It looks like you want to work backward from u0.p1.root.1, so the
following query may be close to what you want:
traverse inE('rootSphere', 'children'), outV() from (select from Circle where name='u0.p1.root.1');
(I have given the name "Circle" to the class of all circles in your diagram.)
When run on the graph as shown in the diagram, the above query produces:
----+-----+----------+------------+-----------+-----+-----+-------------+--------------+-----------+--------------
# |@RID |@CLASS |name |in_children|out |in |in_rootSphere|out_children |in_projects|out_rootSphere
----+-----+----------+------------+-----------+-----+-----+-------------+--------------+-----------+--------------
0 |#11:3|Circle |u0.p1.root.1|[#15:3] |null |null |null |null |null |null
1 |#15:3|children |null |null |#11:2|#11:3|null |null |null |null
2 |#11:2|Circle |u0.p1.root |null |null |null |[#14:1] |[#15:2, #15:3]|null |null
3 |#14:1|rootSphere|null |null |#11:1|#11:2|null |null |null |null
4 |#11:1|Circle |u0.p1 |null |null |null |null |null |[size=1] |[#14:1]
----+-----+----------+------------+-----------+-----+-----+-------------+--------------+-----------+--------------
In any case, one of the problems you ran into arises from the fact that out() restricts the output to vertices, whereas you want nodes and edges.
Another problem you encountered is your use of MAXDEPTH. The OrientDB documentation is not so clear about MAXDEPTH,
so consider this query and the results:
traverse outE('rootSphere', 'children'), inV() from (select from V where name='u0.p1') maxdepth 3;
----+-----+----------+------------+-----------+--------------+-----+-----+-------------+--------------+-----------
# |@RID |@CLASS |name |in_projects|out_rootSphere|out |in |in_rootSphere|out_children |in_children
----+-----+----------+------------+-----------+--------------+-----+-----+-------------+--------------+-----------
0 |#11:1|Circle |u0.p1 |[size=1] |[#14:1] |null |null |null |null |null
1 |#14:1|rootSphere|null |null |null |#11:1|#11:2|null |null |null
2 |#11:2|Circle |u0.p1.root |null |null |null |null |[#14:1] |[#15:2, #15:3]|null
3 |#15:2|children |null |null |null |#11:2|#11:4|null |null |null
4 |#11:4|Circle |u0.p1.root.0|null |null |null |null |null |null |[#15:2]
5 |#15:3|children |null |null |null |#11:2|#11:3|null |null |null
6 |#11:3|Circle |u0.p1.root.1|null |null |null |null |null |null |[#15:3]
----+-----+----------+------------+-----------+--------------+-----+-----+-------------+--------------+-----------
MAXDEPTH must be set to 3 here to reach the children.