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git-svn-id: file:///home/ksmith/gitmigration/svn/xmpp/trunk@2942 4b5297f7-1745-476d-ba37-a9c6900126ab
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Peter Saint-Andre 2009-04-01 19:56:52 +00:00
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xep-0248.xml
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<p>In terms of graph theory, the set of nodes hosted at a pubsub service is a directed acyclic graph. <note>See <link url='http://en.wikipedia.org/wiki/Directed_acyclic_graph'>http://en.wikipedia.org/wiki/Directed_acyclic_graph</link>.</note> The particular graph types can be further described as follows:</p>
<ol>
<li>If there are no collection nodes, we say that the graph is simply a <strong>flat set</strong> of nodes without connections because there are no arcs between nodes, i.e., no node is the direct predecessor of another node (here we use the less formal phrase that no node is the parent of any other child node).</li>
<li>If there may be multiple paths between between any two given nodes (where the path may include intermediate collection nodes), the graph is a <strong>Directed Acyclic Graph</strong> or "DAG" <note>See <link url='http://en.wikipedia.org/wiki/Directed_acyclic_graph'>http://en.wikipedia.org/wiki/Directed_acyclic_graph</link>.</note> because a given node may be the child of multiple parents.</li>
<li>If there may be multiple paths between any two given nodes (where the path may include intermediate collection nodes), the graph is a <strong>Directed Acyclic Graph</strong> or "DAG" <note>See <link url='http://en.wikipedia.org/wiki/Directed_acyclic_graph'>http://en.wikipedia.org/wiki/Directed_acyclic_graph</link>.</note> because a given node may be the child of multiple parents.</li>
<li>If there is only one path between any two given nodes (where the path may include intermediate collection nodes), the graph is a <strong>Tree</strong> <note>See <link url='http://en.wikipedia.org/wiki/Tree_(graph_theory)'>http://en.wikipedia.org/wiki/Tree_(graph_theory)</link>.</note> because a given node may be the child of only one collection node.</li>
<li>If there is a root collection node but there are no internal collection nodes, we say informally that the graph has a <strong>depth</strong> of 1 because all of the connections from leaf nodes to the root collection node are direct (i.e., each connection is an arc); this case is equivalent to a flat set with a root collection node and is typically uninteresting.</li>
<li>If there is a root collection node and there are internal collection nodes, we say that the graph has <strong>infinite depth</strong> because there is an unbounded number of arcs between each leaf node and the root collection node; this case is more interesting than a graph of depth=1 since it enables a wide range of trees and hierarchies.</li>