桥中心性——抑郁与焦虑症状之间的"桥"

# 构造一个两社团网络（抑郁 5 个症状、焦虑 5 个症状，模拟边权，仅用于演示方法），
# 按 Jones, Ma & McNally (2021) 的定义计算桥强度（与其他社团节点的边权绝对值之和）
# 与一步桥预期影响（保留符号），并与普通强度对比。
# 输出解读：普通强度最高的是"紧张不安""情绪低落"，桥强度最高的却是"注意力差""睡眠问题"（"疲乏"次之）——
# 它们承担了两个症状群之间的大部分连接，这是共病网络解释中"桥症状"的含义。
# 有负的跨社团边时（如"自我评价低–易激惹"），桥 EI 与桥强度不同。
# 桥中心性依赖事先给定的社团划分；划分改变，桥症状也会改变。
import numpy as np
import networkx as nx

nodes = ["情绪低落", "兴趣减退", "自我评价低", "睡眠问题", "疲乏",       # 抑郁
         "过度担忧", "难以控制担忧", "紧张不安", "易激惹", "注意力差"]   # 焦虑
community = np.array([0] * 5 + [1] * 5)
edges = {(0, 1): .35, (0, 2): .25, (1, 2): .15, (0, 4): .15, (3, 4): .30, (1, 4): .10,
         (5, 6): .40, (5, 7): .20, (6, 7): .25, (7, 8): .20, (6, 9): .10, (8, 9): .10,
         (3, 7): .20, (3, 9): .15, (4, 9): .25, (0, 5): .08, (2, 8): -.05}
W = np.zeros((10, 10))
for (i, j), w in edges.items():
    W[i, j] = W[j, i] = w

strength = np.abs(W).sum(axis=1)
other = community[:, None] != community[None, :]
bridge_strength = (np.abs(W) * other).sum(axis=1)
bridge_ei1 = (W * other).sum(axis=1)

order = np.argsort(bridge_strength)[::-1]
print(f"{'症状':<8}{'社团':>4}{'强度':>8}{'桥强度':>8}{'桥EI(1)':>9}")
for i in order:
    print(f"{nodes[i]:<8}{'抑郁' if community[i] == 0 else '焦虑':>4}{strength[i]:>8.2f}"
          f"{bridge_strength[i]:>8.2f}{bridge_ei1[i]:>9.2f}")
cut = np.quantile(bridge_strength, 0.8)
print("桥强度位于前 20% 的症状（应用研究常用的经验界限，非统计检验）：",
      [nodes[i] for i in range(10) if bridge_strength[i] >= cut])

G = nx.from_numpy_array(np.abs(W))
comms = [set(np.where(community == c)[0]) for c in (0, 1)]
print(f"按给定划分的模块度 Q = {nx.community.modularity(G, comms, weight='weight'):.3f}")

import matplotlib.pyplot as plt

def draw_signed(ax, M, labels, thr, title, node_color="#DDDDDD", node_size=180, pos=None):
    """边宽 ∝ |权重|，蓝色为正边、红色为负边。"""
    n = len(labels)
    pos = nx.circular_layout(range(n)) if pos is None else pos
    G = nx.Graph(); G.add_nodes_from(range(n))
    G.add_weighted_edges_from((i, j, M[i, j]) for i in range(n) for j in range(i + 1, n) if abs(M[i, j]) > thr)
    ws = [d["weight"] for _, _, d in G.edges(data=True)]
    nx.draw_networkx_edges(G, pos, ax=ax, width=[max(1.0, 8 * abs(w)) for w in ws],
                           edge_color=["#4477AA" if w > 0 else "#CC6677" for w in ws])
    nx.draw_networkx_nodes(G, pos, ax=ax, node_size=node_size, node_color=node_color, edgecolors="k")
    lab_pos = {k: (1.22 * np.asarray(v)) for k, v in pos.items()}
    nx.draw_networkx_labels(G, lab_pos, labels=dict(enumerate(labels)), ax=ax, font_size=9)
    ax.plot([], [], color="#4477AA", lw=2, label="positive")
    ax.plot([], [], color="#CC6677", lw=2, label="negative")
    ax.legend(loc="lower right", fontsize=7, frameon=False)
    ax.set_title(title, fontsize=10); ax.set_aspect("equal"); ax.axis("off")
    ax.set_xlim(-1.45, 1.45); ax.set_ylim(-1.45, 1.45)

abbr = ["Sad", "Anh", "Wth", "Slp", "Fat", "Wry", "Ctl", "Nrv", "Irr", "Con"]   # 前 5 个抑郁，后 5 个焦虑
fig, axes = plt.subplots(1, 2, figsize=(10, 4.4))
draw_signed(axes[0], W, abbr, 0, "Depression (orange) and anxiety (blue) symptoms",
            node_color=np.where(community == 0, "#EE8866", "#77AADD"),
            node_size=60 + 140 * bridge_strength / bridge_strength.max())
axes[0].text(0, -1.42, "node size = bridge strength", ha="center", fontsize=8)
x = np.arange(10)
axes[1].bar(x - 0.2, strength, 0.4, color="#BBBBBB", label="strength")
axes[1].bar(x + 0.2, bridge_strength, 0.4, color="#4477AA", label="bridge strength")
axes[1].set_xticks(x, abbr)
axes[1].set(ylabel="Sum of |edge weights|", title="Bridge symptoms differ from the most central ones")
axes[1].legend(fontsize=8)
plt.tight_layout(); plt.show()