Chapter 7
Table 7.1, Table 7.2, Table 7.3, Table 7.4 and Table 7.5 summarize the mathematical templates.
Tree Templates
Template |
Synopsis |
UML diagram |
Use when |
Frequency |
---|---|---|---|---|
Hardcoded tree |
Specifies a type sequence, one for each level of the hierarchy. |
The levels in a tree are known and ordered. |
Seldom |
|
Simple tree |
Treats all nodes the same. |
A tree concerns only data structure. |
Common |
|
Structured tree |
Differentiates leaf nodes from branch nodes. |
Branch nodes and leaf nodes differ. |
Common |
|
Overlapping tree |
Permits a node to belong to multiple trees. |
A node can belong to more than one tree. |
Occasional |
|
Tree changing over time |
Stores variants of a tree over time. |
There is history to record. |
Occasional |
|
Degenerate node and edge |
Groups a parent with its children. |
There is data for the parent-child grouping. |
Rare |
Directed Graph Templates
Template |
Synopsis |
UML diagram |
Use when |
Frequency |
---|---|---|---|---|
Simple DG |
Treats all nodes the same. |
Edges are unimportant; nodes have the same kind of data. The DG is acyclic. |
Occasional |
|
Structured DG |
Differentiates leaf nodes from branch nodes. |
Edges are unimportant; branch nodes and leaf nodes have different data. The DG is acyclic. |
Occasional |
|
Node-edge DG |
Treats nodes and edges as peers. |
Nodes and edges can both have data; there can be multiple edges between a pair of nodes. |
Common |
|
Connection DG |
Promotes a node-edge connection to an entity type. |
Connections have data. |
Occasional |
|
Simple DG changing over time |
Stores variants of a DG over time. |
There is history to record; edges are unimportant. The DG is acyclic. |
Seldom |
|
Node-edge DG changing over time |
Stores variants of a DG over time. |
There is history to record; edges are important. |
Occasional |
Undirected Graph Templates
Template |
Synopsis |
UML diagram |
Use when |
Frequency |
---|---|---|---|---|
Node-edge UDG |
Treats nodes and edges as peers. |
No edge connects to the same node. |
Occasional |
|
Connection UDG |
Promotes a node-edge connection to an entity type. |
Connections have data or an edge connects to the same node. |
Occasional |
|
UDG changing over time |
Stores variants of a UDG over time. |
There is history to record. |
Seldom |
Item Description Templates
Template |
Synopsis |
UML diagram |
Use when |
Frequency |
---|---|---|---|---|
Item description |
Relates data and metadata in the same model. |
The same model relates data and metadata. |
Frequent |
|
Homomorphism |
Expresses an analogy between two item description templates. |
Item description templates are involved in an analogy. |
Occasional |