Institution: | aStowers Institute for Medical Research, 1000 E. 50th Street, Kansas City, MO 64110, United States bCenter for Integrative Bioinformatics Vienna, Max F. Perutz Laboratories, Dr. Bohr Gasse 9, A-1030 Vienna, Austria cUniversity of Vienna, Medical University of Vienna, Vienna, Austria dUniversity of Veterinary Medicine Vienna, Vienna, Austria |
Abstract: | We introduce a novel graph class we call universal hierarchical graphs (UHG) whose topology can be found numerously in problems representing, e.g., temporal, spacial or general process structures of systems. For this graph class we show, that we can naturally assign two probability distributions, for nodes and for edges, which lead us directly to the definition of the entropy and joint entropy and, hence, mutual information establishing an information theory for this graph class. Furthermore, we provide some results under which conditions these constraint probability distributions maximize the corresponding entropy. Also, we demonstrate that these entropic measures can be computed efficiently which is a prerequisite for every large scale practical application and show some numerical examples. |