網路結構分析從社群劃分到團體識別

import networkx as nx
import networkx.community as nxcom
import matplotlib.pyplot as plt
import itertools

# --- 創建 Zachary 空手道網路 ---
G_karate_demo = nx.karate_club_graph()

# --- Girvan-Newman 迭代式社群劃分 (獲取四個社群) ---
communities_gn_4 = []
print("\n--- 使用 Girvan-Newman 演算法獲取四個社群 ---")
try:
    girvan_newman_iterator = nxcom.girvan_newman(G_karate_demo)

    # 使用 itertools.islice 跳過前兩個分割，獲取第三個分割 (通常產生 4 個社群)
    # islice(iterator, start, stop) - stop 是 exclusive
    communities_gn_4 = next(itertools.islice(girvan_newman_iterator, 2, 3))

    num_communities_gn_4 = len(communities_gn_4)
    print(f"Girvan-Newman 迭代 3 得到的社群數量: {num_communities_gn_4}")
    print("四個社群的大小:")
    for i, comm in enumerate(communities_gn_4):
        print(f"  社群 {i+1}: {len(comm)} 個節點")

except Exception as e:
    print(f"獲取四個社群時發生錯誤: {e}")

# --- 團體 (Cliques) 查找與分析 ---
print("\n--- 查找團體 (Cliques) ---")
cliques = []
max_clique = []
try:
    # 查找所有團體
    cliques = list(nx.find_cliques(G_karate_demo))
    print(f"找到的團體總數: {len(cliques)}")

    # 查找最大團體
    if cliques:
        max_clique = max(cliques, key=len)
        print(f"最大團體 (Maximal Clique) 包含 {len(max_clique)} 個節點: {max_clique}")
    else:
        print("網路中未找到任何團體。")

except Exception as e:
    print(f"查找團體時發生錯誤: {e}")

# --- 視覺化輔助函數 (沿用前述定義) ---
def set_node_community(G, communities_list):
    if not communities_list: return
    for c, nodes_in_community in enumerate(communities_list):
        for node in nodes_in_community:
            G.nodes[node]['community'] = c + 1

def set_edge_community(G):
    for u, v in G.edges():
        if 'community' in G.nodes[u] and 'community' in G.nodes[v]:
            if G.nodes[u]['community'] == G.nodes[v]['community']:
                G.edges[u, v]['community'] = G.nodes[u]['community']
            else:
                G.edges[u, v]['community'] = 0
        else:
            pass

def get_color(community_id, n_communities, low=0.1, high=0.9):
    if community_id == 0: return (0.5, 0.5, 0.5) # 灰色
    if n_communities <= 1: return (0.8, 0.2, 0.2)
    normalized_community_id = (community_id - 1) / (n_communities - 1)
    return plt.cm.viridis(normalized_community_id)

# --- 視覺化 Girvan-Newman 四個社群 ---
if communities_gn_4 and G_karate_demo.number_of_nodes() > 0:
    print("\n--- 繪製 Girvan-Newman 四個社群結構圖 ---")
    # 設置節點和邊的社群屬性
    set_node_community(G_karate_demo, communities_gn_4)
    set_edge_community(G_karate_demo)

    # 準備節點顏色
    n_communities_gn_4 = len(communities_gn_4)
    node_colors_gn_4 = []
    for node in G_karate_demo.nodes():
        community_id = G_karate_demo.nodes[node].get('community', 0)
        node_colors_gn_4.append(get_color(community_id, n_communities_gn_4))

    # 準備邊列表與顏色
    external_edges_gn_4 = []
    internal_edges_gn_4 = []
    internal_edge_colors_gn_4 = []

    for u, v, d in G_karate_demo.edges(data=True):
        community_id = d.get('community', 0)
        if community_id == 0:
            external_edges_gn_4.append((u, v))
        else:
            internal_edges_gn_4.append((u, v))
            internal_edge_colors_gn_4.append(get_color(community_id, n_communities_gn_4))

    # 計算佈局
    karate_pos = nx.spring_layout(G_karate_demo, seed=42, k=0.3)

    plt.figure(figsize=(10, 8))

    # 繪製外部邊
    nx.draw_networkx(
        G_karate_demo, pos=karate_pos, node_size=0,
        edgelist=external_edges_gn_4, edge_color="#333333", width=0.5, alpha=0.4, style='dashed'
    )

    # 繪製節點和內部邊
    nx.draw_networkx(
        G_karate_demo, pos=karate_pos,
        node_color=node_colors_gn_4, node_size=300, alpha=0.9,
        edgelist=internal_edges_gn_4, edge_color=internal_edge_colors_gn_4, width=1.5, alpha=0.7
    )

    nx.draw_networkx_labels(G_karate_demo, karate_pos, font_size=10, font_weight='bold')

    plt.title("Zachary Karate Club Network - Girvan-Newman Communities (4 Communities)", fontsize=16)
    plt.axis('off')
    plt.show()

else:
    print("\n無法繪製四個社群的視覺化，因為社群偵測失敗或網路為空。")

# --- 視覺化最大團體 ---
if max_clique and G_karate_demo.number_of_nodes() > 0:
    print("\n--- 視覺化最大團體 (Maximal Clique) ---")

    # 設置節點顏色：最大團體節點為醒目顏色，其他為灰色
    node_colors_max_clique = [(0.5, 0.5, 0.5) for _ in G_karate_demo.nodes()] # 預設灰色
    max_clique_nodes = set(max_clique)

    for i, v in enumerate(G_karate_demo.nodes()):
        if v in max_clique_nodes:
            node_colors_max_clique[i] = (0.9, 0.2, 0.2) # 醒目紅色

    plt.figure(figsize=(10, 8))

    # 繪製網路，強調最大團體節點
    nx.draw_networkx(
        G_karate_demo, pos=karate_pos,
        node_color=node_colors_max_clique, node_size=300, alpha=0.9,
        edge_color="#333333", width=0.5, alpha=0.4, style='dashed' # 繪製所有邊
    )

    nx.draw_networkx_labels(G_karate_demo, karate_pos, font_size=10, font_weight='bold')

    plt.title("Zachary Karate Club Network - Maximal Clique Highlighted", fontsize=16)
    plt.axis('off')
    plt.show()

    print("最大團體視覺化完成，標示出網路中最密集連接的節點群組。")

else:
    print("\n無法視覺化最大團體，因為未找到團體或網路為空。")