Why does Spark think this is a cross / Cartesian join

This happens because you join structures sharing the same lineage and this leads to a trivially equal condition:

res2.explain()

== Physical Plan ==
org.apache.spark.sql.AnalysisException: Detected cartesian product for INNER join between logical plans
Join Inner, ((idx#204L = key1#209L) && (key2#210L = idx#204L))
:- Filter isnotnull(idx#204L)
:  +- LogicalRDD [idx#204L, val#205]
+- Filter ((isnotnull(key2#210L) && (key2#210L = key1#209L)) && isnotnull(key1#209L))
   +- LogicalRDD [key1#209L, key2#210L, val#211L]
and
LogicalRDD [idx#235L, val#236]
Join condition is missing or trivial.
Use the CROSS JOIN syntax to allow cartesian products between these relations.;

In case like this you should use aliases:

from pyspark.sql.functions import col

rdd1 = spark.createDataFrame(...).alias('rdd1')
rdd2 = spark.createDataFrame(...).alias('rdd2')

res1 = rdd1.join(rdd2, col('rdd1.idx') == col('rdd2.key1')).alias('res1')
res1.join(rdd1, on=col('res1.key2') == col('rdd1.idx')).explain()
== Physical Plan ==
*SortMergeJoin [key2#297L], [idx#360L], Inner
:- *Sort [key2#297L ASC NULLS FIRST], false, 0
:  +- Exchange hashpartitioning(key2#297L, 200)
:     +- *SortMergeJoin [idx#290L], [key1#296L], Inner
:        :- *Sort [idx#290L ASC NULLS FIRST], false, 0
:        :  +- Exchange hashpartitioning(idx#290L, 200)
:        :     +- *Filter isnotnull(idx#290L)
:        :        +- Scan ExistingRDD[idx#290L,val#291]
:        +- *Sort [key1#296L ASC NULLS FIRST], false, 0
:           +- Exchange hashpartitioning(key1#296L, 200)
:              +- *Filter (isnotnull(key2#297L) && isnotnull(key1#296L))
:                 +- Scan ExistingRDD[key1#296L,key2#297L,val#298L]
+- *Sort [idx#360L ASC NULLS FIRST], false, 0
   +- Exchange hashpartitioning(idx#360L, 200)
      +- *Filter isnotnull(idx#360L)
         +- Scan ExistingRDD[idx#360L,val#361]

For details see SPARK-6459.

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