Networkx 统计推断

Question

我有一个使用 networkx 成功创建的有向加权图。

我正在尝试在此网络上生成一些统计推断，但我遇到了麻烦。他们在这里：

(i) 网络的平均度数。（我能找到的唯一一个是average_degree_connectivity，returns一个字典，而不是一个全网平均度的浮点数）

(ii) 网络的平均加权度。 (同上)

(iii) 网络的平均聚类系数。（我知道我必须使用 nx.average_clustering(g)，但是我如何考虑它是加权有向图这一事实？我不断收到错误消息： NetworkXError: ('Clustering algorithms are not defined ', 'for directed graphs.') )

谢谢！

Answer 1

(i) The Average degree of the network. (The only one I could find was average_degree_connectivity, which returns a dictionary and not a single float with the average degree of the whole network)

假设您的 Graph 对象是 G。

degrees = G.degree()
sum_of_edges = sum(degrees.values())

计算平均值只是除以节点数的问题。

(ii) The Average weighted degree of the network. (same as above)

获取所有节点的列表，为每个节点获取所有边的列表，为每个节点求和权重属性:

edgesdict = G.edge
total = 0
for node_adjacency_dict in edgesdict.valuess():
    total += sum([adjacency.get("weight",0) for adjacency in node_adjacency_dict.values()])

(iii) The Average clustering coefficient of the network. (I know that I have to use nx.average_clustering(g), however how do I take the fact that it is weighted directed graph into consideration? I keep getting the error: NetworkXError: ('Clustering algorithms are not defined ', 'for directed graphs.') )

要点是，在您定义它之前，它的定义并不明确。我认为，对于 Whosebug 的回答来说，这有点繁琐，所以我留给您解决为您的特定问题定义算法的问题。

(iv) The maximum shortest path length in the giant component of the network. (i know you find the giant component as such: giant = max(nx.connected_component_subgraphs(G), key=len) but how do we get the max shortest path length in it?)

运行 ipython 之类的。输入 giant.；你会得到一个你可以用 giant.

做的事情的列表

Answer 2

这里还有一些想法可以添加到@marcus-müller 所写的内容中。

对于平均度数（注意你的有向图，这是进出度数的总和）

In [1]: import networkx as nx
G
In [2]: G = nx.DiGraph()

In [3]: G.add_edge(1,2,weight=7)

In [4]: G.add_edge(3,4,weight=17)

In [5]: sum(G.degree().values())/float(len(G))
Out[5]: 1.0

In [6]: sum(G.degree(weight='weight').values())/float(len(G))
Out[6]: 12.0

NetworkX 中没有加权定向聚类的定义。已经有提案 https://github.com/networkx/networkx/issues/859 但还没有人完成实施。

对于有向图，最大连通分量的概念分为两个定义。弱连通分量是指当您考虑图的无向版本（用无向边替换每条有向边）时连通的分量。强连通组件是指每对节点都可以相互访问（有路径）的组件。

Answer 3

关于第 (i) 点：网络的平均度数，对于有向图， Networkx 内部计算如下：

nnodes = G.number_of_nodes()
deg = sum(d for n, d in G.in_degree()) / float(nnodes)
info += "Average in degree: %8.4f\n" % deg
deg = sum(d for n, d in G.out_degree()) / float(nnodes)
info += "Average out degree: %8.4f" % deg

你可以check it on github.

Answer 4

自 Networkx 2.5 (2021) 起，您可以使用 networkx.info(G) 获取图形的平均度数

代码：

print(nx.info(G))

输出：

Name:
Type: Graph
Number of nodes: 85
Number of edges: 63
Average degree:   1.4824

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