Contents > 8 Defining Custom Design Metrics and Rules > 8.1 Definition of Metrics > 8.1.6 Connected Components

### 8.1.6 Connected Components

The `connectedcomponents` procedure is used to count the
connected components in a graph. The procedure uses element sets to
obtain information about nodes and edges of the graph.
The procedure has four attributes:

`set` (required): the element set that constitutes the
nodes of the graph.
`nodes` (required): a set expression that returns, for a
node, the set of connected nodes to which there is an (outgoing) edge.
`undirected` (optional): takes values "true" or "false".
The default value is "false" and the procedure calculates the strongly
connected components of the directed graph. When set to "true", the
connected components of the underlying undirected graph will be
computed (i.e., the direction of edges is ignored, an edge can always
be followed in both ways).
`minnodes` (optional): only counts connected components
exceeding a certain size. For example, if you specify minnodes="3",
only connected components that have at least three nodes will be
reported.

For example, to calculate the number of inheritance hierarchies among
the classes in a package, we define three element sets (see
Section 8.2 "Definition of Sets"):
- set Classes: the set of classes in a package
- set Parents: the set of parent classes of a class
- set Children: the set of children classes of a class

We can then calculate the number of connected components in the
inheritance hierarchy as follows:
<metric name="InhHierarchies" domain="package">
<description>The number of inheritance hierarchies.</description>
<connectedcomponents set="Classes" nodes="Parents+Children" />
</metric>

The following example uses an undirected graph and only counts
connected components with at least two nodes (i.e., ignoring isolated
classes that do not participate in any inheritance relationship):
<metric name="InhHierarchies" domain="package">
<description>The number of non-trivial inheritance hierarchies.</description>
<connectedcomponents set="Classes" nodes="Parents" undirected="true"
minnodes="2" />
</metric>