Subgraph matching in Cypher

Assume that in an application, the user gives us a graph and we want to consider it as a pattern and find all occurrences of the pattern in the neo4j database. If we knew what the pattern is, we could write the pattern as a Cypher query and run it against our database. However, now we do not know what the pattern is beforehand and receive it from the user in the form of a graph. How can we perform a pattern matching on the database based on the given graph (pattern)? Is there any apoc for that? Any external library?

One way of doing this is to decompose your input graph into edges and create a dynamic cypher from it. I have worked on this quite some time ago, and the solution below is not perfect but indicates a possible direction.
For example, if you feed this graph.

and you take the id(node) from the graph, (i am not taking the rel ids, this is one of the imperfections)

this query

WITH $nodeids AS selection
UNWIND selection AS s
WITH selection,
     SPLIT(left('a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z',SIZE(selection)*2-1),",") AS nodeletters
WITH selection, 
     REDUCE (acc="", nl in nodeletters | 
       CASE acc 
         WHEN "" THEN acc+nl 
         ELSE acc+','+nl 
       END) AS rtnnodes
MATCH (n) WHERE id(n) IN selection
WITH COLLECT(n) AS nodes,selection,nodeletters,rtnnodes
UNWIND nodes AS n
UNWIND nodes AS m
MATCH (n)-[r]->(m)
    +nodeletters[REDUCE(x=[-1,0], i IN selection | CASE WHEN i = id(n) THEN [x[1], x[1]+1] ELSE [x[0], x[1]+1] END)[0]]
    +TRIM(REDUCE(acc = '', p IN labels(n)| acc + ':'+ p))+")-[:"+type(r)+"]->("
    + nodeletters[REDUCE(x=[-1,0], i IN selection | CASE WHEN i = id(m) THEN [x[1], x[1]+1] ELSE [x[0], x[1]+1] END)[0]]
    +TRIM(REDUCE(acc = '', p IN labels(m)| acc + ':'+ p))+")" as z,rtnnodes
WITH COLLECT(z) AS parts,rtnnodes
WITH REDUCE(y=[], x in range(0, size(parts)-1) | y + replace(parts[x],"[","[r" + (x+1))) AS parts2,
     REDUCE (acc="", x in range(0, size(parts)-1)  | CASE acc WHEN "" THEN acc+"r"+(x+1) ELSE acc+",r"+(x+1) END) AS rtnrels,
    REDUCE (acc="MATCH ",p in parts2 | 
      CASE acc 
        WHEN "MATCH " THEN acc+p 
        ELSE acc+','+p 
      " RETURN  "+
      " LIMIT "+{limit} 
      AS cypher

returns something like

cypher: "MATCH (a:Person)-[r1:DRIVES]->(b:Car),(a:Person)-[r2:KNOWS]->(c:Person) RETURN a,b,c,r1,r2 LIMIT 50"

which you can feed to the next query.

In Graphileon, you can just select the nodes, and the result will be visualized as well.