三元组

根据 Snijders, T. (2012) 的论文“传递性与三元组”（牛津大学），共有 16 种可能的三元组类型。该图展示了在有向网络中可以识别出的 16 种三元组类型。在分析社交网络时，三元组关系特别有用。前三位数字表示互惠、非对称和空二元组（双向、单向和无边）的数量，字母表示方向（Orientation），分别为向上（Up，U）、向下（Down，D）、循环（Cyclical，C）或传递（Transitive，T）。

import networkx as nx
import matplotlib.pyplot as plt

fig, axes = plt.subplots(4, 4, figsize=(10, 10))
triads = {
    "003": [],
    "012": [(1, 2)],
    "102": [(1, 2), (2, 1)],
    "021D": [(3, 1), (3, 2)],
    "021U": [(1, 3), (2, 3)],
    "021C": [(1, 3), (3, 2)],
    "111D": [(1, 2), (2, 1), (3, 1)],
    "111U": [(1, 2), (2, 1), (1, 3)],
    "030T": [(1, 2), (3, 2), (1, 3)],
    "030C": [(1, 3), (3, 2), (2, 1)],
    "201": [(1, 2), (2, 1), (3, 1), (1, 3)],
    "120D": [(1, 2), (2, 1), (3, 1), (3, 2)],
    "120U": [(1, 2), (2, 1), (1, 3), (2, 3)],
    "120C": [(1, 2), (2, 1), (1, 3), (3, 2)],
    "210": [(1, 2), (2, 1), (1, 3), (3, 2), (2, 3)],
    "300": [(1, 2), (2, 1), (2, 3), (3, 2), (1, 3), (3, 1)],
}

for (title, triad), ax in zip(triads.items(), axes.flatten()):
    G = nx.DiGraph()
    G.add_nodes_from([1, 2, 3])
    G.add_edges_from(triad)
    nx.draw_networkx(
        G,
        ax=ax,
        with_labels=False,
        node_color=["green"],
        node_size=200,
        arrowsize=20,
        width=2,
        pos=nx.planar_layout(G),
    )
    ax.set_xlim(val * 1.2 for val in ax.get_xlim())
    ax.set_ylim(val * 1.2 for val in ax.get_ylim())
    ax.text(
        0,
        0,
        title,
        fontsize=15,
        fontweight="extra bold",
        horizontalalignment="center",
        bbox={"boxstyle": "square,pad=0.3", "fc": "none"},
    )
fig.tight_layout()
plt.show()