<p>(1) the author could be referencing methods of representing graphs in matrix form, <a href="https://en.wikipedia.org/wiki/Adjacency_matrix" rel="nofollow noreferrer">like this example</a></p>

<p>(2) not sure about "search trees", though if you can represent hash tables as a graph, then there are some methods to optimize them, <a href="https://arxiv.org/pdf/1711.08267.pdf" rel="nofollow noreferrer">like this example</a>.</p>
Hash tables in graph theory
<p>I am reading an article on Hash tables. Here is the text snippet.</p>

<blockquote>
  <p>A hash table is useful for any graph theory problem where the nodes
  have real names instead of numbers. Here, as the input is read,
  vertices are assigned integers from 1 onwards by order of appearance.
  Again, the input is likely to have large groups of alphabetized
  entries. For example, the vertices could be computers. Then if one
  particular installation  lists its computers as ibm1, ibm2, ibm3, . .
  . , there could be a dramatic effect on efficiency if a search tree is
  used.</p>
</blockquote>

<p>My quesitons on above text</p>

<ol>
<li><p>What does author mean "as input is read, verticies are assigned integers from 1 onward" don't we have calculate hash key for input read?</p></li>
<li><p>What does author mean by "there could be a dramatic effect on efficiency if a search tree is used."?</p></li>
<li><p>How hash tables are helpful in graph theory problems when compared to search tree?</p></li>
</ol>

<p>Thanks!</p>