Let say our objects are connected graphs. They are to be classified into two categories, say A and B. However, for our purpose attributes for each graph is equal to the number of vertex of the graph which is allowed to vary. We may assume that our vertices are numbered with some arbitrary order. The attributes are some vertex invariants. Let X be the vector of vertex invariants for a particular graph.
For graph with attribute vector X, its probability of being in category A is $$P(A|X) = \frac{P(X|A)P(A)}{P(X)}$$
Usually we use $P(X) = \prod_{i=1}^kP(x_i)$ and $P(X|A) = \prod_{i=1}^k P(x_i|A)$ and $k$ is a fixed integer and is equal to the dimension of attribute vector. However, in my case $k$ varies and is equal to the number of vertices in the graph.
The form of the above expression is adaptable even when $k$ is varying. However, do we need to do some other adjustment or "normalization" to account for the varying size of the attributes? Some reference where Bayesian method has been used for varying number of attributes might be helpful.