An isolate is a node which is not connected to any other node in the graph. This is the same as saying that the node has no edges (neither incoming nor outgoing), or has degree of 0.

Given a graph, Delete Isolates will remove all isolates from the graph.

When one is interested in the relationships between nodes in a graph, it is common to want to ignore nodes which are not involved with any other nodes. Remove Isolates will eliminate these nodes, allowing you to focus on the interesting part of the graph.

Any operation which removes edges has the possibility of producing isolates, so if you want to keep isolates out of your graph you should run this after every edge eliminating algorithm. You can also use the Network Analysis Toolkit to count the number of isolates currently in your graph.