# Union and Intersection

This Gist tries to anwser This question on the Neoj4 mailing list:

I have networks, which have many "egos" that appear in those networks. These egos, in turn, occur in many different networks - basic many-to-many relationship, and in the context of a graph db, a bipartite network. In practice, my data looks something like this (pardon whatever silly format I’m about to write it as):

```Network 1: [Ego 1, Ego 2, Ego, 3, Ego 4]
Network 2: [Ego 2, Ego 4, Ego, 5, Ego 6]
Network 3: [Ego 4, Ego 5, Ego, 7, Ego 8, Ego 9, Ego 10]```

What I would like out of this data is something like the following:

I want to know the relationship that Network 1 has with Networks 2 and 3. Specifically, I want to measure the overlap in a specific way - the count of the intersection of egos for two networks divided by the count of the union of egos. In other words, a comparison of Network 1 and Network 2 would yield the following steps:

intersection = [Ego 2, Ego 4], 2 total union = [Ego 1, Ego 2, Ego 3, Ego 4, Ego 5, Ego 6], 6 total intersection/union = 1/3

I would then say that these two networks are 33% similar (I’m open to other ways to calculate similarity in the spirit of what I’m trying to do here).

``````CREATE (n1:Network{name:'Network1'})
CREATE (n2:Network{name:'Network2'})
CREATE (n3:Network{name:'Network3'})
CREATE (e1:Ego{name:'Ego1'})
CREATE (e2:Ego{name:'Ego2'})
CREATE (e3:Ego{name:'Ego3'})
CREATE (e4:Ego{name:'Ego4'})
CREATE (e5:Ego{name:'Ego5'})
CREATE (e6:Ego{name:'Ego6'})
CREATE (e7:Ego{name:'Ego7'})
CREATE (e8:Ego{name:'Ego8'})
CREATE (e9:Ego{name:'Ego9'})
CREATE (e10:Ego{name:'Ego10'})
CREATE (n1)<-[:APPEARANCE]-(e1)
CREATE (n1)<-[:APPEARANCE]-(e2)
CREATE (n1)<-[:APPEARANCE]-(e3)
CREATE (n1)<-[:APPEARANCE]-(e4)
CREATE (n2)<-[:APPEARANCE]-(e2)
CREATE (n2)<-[:APPEARANCE]-(e4)
CREATE (n2)<-[:APPEARANCE]-(e5)
CREATE (n2)<-[:APPEARANCE]-(e6)
CREATE (n3)<-[:APPEARANCE]-(e4)
CREATE (n3)<-[:APPEARANCE]-(e5)
CREATE (n3)<-[:APPEARANCE]-(e7)
CREATE (n3)<-[:APPEARANCE]-(e8)
CREATE (n3)<-[:APPEARANCE]-(e9)
CREATE (n3)<-[:APPEARANCE]-(e10)``````

# The intersection between Network 1 and the other Networks

``MATCH (network:Network {name: 'Network1'})<-[:APPEARANCE]-(ego:Ego)-[:APPEARANCE]->(alter_network:Network) return distinct(alter_network.name), count(ego), collect(ego.name)``

# The union between Network 1 and Network 2

``````MATCH (n1:Network {name: 'Network1'}),(ego:Ego),(n2:Network{name:'Network2'})
WHERE (n1)<-[:APPEARANCE]-(ego) OR (n2)<-[:APPEARANCE]-(ego)
return count(ego), collect(ego.name)``````