A harmonious unifying hybrid preferential model and its universal properties for complex dynamical networks

To describe the real world which is a harmonious unification world with both determinism and randomness, we propose a harmonious unifying hybrid preferential model (HUHPM) of a certain class of complex dynamical networks. HUHPM is governed only by the total hybrid ratio d/r according to the practical need. As some typical examples, the concepts and methods of the HUHPM are applied to the un-weighted BA model proposed by Barabasi et al., the weighted BBV model proposed by Barat et al. and the weighted TDE model proposed by Wang et al. to get the so-called HUHPM-BA network, HUHPM-BBV network and HUHPM-TDE network. These HUHPM networks are investigated both analytically and numerically. It is found that the HUHPM reveals several universal properties, which more approach to the real-world networks for both un-weighted and weighted networks and have potential for applications.