对Email数据集，用Katz算法进行链路预测，设置训练集比例为90%，并比较AUC值和Precision(L=100,200)

Katz算法是一种基于路径衰减因子的链路预测算法。对于Email数据集，我们可以使用Katz算法进行链路预测，并比较AUC值和Precision。

首先，我们需要将数据集分为训练集和测试集。设置训练集比例为90%，可以使用sklearn库中的train_test_split函数进行随机划分：

from sklearn.model_selection import train_test_split

# 加载数据集
edges = []
with open("email-Eu-core.txt") as f:
    for line in f:
        if line.startswith("#"):
            continue
        edge = line.strip().split()
        edges.append((int(edge[0]), int(edge[1])))

# 划分训练集和测试集
train_edges, test_edges = train_test_split(edges, test_size=0.1, random_state=42)

接下来，我们可以使用NetworkX库构建Email数据集的图：

import networkx as nx

# 构建无向图
graph = nx.Graph()
graph.add_edges_from(train_edges)

然后，可以使用Katz算法进行链路预测。Katz算法的核心思想是通过路径衰减因子来计算任意两个节点之间的相似度。Katz算法的公式如下：

$$
s_{i,j}=\sum_{l=1}^{\infty}\beta^l\cdot A^l_{i,j}
$$

其中，$A$是邻接矩阵，$\beta$是路径衰减因子，$s_{i,j}$表示节点$i$和节点$j$之间的相似度。

Katz算法的实现可以使用NetworkX库中的katz_similarity函数：

from networkx.algorithms.link_prediction import katz_similarity

# 计算相似度
katz_scores = katz_similarity(graph, max_l=200, beta=0.01)

最后，我们可以使用sklearn库中的roc_auc_score和average_precision_score函数分别计算AUC值和Precision：

from sklearn.metrics import roc_auc_score, average_precision_score

# 计算AUC值
y_true = [1 if edge in test_edges else 0 for edge in graph.edges()]
y_scores = [katz_scores[edge] for edge in graph.edges()]
auc = roc_auc_score(y_true, y_scores)

# 计算Precision
k = 100
top_k_edges = sorted(graph.edges(), key=lambda x: katz_scores[x], reverse=True)[:k]
y_true = [1 if edge in test_edges else 0 for edge in top_k_edges]
y_scores = [katz_scores[edge] for edge in top_k_edges]
precision = average_precision_score(y_true, y_scores)

将上述代码整合起来，可以得到完整的Katz算法代码实现：

import networkx as nx
from sklearn.model_selection import train_test_split
from networkx.algorithms.link_prediction import katz_similarity
from sklearn.metrics import roc_auc_score, average_precision_score

# 加载数据集
edges = []
with open("email-Eu-core.txt") as f:
    for line in f:
        if line.startswith("#"):
            continue
        edge = line.strip().split()
        edges.append((int(edge[0]), int(edge[1])))

# 划分训练集和测试集
train_edges, test_edges = train_test_split(edges, test_size=0.1, random_state=42)

# 构建无向图
graph = nx.Graph()
graph.add_edges_from(train_edges)

# 计算相似度
katz_scores = katz_similarity(graph, max_l=200, beta=0.01)

# 计算AUC值
y_true = [1 if edge in test_edges else 0 for edge in graph.edges()]
y_scores = [katz_scores[edge] for edge in graph.edges()]
auc = roc_auc_score(y_true, y_scores)

# 计算Precision
k = 100
top_k_edges = sorted(graph.edges(), key=lambda x: katz_scores[x], reverse=True)[:k]
y_true = [1 if edge in test_edges else 0 for edge in top_k_edges]
y_scores = [katz_scores[edge] for edge in top_k_edges]
precision = average_precision_score(y_true, y_scores)

print("Katz Algorithm")
print("AUC: {:.4f}".format(auc))
print("Precision@{}: {:.4f}".format(k, precision))

其中，max_l参数表示路径的最大长度，beta参数表示路径衰减因子。根据实验结果，可以比较不同路径长度和路径衰减因子下的AUC值和Precision。