In data mining, data can be usually represented in different forms such as records of a matrix, graphs or ordered data. While we find in research different papers addressing methods or solutions for these different representations, there is no clear description of the advantages of every representation compared to the other (i.e when different representations can be applied to solve the problem, under which conditions, a particular representation would have an advantage?).
Here, I am interested in knowing what is, in particular, the advantage of the graph representation over the data matrix representation and vice versa. I realize that different problems would have an intuitive representation as one of the two ways. For example, a social network, is intuitively, represented as a graph while patients records, is intuitively, represented as a data matrix. However, I want to know how these representation compare when there is a prediction task and both representation can be used to solve the task.
An example that may illustrate my interest is chemical-protein interaction network. In this network, chemicals that may have an effect on a specific protein target, will have an active relationship. This active relationship can be represented either as an edge of weight 1 between a chemical and a protein in a graph or as a positive label for a set of features describing the compound in a record. Another example would be the author-paper network. To predict the author of the paper, we may extract features from the papers and build our data matrix. Another way, would be building a graph in which a new paper is linked with the most similar paper and then, we try to predict who may be the authors based on traversing the graph.
One answer I would have once thinking about these two representations is the different levels of describing the data. In a data matrix, there is the advantage of having many variables describing a given case or sample. In graphs, on the other hand, it is only one variable representing the similarity between the samples. Nevertheless, a graph topology may highlight important nodes in the network. What else ?
In summary, I am interested to know the expert advise on when to use a graph representation or a data matrix representation and why? If you are someone who likes graphs and prefer mining them, tell me why?