Given an unrooted binary tree whose leaves are vertices of degree one that are labelled bijectively by a set $S$. We define a categorical attribute $A$ ($|A|<<|S|$) and each leaf is assigned a value from this set. Internal vertices (degree 3) are unlabelled and attributes are unknown. Edges are weighted. I would like to quantify the association or clustering of these attributes in the tree. For example if $A=\{red,blue,green\}$, I would like to know if $red$ is more often associated with $blue$ than $green$. If a tree shows no association between attributes we could remove an internal vertex and the resulting 3 trees would contain one colour each. Any suggestion about the kind of measure/index I could use to assess the clustering of these attributes?
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$\begingroup$ What does it mean for a colour to be associated with another colour? $\endgroup$– Ben BarberJun 20, 2014 at 9:52
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$\begingroup$ @BenBarber "Association" might not be the best term. Red and blue would be associated if the average geodesic distance between red and blue vertices is significantly less than the average distance between red and green, and blue and green vertices. The goal is to use a measure to compare graphs. $\endgroup$– MattJun 23, 2014 at 23:30
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