Definition

1. A <Feature Node> FN has the following relationship with its <Connected Feature Edge> components, if any exist.

   1.1	For each <Feature Edge> that has FN as a starting node, FN shall have a <Connected Feature Edge> that associates to that <Feature Edge>.
   1.2	For each <Feature Edge> that has FN as an ending node, FN shall have a <Connected Feature Edge> that associates to that <Feature Edge>.
   1.3	If FN is neither a starting nor an ending node of a given <Feature Edge>, that <Feature Edge> shall not appear among the associates of any of FN's <Connected Feature Edge> components.
   1.4	Consequently, for any given <Feature Edge> FE of which FN is a starting or ending node, FE shall appear among the associates of FN's <Connected Feature Edge> components either: once, if FN is FE's starting node and not its ending node, once, if FN is FE's ending node and not its starting node, twice, if FE is a loop.




2. A <Geometry Node> GN has the following relationship with its <Connected Geometry Edge> components, if any exist.

   2.1	For each <Geometry Edge> that has GN as a starting node, GN shall have a <Connected Geometry Edge> that associates to that <Geometry Edge>.
   2.2	For each <Geometry Edge> that has GN as an ending node, GN shall have a <Connected Geometry Edge> that associates to that .
   2.3	If GN is neither a starting nor an ending node of a given <Geometry Edge>, that <Geometry Edge> shall not appear among the associates of any of GN's <Connected Geometry Edge> components.
   2.4	Consequently, for any given <Geometry Edge> GE of which GN is a starting or ending node, GE shall appear among the associates of GN's <Connected Geometry Edge> components either: once, if GN is GE's starting node and not its ending node, once, if GN is GE's ending node and not its starting node, twice, if GE is a loop.

Rationale

<Connected Feature Edge> is the one-directional topological relationship connecting a <Feature Node> to the ordered set of ordered collection(s) of <Feature Edges> that have it as an endpoint. If there are no such < Feature Edges>, then by definition there is no <Connected Feature Edge> on that <Feature Node>.

<Connected Geometry Edge> is the one-directional topological relationship connecting a <Geometry Node> to the ordered set of ordered collection(s) of <Geometry Edges> that have it as an endpoint. If there are no such < Geometry Edges>, then by definition there is no <Connected Geometry Edge> on that <Geometry Node>.

Example

1. Consider a <Feature Edge> A that has distinct starting and ending <Feature Nodes> X1 and X2.

   X1 shall have at least one <Connected Feature Edge> component, which associates to A, and X2 shall have at least one <Connected Feature Edge> component, which associates to A.

2. Consider <Geometry Node> Y that is not the endpoint of any <Geometry Edge>. If Y is mistakenly created with a <Connected Geometry Edge>, then Y is invalid, since the <Connected Geometry Edge> implies that Y does belong to some <Geometry Edge>.

FAQs

For a loop edge (that is, an edge wherein the same node appears as both the starting and ending node), how many times does the edge appear in that node's <Connected Feature Edge> / <Connected Geometry Edge> lists?

Twice. Non-loop edges would appear only once.