TL;DR
Here's a start:
MATCH p=(u:User {id: $theID})-[:r]->()<-[:m]-(a:Article)
WITH a, COUNT(p) as rank
RETURN a.name, rank
ORDER BY rank DESC
LIMIT $n
The idea here is to just count all the paths from the user to each article and then use that as a rank. The more paths, i.e., the more common specialties and keywords, the higher the rank.
The long version ... More data, "rank" validation
I'm pretty sure your queries will evolve as your graph database grows and you adjust the schema, i.e., you probably will have more relationship types and connections.
To have more data to play with, I generated some fake doctors, articles, etc. I'm pretty sure there's a better way to do this.
MERGE (p:Profession {name: "Doctor"})
WITH p, ["Fred","Wilma","Pebbles","Dino","Barney","Betty","Bamm-bamm", "Hoppy"] as doctors
UNWIND doctors as doc
MERGE (d:User {name: doc})-[:R]->(p);
WITH ["Oncology", "Pathology","Pediatrics","ENT","Radiology","Dermatology"] as specialties
UNWIND specialties as spec
MERGE (:Specialty {name: spec});
MATCH (d:User)
WITH d, ["Oncology", "Pathology","Pediatrics","ENT","Radiology","Dermatology"] as specialties
UNWIND apoc.coll.randomItems(specialties, toInteger(apoc.text.random(1,"00111223"))) as docspec
MATCH (spec:Specialty {name: docspec})
MERGE (d)-[:R]->(spec);
WITH ["Knee Surgery","Ear Injury","Throat Cultures","Radial fractures", "Arm rash", "Mole color"] as keywords
UNWIND keywords as key
MERGE (:Keyword {name: key});
MATCH (d:User)
WITH d, ["Knee Surgery","Ear Injury","Throat Cultures","Radial fractures", "Arm rash", "Mole color"] as keywords
UNWIND apoc.coll.randomItems(keywords, toInteger(apoc.text.random(1,"01112233"))) as docword
MATCH (key:Keyword {name: docword})
MERGE (d)-[:R]->(key);
MATCH (p:Profession {name: "Doctor"})
WITH p, ["Useful article","Cool article","Awesome article","Research article","Nifty article","Health article"] as articles
UNWIND articles as art
MERGE (:Article {name: art})-[:M]->(p);
MATCH (art:Article)
WITH art, ["Oncology", "Pathology","Pediatrics","ENT","Radiology","Dermatology"] as specialties
UNWIND apoc.coll.randomItems(specialties, toInteger(apoc.text.random(1,"111223"))) as artspec
MATCH (spec:Specialty {name: artspec})
MERGE (art)-[:M]->(spec);
MATCH (art:Article)
WITH art, ["Knee Surgery","Ear Injury","Throat Cultures","Radial fractures", "Arm rash", "Mole color"] as keywords
UNWIND apoc.coll.randomItems(keywords, toInteger(apoc.text.random(1,"1112233"))) as artword
MATCH (key:Keyword {name: artword})
MERGE (art)-[:M]->(key);
Here's the intertwined mess.

Now looking at just one "doctor":
MATCH p=(u:User {name: "Barney"})-[:R]->()<-[:M]-(a:Article)
RETURN p
... you can see all the articles he's connected to.

So, let's rank them by the number of connections to the doctor.
MATCH p=(u:User {name: "Barney"})-[:R]->()<-[:M]-(a:Article)
WITH a, COUNT(p) as rank
RETURN a.name, rank
ORDER BY rank DESC

Dr. Barney probably would be interested in "Nifty article".
There are lots of ways to rank, this is a just a simple way.
:Article
s using only one of:Keyword
,:Profession
, or:Specialty
for a:User
? – rickhg12hsCypher
code. They like use cases too. – rickhg12hs