The Structural Dynamics of Complex Networks
Open AccessReal-world networks are far from random. The underlying structure of the fundamental degrees of freedom for a network which are the links between its constituent nodes is intrinsically complex. This research ascribes the scale-free, small-world and transitive properties to the inherent complexity in networks and studies the origination of complexity to obtain various useful results for the Ring-Star and Triad models. The principal determinant for the apparent structure in Ring-Star networks is linked to its optimized functionality, the function of interest being transportation or dissemination across the network. Similarly, the stability of dynamics on three-node motifs is considered for a particular diffusion model with the functional optimality being the stable sub-structures upon which the network grows. Results for a series of optimal rings and two disjoint optimal rings sharing a common hub are obtained. An insufficient but necessary condition on the complex nature of the interaction between the Ring-Star nodes in an evolutionary game-theoretic context is provided. Also, fixed-point stability analysis has been done for a particular diffusion model on Cyclic and Transitive triads. Consequently, a stable triad is treated as a complex sub-structure upon which the network further grows. Finally, several useful results for a binodal SIR model on a dynamical network setting have been derived.
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