demo.number_of_edges() > G_internet_demo.number_of_nodes() * 2: break

print("\n--- 獲取最小割大小與計算全局連通性 
---
")

networks_to_analyze = {
    "Karate Club": (G_karate_demo, mr_hi_node, john_a_node),
    "Electric Grid": (G_electric_demo, 0, 15), # 隨機選擇一對節點
    "GÉANT Internet": (G_internet_demo, 0, 10) # 隨機選擇一對節點
}

for name, (G, s, t) in networks_to_analyze.items():
    if G and G.number_of_nodes() >= 2:
        try:
            # 獲取兩個節點間的最小割大小
            node_cut_size = nx.node_connectivity(G, s, t)
            edge_cut_size = nx.edge_connectivity(G, s, t)
            print(f"{name} - 節點 {s} 與 {t} 間的節點連通度: {node_cut_size}")
            print(f"{name} - 節點 {s} 與 {t} 間的邊連通度: {edge_cut_size}")

            # 計算全局節點連通度 (可能耗時)
            # 全局節點連通度
            global_node_conn = nx.node_connectivity(G)
            print(f"{name} - 全局節點連通度: {global_node_conn}")

            # 全局邊連通度 (如果需要，但通常更耗時)
            # global_edge_conn = nx.edge_connectivity(G)
            # print(f"{name} - 全局邊連通度: {global_edge_conn}")

            # 計算平均節點連通度 (可能非常耗時)
            # avg_node_conn = nx.average_node_connectivity(G)
            # print(f"{name} - 平均節點連通度: {avg_node_conn:.4f}")

        except nx.NetworkXNoPath:
            print(f"{name} - 節點 {s} 和 {t} 不連通，或網路不連通。")
        except Exception as e:
            print(f"{name} - 計算時發生錯誤: {e}")
    else:
        print(f"{name} - 節點數不足或網路為空。")

# 為了演示，我們單獨計算平均節點連通度
print("\n--- 計算平均節點連通度 (可能耗時) 
---
")
try:
    avg_node_conn_karate = nx.average_node_connectivity(G_karate_demo)
    print(f"空手道網路 - 平均節點連通度: {avg_node_conn_karate:.4f}")
except Exception as e:
    print(f"空手道網路 - 計算平均節點連通度時出錯: {e}")

try:
    avg_node_conn_electric = nx.average_node_connectivity(G_electric_demo)
    print(f"電網網路 - 平均節點連通度: {avg_node_conn_electric:.4f}")
except Exception as e:
    print(f"電網網路 - 計算平均節點連通度時出錯: {e}")

try:
    avg_node_conn_internet = nx.average_node_connectivity(G_internet_demo)
    print(f"網際網路網路 - 平均節點連通度: {avg_node_conn_internet:.4f}")
except Exception as e:
    print(f"網際網路網路 - 計算平均節點連通度時出錯: {e}")