I don't understand why there should only be 2^(n(n-1)/2) "features" for a graph on n vertices.
If we define a graph feature as a real-valued function acting on graphs, and suppose we are fixing the size of the graph to n vertices, then we can view a feature as a vector in 2^(n(n-1)/2)-dimensional space. Now, while there are only 2^(n(n-1)/2) basis functions, there are infinitely many such functions. Obviously, there is some repetition involved (e.g. f and 2f are most likely equivalent for the intended exploitation task). However, it seems like there are more than 2^(n(n-1)/2) features that could be used for some form of inference.
I don't understand why there should only be 2^(n(n-1)/2) "features" for a graph on n vertices.
If we define a graph feature as a real-valued function acting on graphs, and suppose we are fixing the size of the graph to n vertices, then we can view a feature as a vector in 2^(n(n-1)/2)-dimensional space. Now, while there are only 2^(n(n-1)/2) basis functions, there are infinitely many such functions. Obviously, there is some repetition involved (e.g. f and 2f are most likely equivalent for the intended exploitation task). However, it seems like there are more than 2^(n(n-1)/2) features that could be used for some form of inference.