<blockquote>
  <p>But the idea I have is nodes that would be bumped into very rarely when someone is transitting between two other arbitrary nodes. </p>
</blockquote>

<p>As @Joel mentioned, there are many centrality measures available, and there are often strong correlations between them such that many of them will probably give you more or less what you want. </p>

<p>That being said, I think the class of centrality measures that most closely reflect your intuition are based on <a href="https://en.wikipedia.org/wiki/Random_walk_closeness_centrality" rel="nofollow noreferrer">random walks</a>. Some of these are pretty costly to compute (although see <a href="https://arxiv.org/pdf/1808.02912.pdf" rel="nofollow noreferrer">this paper</a> for some recent improvements on that front) but luckily there is a strong <a href="https://users.cs.duke.edu/~kamesh/ModernAlg/lec8.pdf" rel="nofollow noreferrer">correspondence between the Eigenvector centrality and the frequency with which nodes are visited by a random walker</a>. </p>

<p>The implementation in networkx is available via <code>networkx.algorithms.centrality.eigenvector_centrality</code>. </p>
Measuring the "remoteness" of a node in a graph
<p>I mapped out all the edges of a graph in the ancient BBS game 'TradeWars 2002'. There are 1000 nodes.  The graph is officially a directed graph,  although most edges between nodes are undirected.  The graph is strongly connected.</p>

<p>I modelled the universe in <code>networkx</code>.  I'd like to use networkx methods to identify the "most remote" nodes in the network.  I don't know how to articulate "most-remote" in graph theory terminology though.  But the idea I have is nodes that would be bumped into very rarely when someone is transitting between two other arbitrary nodes.  And the idea that on the edge of the well-connected nodes,  there might be a string of nodes that extend out along a single path that terminates.</p>

<p>I visualization of what I imagine is node 733.  Pretty unlikely someone accidentally stumbles onto that one, compared to other better-connected nodes.</p>

<p>What could I use from networkx library to quantify some measure of 'remoteness'?</p>

<p><a href="https://i.stack.imgur.com/ZNZPW.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/ZNZPW.png" alt="enter image description here"></a></p>

<p>This is the entire universe:</p>

<p><a href="https://i.stack.imgur.com/FxRbQ.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/FxRbQ.png" alt="enter image description here"></a></p>