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# Python怎么实现多对多网络结构
## 1. 多对多网络结构概述
多对多（Many-to-Many）网络结构是图论和复杂网络分析中的重要模型，指网络中任意两个节点之间可以存在多条连接关系。这种结构广泛应用于社交网络分析、推荐系统、生物网络建模等领域。
### 1.1 典型应用场景
- **社交网络**：用户之间的关注/被关注关系
- **交通网络**：城市之间的多条航线/路线
- **知识图谱**：实体间的多重关系
- **推荐系统**：用户-商品的多维交互
## 2. 基础数据结构实现
### 2.1 使用邻接列表
```python
class ManyToManyGraph:
def __init__(self):
self.adjacency_list = {}
def add_node(self, node):
if node not in self.adjacency_list:
self.adjacency_list[node] = {}
def add_edge(self, node1, node2, relation_type, weight=1):
self.add_node(node1)
self.add_node(node2)
if node2 not in self.adjacency_list[node1]:
self.adjacency_list[node1][node2] = []
self.adjacency_list[node1][node2].append((relation_type, weight))
# 对于无向图需要双向添加
if node1 not in self.adjacency_list[node2]:
self.adjacency_list[node2][node1] = []
self.adjacency_list[node2][node1].append((relation_type, weight))
import networkx as nx
# 创建多重有向图
G = nx.MultiDiGraph()
# 添加带属性的边
G.add_edge('user1', 'user2', relation='follow', weight=0.8)
G.add_edge('user1', 'user2', relation='like', weight=0.5)
G.add_edge('user2', 'user1', relation='mention', weight=0.3)
# 查询节点间的所有关系
relations = G.get_edge_data('user1', 'user2')
print(relations) # 输出所有关系及属性
from sqlalchemy import create_engine, Column, Integer, String, Float, ForeignKey
from sqlalchemy.orm import relationship, sessionmaker
from sqlalchemy.ext.declarative import declarative_base
Base = declarative_base()
class User(Base):
__tablename__ = 'users'
id = Column(Integer, primary_key=True)
name = Column(String(50))
relationships = relationship("Relationship", back_populates="source")
class Relationship(Base):
__tablename__ = 'relationships'
id = Column(Integer, primary_key=True)
source_id = Column(Integer, ForeignKey('users.id'))
target_id = Column(Integer, ForeignKey('users.id'))
relation_type = Column(String(50))
weight = Column(Float)
source = relationship("User", foreign_keys=[source_id], back_populates="relationships")
target = relationship("User", foreign_keys=[target_id])
# models.py
from django.db import models
class User(models.Model):
name = models.CharField(max_length=100)
connections = models.ManyToManyField(
'self',
through='Relationship',
symmetrical=False,
related_name='related_to'
)
class Relationship(models.Model):
from_user = models.ForeignKey(User, related_name='from_rels', on_delete=models.CASCADE)
to_user = models.ForeignKey(User, related_name='to_rels', on_delete=models.CASCADE)
relation_type = models.CharField(max_length=50)
created = models.DateTimeField(auto_now_add=True)
class Meta:
unique_together = ('from_user', 'to_user', 'relation_type')
from neo4j import GraphDatabase
class Neo4jManyToMany:
def __init__(self, uri, user, password):
self.driver = GraphDatabase.driver(uri, auth=(user, password))
def create_relationship(self, node1, node2, rel_type, properties=None):
with self.driver.session() as session:
session.write_transaction(
self._create_and_return_relationship,
node1, node2, rel_type, properties or {}
)
@staticmethod
def _create_and_return_relationship(tx, node1, node2, rel_type, properties):
query = (
"MERGE (a:Node {name: $node1}) "
"MERGE (b:Node {name: $node2}) "
"CREATE (a)-[r:" + rel_type + "]->(b) "
"SET r += $properties "
"RETURN r"
)
result = tx.run(query, node1=node1, node2=node2, properties=properties)
return result.single()[0]
import networkx as nx
import pandas as pd
def analyze_multirelational_network(G):
metrics = {}
# 基础指标
metrics['nodes'] = G.number_of_nodes()
metrics['edges'] = G.number_of_edges()
# 按关系类型计算
relation_types = set()
for u, v, data in G.edges(data=True):
relation_types.add(data['relation'])
relation_metrics = {}
for rel in relation_types:
subgraph = nx.MultiDiGraph(
(u, v, d) for u, v, d in G.edges(data=True) if d['relation'] == rel
)
relation_metrics[rel] = {
'edges': subgraph.number_of_edges(),
'density': nx.density(subgraph),
'reciprocity': nx.reciprocity(subgraph)
}
metrics['relations'] = relation_metrics
return pd.DataFrame.from_dict(metrics, orient='index')
class SocialNetworkAnalyzer:
def __init__(self):
self.graph = nx.MultiDiGraph()
def import_from_csv(self, filepath):
df = pd.read_csv(filepath)
for _, row in df.iterrows():
self.graph.add_edge(
row['source'],
row['target'],
relation=row['relation'],
weight=row.get('weight', 1.0),
timestamp=row.get('timestamp')
)
def recommend_connections(self, user, max_recommendations=5):
# 基于Jaccard相似度的推荐
neighbors = set(self.graph.successors(user)) | set(self.graph.predecessors(user))
scores = []
for node in self.graph.nodes():
if node != user and not self.graph.has_edge(user, node):
node_neighbors = set(self.graph.successors(node)) | set(self.graph.predecessors(node))
similarity = len(neighbors & node_neighbors) / len(neighbors | node_neighbors)
scores.append((node, similarity))
return sorted(scores, key=lambda x: -x[1])[:max_recommendations]
from networkx.algorithms.community import greedy_modularity_communities
communities = list(greedy_modularity_communities(G))
subgraphs = [G.subgraph(c) for c in communities]
from scipy.sparse import lil_matrix
def to_sparse_matrix(G, relation_type):
nodes = sorted(G.nodes())
node_index = {n: i for i, n in enumerate(nodes)}
matrix = lil_matrix((len(nodes), len(nodes)))
for u, v, data in G.edges(data=True):
if data['relation'] == relation_type:
matrix[node_index[u], node_index[v]] = data.get('weight', 1)
return matrix
from multiprocessing import Pool
def parallel_shortest_path(G, nodes):
with Pool() as pool:
results = pool.starmap(nx.shortest_path_length, [(G, n) for n in nodes])
return dict(zip(nodes, results))
from pyvis.network import Network
def visualize_network(G):
net = Network(notebook=True, directed=True)
# 添加节点
for node in G.nodes():
net.add_node(node, label=str(node))
# 添加边
for u, v, data in G.edges(data=True):
net.add_edge(u, v, title=data['relation'], weight=data.get('weight', 1))
# 设置物理布局
net.toggle_physics(True)
net.show('network.html')
本文详细介绍了Python中实现多对多网络结构的多种方法，包括：
注意：实际项目中选择实现方式时，应根据数据规模（节点和边的数量）、查询模式（是否需要频繁查询特定类型的关系）和性能要求（实时性要求）来权衡选择最合适的方案。 “`
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