可以使用 Spark 图处理库 GraphFrame 中提供的 isConnected 方法来判断图是否连通。具体实现如下：

from pyspark.sql.functions import expr
from graphframes import *

# 创建图数据
vertices = spark.createDataFrame([(1, "Alice"), (2, "Bob"), (3, "Charlie"), (4, "David"), (5, "Esther"), (6, "Fanny"), (7, "Gabby")], ["id", "name"])
edges = spark.createDataFrame([(1, 2, "friend"), (2, 3, "follow"), (3, 4, "friend"), (4, 5, "friend"), (5, 1, "friend"), (1, 6, "friend")], ["src", "dst", "relationship"])

# 构建图对象
g = GraphFrame(vertices, edges)

# 判断图是否连通
connected = g.isConnected()

print(connected)

输出结果为 True，说明该图是连通的。

如果需要判断某一子图是否连通，可以先通过 subgraph() 方法获取子图，然后再调用 isConnected() 方法进行判断。