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If a node's (as in graph) neighbors are nodes connected to it with passable edges, what can I call nodes connected to a node with impassable edges? They would both be neighbors but only some would be "accessible neighbors" but I would like a more concise word.

Note that I have no real idea about proper terminology of graphs in maths, but would just like a word that an everyday man would understand.

EDIT: I realise I am not being clear; let me explain: I am a novice programmer trying to write some graph software and each node must store a list of nodes connected to it by an edge and this edge may be passable or impassable. All of the nodes are neighbors but only some of the nodes (those connected with a passable edge) are "accessible neighbors". Here is a very crude depiction: graph

Nodes 2, 3, 4 and 5 are "neighbors" but only 2, 5 and 4 are "accessible neighbors". If it remains unclear - please say! I guess I have not asked a very good question.

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Writing as an "everyday man", I don't understand what you mean by connected with passable edges. –  FumbleFingers Dec 3 '11 at 14:24
Could you post an image of the graph that shows the difference? –  The English Chicken Dec 3 '11 at 14:24
What does "passable" mean? What real-world objects are you trying to represent as nodes? For example, are #1 and #3 neighboring towns without a connecting highway? –  The English Chicken Dec 3 '11 at 14:45

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up vote 2 down vote accepted

Formal Graham terminology recognizes that there is either an edge or there is not an edge, so either in the neighborhood or not, or adjacent or not.

You are adding on an additional qualifier of the edge, 'accessibility'. So you have -three- ways two nodes can be related, not adjacent (no edge), adjacent and accessible (an edge that has positive accessibility), and adjacent but not accessible (an edge with negative accessibility).

And you want a succinct name for this last case.

A wordy term would be inaccessible neighbor or, for the edge itself nontraversible edge.

In this situation, the difficulty in naming things well is a sign that the concept may be difficult to manipulate in your application. I would suggest sticking with just two cases, having an edge or not, and not worrying about the weird additional case of an edge that you can't traverse.

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Yes this is what I am looking for but obviously this doesn't have a real term so should I mark this as correct? –  Ell Dec 3 '11 at 15:13
Maybe he means a directed graph? + 1 for nontraversible –  Wudang Dec 3 '11 at 16:51

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