<p>Short answer: <strong>NO!</strong></p>

<p>You can't use a internal index to justify the choose of a algorithm over another. <strong>Why?</strong></p>

<p>Because evaluation indexes were designed to evaluate clustering results, i.e., partitions and hierarchies. You can only use them to access the quality of a clustering and therefore justify its choice over the others options. But again, you can't use them to justify choosing a particular algorithm to apply on a <strong>different dataset</strong> based on a single previous experiment.</p>

<p>For this task, several benchmarks are needed to determine which algorithms are generally better and should be tried first. Here some paper about it: <a href="https://arxiv.org/abs/0908.1062" rel="nofollow noreferrer">Community detection algorithms: a comparative analysis</a>.</p>

<p><strong>Edit:</strong> What I am saying is, your validation indexes may show that the <code>fast.greed</code>'s solution is better than the <code>walk.trap</code>'s. However, they do not explain why you chose these algorithms instead of any others. Only your data, your assumptions, and your constraints could do that.</p>

<blockquote>
  <p>Also, is there any way to validate a disconnected graph?</p>
</blockquote>

<p>Theoretically, any evaluation index can do this. Technically, some implementations don't handle disconnected components.</p>
Can I choose clustering methods base on internal validation result?
<p>From what I understand, it is usually difficult to select the best possible clustering method for your data priori, and we can use cluster validity to compare the results of different clustering algorithms and choose the one with the best validation scores.</p>

<p>I use an internal validation function from R <code>stats</code> package on my clustering result (for clustering methods I used R <code>igraph</code> <code>fast.greedy</code> and <code>walk.trap</code>).
The outcome is a list of many validation scores.</p>

<p>In the list, almost in every validation Fast greedy method has better scores than Walk trap, except in <code>entropy</code> walk trap method has a better score.</p>

<p>Can I use this validation result list as one of my reasons to explain to others why I choose Fast greedy method rather than walk trap method?  </p>

<p>Also, is there any way to validate a disconnected graph?</p>