PATTERNS OF DATA MODELING- P17 pps

Figure 4.1 shows two examples of undirected graphs.. 64 Chapter 4 / Undirected Graph TemplateThere is no undirected graph counterpart to the simple and structured templates of directed g

3.7 Chapter Summary 61

Template

Simple DG Treats all nodes

the same

Edges are unim-portant; nodes have the same kind of data The

DG is acyclic

Occasional

Structured

DG

Differentiates leaf nodes from branch nodes

Edges are unim-portant; branch nodes and leaf nodes have differ-ent data The DG

is acyclic

Occasional

Node and

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 the con-nection between a node and an edge

to an entity type

There is data for the connection itself as well as for nodes and edges

Occasional

Simple DG

changing

over time

Stores multiple variants of a DG

Extract a particu-lar DG by speci-fying a time

A DG changes over time; edges are unimportant

The DG is acy-clic

Seldom

Node and

edge DG

changing

over time

Stores multiple variants of a DG

Extract a particu-lar DG by speci-fying a time

A DG changes over time; edges are important

Occasional

Table 3.1 Summary of the Directed Graph Templates

Note: This table can help you choose among the directed graph templates.

62 Chapter 3 / Directed Graph Template

Bibliographic Notes

Page 89 of [Hay-1996] has an example of projects that involve the node and edge directed graph

References

[Hay-1996] David C Hay Data Model Patterns: Conventions of Thought New York, New York:

Dorsett House, 1996.

4

Undirected Graph Template

The undirected graph is also a term from graph theory An undirected graph is a set of nodes

and a set of edges Each edge connects two nodes (which may be the same) The nodes of an undirected graph can have any number of edges Undirected graphs arise for applications with important topology or connectivity For example, the network of members on the LinkedIn Web site is an undirected graph

Figure 4.1 shows two examples of undirected graphs

There are three templates for undirected graphs

• Node and edge undirected graph Regards nodes and edges as peers Use as the

de-fault template when there are no edges that connect to the same node

• Connection undirected graph Promotes the connection between a node and an edge

to an entity type Use when there is data for the connection itself

• Undirected graph changing over time Stores variants of a node and edge undirected

graph A particular undirected graph can be extracted by specifying a time Use when the history of an undirected graph must be recorded

Figure 4.1 Sample undirected graphs An undirected graph is a set of

nodes and a set of edges that connect the nodes

B c

d

e

F

A

f

g

r

s t

64 Chapter 4 / Undirected Graph Template

There is no undirected graph counterpart to the simple and structured templates of directed

graphs The simple counterpart violates the symmetry antipattern (see Chapter 8) The struc-tured counterpart shares a similar flaw as it is not clear which end of an edge should be the parent and which should be the child In principle, it would be possible to add time intervals

to the connection template, but we have never seen a need for this in practice

4.1 Node and Edge Undirected Graph Template

4.1.1 UML Template

Figure 4.2 shows the UML template for node and edge undirected graphs

A UDG (undirected graph) is a set of nodes and a set of edges that connect nodes (Note:

in an undirected graph all nodes do not have to be connected.) You need not show UDG in a

use of the template A Node is an entity type whose records are organized as an undirected graph An Edge is a coupling between Nodes.

With this template the names of nodes and edges are globally unique There is no context

to provide an alternative approach to naming

Figure 4.2 lacks the constraint that related nodes and edges must all belong to the same undirected graph The template also cannot handle edges that connect twice to the same node

(the “2” in Figure 4.2 refers to two different nodes); use the connection undirected graph if

an edge connects twice to the same node

4.1.2 IDEF1X Template

Figure 4.3 restates Figure 4.2 with the IDEF1X notation The following are foreign keys:

udgID references UDG, edgeID references Edge, and nodeID references Node The “2”

mul-tiplicity in Figure 4.2 becomes “many” mulmul-tiplicity in a database design

4.1.3 SQL Queries

Figure 4.4 and Figure 4.5 show SQL queries for common traversals of the template The co-lon prefix denotes variable values that must be provided for each query

<UDG>

<Edge>

<Node>

*

2

Figure 4.2 Node and edge undirected graph: UML template Use as the

default template when no edges connect to the same node

4.1 Node and Edge Undirected Graph Template 65

4.1.4 Sample Populated Tables

Figure 4.6 shows node and edge undirected graph tables populated with data The values of the IDs are arbitrary, but internally consistent

4.1.5 Examples

Undirected graphs occur only occasionally and when they occur, the node and edge template

is often appropriate

The LinkedIn Web site is popular for professional networking Members can connect to other members and find those who are closely connected via intermediate colleagues Such contacts can be useful for seeking employers, seeking employees, and sharing information

An undirected graph is the proper representation because there is a lack of direction in con-nections between members It does not matter who initiated the contact; all that matters is that pairs of members are connected Furthermore, it makes no sense for a member to con-nect to himself or herself Thus the limitation of the node and edge template is not a problem

Figure 4.3 Node and edge undirected graph: IDEF1X template

nodeID

udgID (FK)

nodeName (AK1.1)

Node

edgeID udgID (FK) edgeName (AK1.1)

Edge Node_Edge

nodeID (FK) edgeID (FK)

udgID

UDG

Figure 4.4 Node and edge undirected graph: SQL query Find the edges for a node

SELECT E.edgeID, E.edgeName

FROM Node as N

INNER JOIN Node_Edge AS NE ON N.nodeID = NE.nodeID

INNER JOIN Edge AS E ON NE.edgeID = E.edgeID

WHERE N.nodeID = :aNodeID

ORDER BY E.edgeName;

Figure 4.5 Node and edge undirected graph: SQL query Find the nodes for an edge

SELECT N.nodeID, N.nodeName

FROM Edge AS E

INNER JOIN Node_Edge AS NE ON E.edgeID = NE.edgeID

INNER JOIN Node AS N ON NE.nodeID = N.nodeID

WHERE E.edgeID = :anEdgeID

ORDER BY N.nodeName;