PageRank实战-西游记人物节点重要程度

二叉树上的我收录于机器学习 python

2023-09-27 约 1992 字预计阅读 4 分钟

PageRank节点重要度

在NetworkX中，计算有向图节点的PageRank节点重要度。

参考资料

networkx官方教程：https://networkx.org/documentation/stable/tutorial.html

nx.Graph https://networkx.org/documentation/stable/reference/classes/graph.html#networkx.Graph

给图、节点、连接添加属性：https://networkx.org/documentation/stable/tutorial.html#attributes

读写图：https://networkx.org/documentation/stable/reference/readwrite/index.html

导入工具包

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import networkx as nx # 图数据挖掘
import numpy as np # 数据分析
import random # 随机数
import pandas as pd
 
# 数据可视化
import matplotlib.pyplot as plt
%matplotlib inline
plt.rcParams['font.sans-serif']=['SimHei']  # 用来正常显示中文标签  
plt.rcParams['axes.unicode_minus']=False  # 用来正常显示负号

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G = nx.star_graph(7)

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nx.draw(G, with_labels = True)

计算PageRank节点重要度

数据下载地址：http://www.openkg.cn/dataset/ch4masterpieces

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pagerank = nx.pagerank(G, alpha=0.8)

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pagerank

{0: 0.4583348922684132,
 1: 0.07738072967594098,
 2: 0.07738072967594098,
 3: 0.07738072967594098,
 4: 0.07738072967594098,
 5: 0.07738072967594098,
 6: 0.07738072967594098,
 7: 0.07738072967594098}

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# 导入 csv 文件定义的有向图
df = pd.read_csv('./triples.csv')

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df

	head	tail	relation	label
0	金蝉子	唐僧	past_life	前世
1	孙悟空	唐僧	apprentice	徒弟
2	猪八戒	唐僧	apprentice	徒弟
3	沙僧	唐僧	apprentice	徒弟
4	白龙马	唐僧	apprentice	徒弟
...	...	...	...	...
104	毗蓝婆菩萨	昴日星官	mother	母亲
105	嫦娥	后羿	wife	妻
106	敖摩昂	敖闰	son	儿
107	哪吒	李靖	son	儿
108	哪吒	如来	apprentice	徒弟

109 rows × 4 columns

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edges = [edge for edge in zip(df['head'], df['tail'])]
 
G = nx.DiGraph()
G.add_edges_from(edges)

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# 可视化
plt.figure(figsize=(15,14))
pos = nx.spring_layout(G, iterations=3, seed=5) #设置为基于弹簧布局，迭代次数为3，次数越多，根据节点之间的相互作用力找到的节点位置越合理
nx.draw(G, pos, with_labels=True)
plt.show()

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pagerank = nx.pagerank(G,                     # NetworkX graph 有向图，如果是无向图则自动转为双向有向图
                       alpha=0.85,            # Damping Factor，阻尼系数，理解这个得理解谷歌矩阵，也就是明白算法本身才行
                       personalization=None,  # 是否开启Personalized PageRank，随机传送至指定节点集合的概率更高或更低
                       max_iter=100,          # 最大迭代次数
                       tol=1e-06,             # 判定收敛的误差
                       nstart=None,           # 每个节点初始PageRank值      
                       dangling=None,         # Dead End死胡同节点
                      )

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sorted(pagerank.items(), key=lambda x: x[1], reverse=True)

