可以使用 Python 的 `matplotlib` 库和 `networkx` 库来绘制超图。以下是实现该功能的代码： ```python import matplotlib.pyplot as plt import networkx as nx import numpy as np from matplotlib.path import Path from matplotlib.patches import PathPatch # 顶点集 V = ["v1", "v2", "v3", "v4", "v5", "v6", "v7", "v8", "v9", "v10", "v11", "v12", "v13"] # 顶点超度序列 vertex_degrees = [2, 2, 1, 2, 2, 2, 2, 1, 2, 1, 1, 1, 2] # 超边集 E = { "e1": ["v1", "v2", "v3", "v4"], "e2": ["v4", "v5", "v6"], "e3": ["v5", "v6", "v7"], "e4": ["v1", "v2", "v7", "v8", "v9"], "e5": ["v9", "v10"], "e6": ["v11", "v12", "v13"], "e7": ["v13"] } # 超边度序列 edge_degrees = [2, 2, 2, 3, 1, 1, 1] # 节点坐标（随机生成） pos = nx.spring_layout(nx.Graph([(node, node) for node in V])) # 生成平滑闭合曲线 def create_smooth_path(nodes): pts = np.array([pos[n] for n in nodes]) if len(pts) == 1: x, y = pts[0] theta = np.linspace(0, 2 * np.pi, 20) verts = np.column_stack([x + 0.15 * np.cos(theta), y + 0.15 * np.sin(theta)]) else: from scipy.spatial import ConvexHull hull = ConvexHull(pts) hull_pts = pts[hull.vertices] cx, cy = np.mean(hull_pts, axis=0) offset_pts = [] for x, y in hull_pts: dx, dy = x - cx, y - cy r = np.hypot(dx, dy) nx, ny = dx / r * 0.2, dy / r * 0.2 offset_pts.append((x + nx, y + ny)) offset_pts.append(offset_pts[0]) verts = np.array(offset_pts) n = len(verts) codes = [Path.MOVETO] if n > 2: codes += [Path.CURVE4] * (n - 2) codes += [Path.CLOSEPOLY] if len(verts) == len(codes) - 1: verts = np.vstack([verts, verts[0]]) return Path(verts, codes) # 绘图 fig, ax = plt.subplots(figsize=(10, 8), dpi=150) ax.set_xlim(-1.5, 1.5) ax.set_ylim(-1.5, 1.5) ax.set_aspect("equal") # 绘制超边平滑圈 for name, nodes in E.items(): path = create_smooth_path(nodes) patch = PathPatch(path, facecolor="none", edgecolor="black", linewidth=1.5) ax.add_patch(patch) # 绘制2-section图（超边内全连接） edges = set() for nds in E.values(): for i in range(len(nds)): for j in range(i + 1, len(nds)): edges.add((nds[i], nds[j])) for u, v in edges: x1, y1 = pos[u] x2, y2 = pos[v] ax.plot([x1, x2], [y1, y2], color="black", linewidth=1.0) # 绘制节点和标签 for node, (x, y) in pos.items(): ax.scatter(x, y, s=230, color="black", zorder=10) ax.text(x + 0.09, y + 0.09, node, fontsize=11, fontweight="bold", zorder=11) # 标注超边名称 edge_labels = { "e1": (-0.8, 0.8), "e2": (0.8, 0.8), "e3": (0.8, -0.8), "e4": (-0.8, -0.8), "e5": (-0.2, -1.2), "e6": (0.2, -1.2), "e7": (0.8, -1.2) } for name, (x, y) in edge_labels.items(): ax.text(x, y, f"${name}$", fontsize=12, fontweight="bold") # 隐藏坐标轴，添加标题 ax.axis("off") ax.text(0, -1.7, "2-section图", fontsize=12, ha="center") ax.text(0, -1.9, "超图的2节图", fontsize=12, ha="center") plt.tight_layout() plt.savefig("hypergraph.png", dpi=300, bbox_inches="tight") plt.show() ``` ### 代码解释： 1. **定义顶点集、顶点超度序列、超边集和超边度序列**：根据用户提供的信息，定义了相应的集合和序列。 2. **生成节点坐标**：使用 `networkx` 的 `spring_layout` 函数随机生成节点的坐标。 3. **生成平滑闭合曲线**：定义了 `create_smooth_path` 函数，用于生成超边的平滑闭合曲线。 4. **绘图**：使用 `matplotlib` 库绘制超图，包括超边的平滑圈、2-section 图、节点和标签，以及超边名称的标注。 ###