Hi,
    To find out whether a relationship exists between two entities or not you can use the following code:
   
For 1 to N:
 
     public bool Is1toNRelationshipExists(IOrganizationService service, string parent, string child)  
     {  
       RetrieveEntityRequest retrieveEntityRequest = new RetrieveEntityRequest  
       {  
         EntityFilters = EntityFilters.Relationships,  
         LogicalName = parent  
       };  
       RetrieveEntityResponse retrieveEntityResponse = (RetrieveEntityResponse)service.Execute(retrieveEntityRequest);  
       foreach (OneToManyRelationshipMetadata rel in retrieveEntityResponse.EntityMetadata.OneToManyRelationships)  
       {  
         if (rel.ReferencingAttribute == child)  
         {  
           return true;  
         }  
       }  
       return false;  
     } 

For N to N:

      
     public bool IsNtoNRelationshipExists(IOrganizationService service, string entity1, string entity2)  
     {  
       RetrieveEntityRequest retrieveEntityRequest = new RetrieveEntityRequest  
       {  
         EntityFilters = EntityFilters.Relationships,  
         LogicalName = entity1  
       };  
       RetrieveEntityResponse retrieveEntityResponse = (RetrieveEntityResponse)service.Execute(retrieveEntityRequest);  
       foreach (ManyToManyRelationshipMetadata rel in retrieveEntityResponse.EntityMetadata.ManyToManyRelationships)  
       {  
         if (rel.Entity2LogicalName == entity2)  
         {  
           return true;  
         }  
       }  
       return false;  
     }  

Hope it helps..!!