NetworkX 最大连通分量共享属性

Question

我知道 NetworkX 中存在用于计算图形连通分量大小的函数。您可以向节点添加属性。在 Axelrod 的文化传播模型中，一个有趣的度量是节点共享多个属性的最大连接组件的大小。在 NetworkX 中有没有办法做到这一点？例如，假设我们有一个通过网络表示的人口。每个节点都有头发颜色和肤色的属性。我怎样才能得到节点的最大组成部分的大小，以便在该子图中每个节点都具有相同的头发和肤色？谢谢

Answer 1

对于一般的数据分析，最好使用pandas。使用像 networkx 或 graph-tool 这样的图形库来确定连接的组件，然后将该信息加载到您可以分析的 DataFrame 中。在这种情况下，pandas groupby 和 nunique（唯一元素的数量）功能将很有用。

这是一个使用 graph-tool (using this network) 的 self-contained 示例。您还可以通过 networkx.

计算连通分量

import numpy as np
import pandas as pd
import graph_tool.all as gt

# Download an example graph
# https://networks.skewed.de/net/baseball
g = gt.collection.ns["baseball", 'user-provider']

# Extract the player names
names = g.vertex_properties['name'].get_2d_array([0])[0]

# Extract connected component ID for each node
cc, cc_sizes = gt.label_components(g)

# Load into a DataFrame
players = pd.DataFrame({
    'id': np.arange(g.num_vertices()),
    'name': names,
    'cc': cc.a
})

# Create some random attributes
players['hair'] = np.random.choice(['purple', 'pink'], size=len(players))
players['skin'] = np.random.choice(['green', 'blue'], size=len(players))

# For the sake of this example, manipulate the data so
# that some groups are homogenous with respect to some attributes.
players.loc[players['cc'] == 2, 'hair'] = 'purple'
players.loc[players['cc'] == 2, 'skin'] = 'blue'

players.loc[players['cc'] == 4, 'hair'] = 'pink'
players.loc[players['cc'] == 4, 'skin'] = 'green'

# Now determine how many unique hair and skin colors we have in each group.
group_stats = players.groupby('cc').agg({
    'hair': 'nunique',
    'skin': ['nunique', 'size']
})

# Simplify the column names
group_stats.columns = ['hair_colors', 'skin_colors', 'player_count']

# Select homogenous groups, i.e. groups for which only 1 unique
# hair color is present and 1 unique skin color is present
homogenous = group_stats.query('hair_colors == 1 and skin_colors == 1')

# Sort from large groups to small groups
homogenous = homogenous.sort_values('player_count', ascending=False)
print(homogenous)

打印以下内容：

    hair_colors  skin_colors  player_count
cc
4             1            1             4
2             1            1             3

NetworkX 最大连通分量共享属性

NetworkX largest connected component sharing attributes

networkx

graph-tool