[('唐僧', 0.13349105557884888),
 ('孙悟空', 0.10498354112014094),
 ('白龙马', 0.09531260474698808),
 ('猪八戒', 0.09247797536009736),
 ('沙僧', 0.07627154154696374),
 ('李世民', 0.052002919751408624),
 ('观音菩萨', 0.026625716774094633),
 ('高翠兰', 0.02579183411604112),
 ('卵二姐', 0.01860884001045803),
 ('太上老君', 0.014430996933862522),
 ('如来', 0.013334300311185142),
 ('牛魔王', 0.010256020230003658),
 ('哪吒', 0.009171370913926254),
 ('灵吉菩萨', 0.007800320258156309),
 ('宼栋', 0.007432108638238391),
 ('昴日星官', 0.007432108638238391),
 ('后羿', 0.007432108638238391),
 ('李靖', 0.006787403654483575),
 ('殷温娇', 0.005344620286308959),
 ('寇梁', 0.005344620286308959),
 ('袁天罡', 0.005344620286308959),
 ('金角', 0.005344620286308959),
 ('银角', 0.005344620286308959),
 ('西海龙王太子', 0.005344620286308959),
 ('弥勒佛', 0.005344620286308959),
 ('毗蓝婆菩萨', 0.005344620286308959),
 ('文殊菩萨', 0.005344620286308959),
 ('普贤菩萨', 0.005344620286308959),
 ('太乙救苦天尊', 0.005344620286308959),
 ('嫦娥', 0.005344620286308959),
 ('南极寿星', 0.005344620286308959),
 ('东来佛祖笑和尚', 0.005344620286308959),
 ('敖闰', 0.005344620286308959),
 ('木吒', 0.004812288400108432),
 ('金吒', 0.004812288400108432),
 ('高玉兰', 0.004116770300385284),
 ('金蝉子', 0.0028889203144616088),
 ('陈光蕊', 0.0028889203144616088),
 ('法明和尚', 0.0028889203144616088),
 ('殷开山', 0.0028889203144616088),
 ('菩提老祖', 0.0028889203144616088),
 ('镇元子', 0.0028889203144616088),
 ('蛟魔王', 0.0028889203144616088),
 ('鹏魔王', 0.0028889203144616088),
 ('狮驼王', 0.0028889203144616088),
 ('猕猴王', 0.0028889203144616088),
 ('禺狨王', 0.0028889203144616088),
 ('天蓬元帅', 0.0028889203144616088),
 ('卷帘大将', 0.0028889203144616088),
 ('西海龙王', 0.0028889203144616088),
 ('西海龙母', 0.0028889203144616088),
 ('敖摩昂太子', 0.0028889203144616088),
 ('西海龙女', 0.0028889203144616088),
 ('李渊', 0.0028889203144616088),
 ('李建成', 0.0028889203144616088),
 ('李元吉', 0.0028889203144616088),
 ('王珪', 0.0028889203144616088),
 ('秦琼', 0.0028889203144616088),
 ('萧瑀', 0.0028889203144616088),
 ('傅奕', 0.0028889203144616088),
 ('魏征', 0.0028889203144616088),
 ('李玉英', 0.0028889203144616088),
 ('房玄龄', 0.0028889203144616088),
 ('杜如晦', 0.0028889203144616088),
 ('徐世绩', 0.0028889203144616088),
 ('徐茂公', 0.0028889203144616088),
 ('许敬宗', 0.0028889203144616088),
 ('马三宝', 0.0028889203144616088),
 ('段志贤', 0.0028889203144616088),
 ('程咬金', 0.0028889203144616088),
 ('虞世南', 0.0028889203144616088),
 ('张道源', 0.0028889203144616088),
 ('张士衡', 0.0028889203144616088),
 ('高太公', 0.0028889203144616088),
 ('高香兰', 0.0028889203144616088),
 ('寇洪', 0.0028889203144616088),
 ('袁守诚', 0.0028889203144616088),
 ('正元龙', 0.0028889203144616088),
 ('二十四路诸天', 0.0028889203144616088),
 ('守山大神', 0.0028889203144616088),
 ('善财童子', 0.0028889203144616088),
 ('捧珠龙女', 0.0028889203144616088),
 ('红孩儿', 0.0028889203144616088),
 ('黑风怪', 0.0028889203144616088),
 ('黄风怪', 0.0028889203144616088),
 ('黄毛貂鼠', 0.0028889203144616088),
 ('铁扇公主', 0.0028889203144616088),
 ('九尾狐狸', 0.0028889203144616088),
 ('狐阿七', 0.0028889203144616088),
 ('鼍龙怪', 0.0028889203144616088),
 ('灵感大王', 0.0028889203144616088),
 ('独角兕大王', 0.0028889203144616088),
 ('玉面公主', 0.0028889203144616088),
 ('金毛犼', 0.0028889203144616088),
 ('黄眉道童', 0.0028889203144616088),
 ('百眼魔君', 0.0028889203144616088),
 ('青狮', 0.0028889203144616088),
 ('白象', 0.0028889203144616088),
 ('大鹏金翅雕', 0.0028889203144616088),
 ('九头狮子', 0.0028889203144616088),
 ('玉兔精', 0.0028889203144616088),
 ('白鹿精', 0.0028889203144616088),
 ('黄眉大王', 0.0028889203144616088),
 ('敖摩昂', 0.0028889203144616088)]

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# 节点尺寸
node_sizes = (np.array(list(pagerank.values())) * 8000).astype(int)

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node_sizes

array([  23, 1067,  839,  739,  610,  762,   23,   42,   23,  416,   23,
         23,   23,   82,   23,   23,   23,   23,   23,   23,  148,  206,
         23,   23,   23,   23,   23,   23,   23,   23,   23,   23,   23,
         23,   23,   23,   23,   23,   23,   23,   23,   23,   23,   23,
         23,   23,   23,   23,   23,   32,   23,   42,   59,   23,   42,
         54,   38,   73,   38,   23,  213,   23,   23,   23,   23,  106,
         23,   23,   23,   62,   23,   42,  115,   42,   23,   23,   23,
         23,   42,   23,   23,   23,   23,   23,   42,   23,   42,   23,
         42,   23,   42,   23,   23,   42,   23,   42,   23,   42,   23,
         42,   59,   59,   23,   42])

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# 节点颜色
M = G.number_of_edges()
edge_colors = range(2, M + 2)
 
 
plt.figure(figsize=(15,14))
 
# 绘制节点
nodes = nx.draw_networkx_nodes(G, pos, node_size=node_sizes, node_color=node_sizes)
 
# 绘制连接
edges = nx.draw_networkx_edges(
    G,
    pos,
    node_size=node_sizes,   # 节点尺寸
    arrowstyle="->",        # 箭头样式
    arrowsize=20,           # 箭头尺寸
    edge_color=edge_colors, # 连接颜色
    edge_cmap=plt.cm.plasma,# 连接配色方案，可选：plt.cm.Blues
    width=4                 # 连接线宽
)
 
# 设置每个连接的透明度
edge_alphas = [(5 + i) / (M + 4) for i in range(M)]
for i in range(M):
    edges[i].set_alpha(edge_alphas[i])
 
# # 图例
# pc = mpl.collections.PatchCollection(edges, cmap=cmap)
# pc.set_array(edge_colors)
# plt.colorbar(pc)
 
ax = plt.gca()
ax.set_axis_off()
plt.show()

/tmp/ipykernel_206894/3554403709.py:12: DeprecationWarning: `alltrue` is deprecated as of NumPy 1.25.0, and will be removed in NumPy 2.0. Please use `all` instead.
  edges = nx.draw_networkx_edges(

目录

PageRank实战-西游记人物节点重要程度

PageRank节点重要度

参考资料

导入工具包

计算PageRank节点重要度