import numpy as np
import networkx as nx
import matplotlib.pyplot as plt
from path_ring import make_ring_lattice
def path_lengths(G):
length_iter = nx.shortest_path_length(G)
for _, dist_map in length_iter:
for _, dist in dist_map.items():
yield dist
def characteristic_path_length(G):
return np.mean(list(path_lengths(G)))
complete = nx.complete_graph(10)
characteristic_path_length(complete) # 0.9
lattice = make_ring_lattice(1000, 10)
characteristic_path_length(lattice) # 50.4
`clustering_coefficient`为每个节点调用`node_clustering`一次。`node_clustering`是以$k$为单位的二次函数，即邻居数。因此：
- 在完整图中，$k = n-1$，所以`node_clustering`是$O(n^2)$，且`clustering_coefficient`是$O(n^3)$。
- 在环形晶格或其他图中，$k$与$n$不成正比的图，`clustering_coefficient`是$O(k^2 n)$。
'''
def node_clustering(G, u):
neighbors = G[u]
k = len(neighbors)
if k < 2:
return np.nan
possible = comb(k, 2)
exist = 0
for v, w in all_pairs_undirected(neighbors):
if G.has_edge(v, w):
exist += 1
return exist / possible
lattice = make_ring_lattice(10, 4)
node_clustering(lattice, 1) # 0.5
def clustering_coefficient(G):
cu = [node_clustering(G, node) for node in G]
return np.nanmean(cu)
clustering_coefficient(lattice) # 0.5
def make_ws_graph(n, k, p):
ws = make_ring_lattice(n, k)
rewire(ws, p)
return ws