Retrieve smallest subgraph for given subjects from RDF graph via SPARQL - sparql

Question

As you might see from the formulation of my question title, I am new to SPARQL and RDF in general, so please excuse me for not being able to formulate the question more precisely.
I am looking for a SPARQL query which returns a list of triples that describe a connected subgraph (assuming that the queried graph is completly connected). I found a solution at SPARQL query to construct sub-graph with select paths (paths have different lengths) but it only works if the passed nodes are directly connected. If for example I have a scenario where I pass nodes that are not connected directly I don't get a result. I would like to get a subgraph (as triples) that is allowed to include additional nodes but has to be connected.
Example: Given Graph G=(V,E), with V={A,B,C,D,E,F,G,H} and E as described in the following picture (predicates are not displayed as they are not important). I would like to find a query which when given {C,E,H} (see picture 1) returns the triples that describe the connected subgraph given in picture 2, that is {(C,E),(E,G),(G,H)}.
Obviously there might be multiple ways in which this can be achieved in an arbitrary graph, so in this case there are two possibilities: 1. A structure should be returned that is the minimum spanning tree of those vertices ({C,E,G,H}) or 2. If this is not possible, a structure should be returned from which a minimum spanning tree can be calculated afterwards
Thanks for any help.

Answer 1

The primary misunderstanding, wrt SPARQL, seems to be in the second paragraph. The predicates ARE important. They are the driving force behind RDF and SPARQL - i.e. naming the "relationships", which are the names of edges. As you'll see below, it's not possible to answer the question without knowing something about the predicate names.
But let me try anyway. Assuming all predicates are named :p1, I think what you may want is something like the following:
CONSTRUCT {
:C :p1 :E .
:E :p1 ?G .
?G :p1 :H .
}
WHERE {
:C :p1 :E .
:E :p1 ?G .
?G :p1 :H .
}
The WHERE clause will find the graph pattern, in your specific example finding a solution for ?G. The CONSTRUCT statement then creates your minimal spanning tree.
Another tip for going from graph theory to RDF and SPARQL is the use of URI's to uniquely name nodes and edges. The above takes a specific XML-based shortcut that assumes a default prefix has been defined. For example, if the default prefix were <http://example.com/graphTheory/>, then replace the : in the above with the prefix, e.g. <http://example.com/graphTheory/p1>.