1. Class Diagrams Defines Graph Structures 2014

2. Association
Describes a set of links between objects, indicating some sort of connection between objects of the involved classes.
Example: A person may have friends.
:friendship
p1:Person
p2:Person f1 *
friendship
Person *
:friendship
:friendship f2
:friendship
p3:Person
p4:Person
:friendship
possible graph structure, i.e., objects with links

3. “ordinary graph” with “ordinary names”f1 *
friendship
Person * f2
defines an infinite set of graphs where the nodes are called Person and the edges are called friendship
end1
edge * *
Node
end2
“ordinary graph” with “ordinary names”
What if we need to attach some information to the edges?

4. Different Types Associations
In UML class diagrams you can distinguish between:
Ordinary Association
Aggregation(weak aggregation/ Shared Association)
Composition (strong aggregation)

5. Aggregation/Composition
Indicates that one object contains objects of a given type, i.e., a whole/part relationship.
No cycles are allowed.
A transitive relation.
the part
the whole
aggregation
using aggregation allows
a department to be shared
among companies
Company
Department *
1..*
Composition aggregation (strong aggregation)
Company
Department 1
1..*
Must be 1 or 0..1
No limitations on this multiplicity

6. Aggregation is a weaker form of aggregation than composition
Aggregation is a weaker form of aggregation than composition. A part instance might be included in more than one aggregation at a time, which is not allowed for composition.
Company
Department
Employee 1
1..* *
1..*
a department can only belong
to one company at a time
an employee can belong to several departments at a time

7. DirectedAcyclicGraph
Composition defines a directed tree and an aggregation defines a directed graph (without cycles).
Using these properties to define a directed graph and directed tree:
DirectedAcyclicGraph
DirectedTree
0..1
0..1 *
0..1
topRoot *
predecessor 1
root
Node
Node
successor  *
child *
edge
edge

8. Do you see errors? DirectedAcyclicGraph Node :Directed- AcyclicGraph
0..1 * *
predecessor
Node
successor  *
:Directed- AcyclicGraph
edge
Do you see errors?
:Node
:Node
:Node
:Node
:Node
:Node
:Node
:Node

9. Do you see errors? DirectedAcyclicGraph Node :Directed- AcyclickGraph
0..1 * *
predecessor
Node
successor  *
:Directed- AcyclickGraph
edge
Do you see errors?
:Node
:Node
:Node
:Node
:Node
:Node
:Node
:Node

10. Do you see errors? DirectedTree Node :DirectedTree :Node :Node :Node
0..1
0..1
topRoot 1
root
Node
child *
edge
:DirectedTree
Do you see errors?
:Node
:Node
:Node
:Node
:Node
:Node
:Node
:Node

11. Do you see errors? DirectedTree Node :DirectedTree :Node :Node :Node
0..1
0..1
topRoot 1
root
Node
child *
edge
:DirectedTree
Do you see errors?
:Node
:Node
:Node
:Node
:Node
:Node
:Node
:Node

12. Deletion Characteristics
UML 2.1 specification: “… If a composite is deleted, all of its parts are normally deleted with it… deleting an element in one part of the graph will also result in the deletion of all elements of the subgraph below that element.”