Investigating the Origins of Fractality Based on Two Novel Fractal Network Models

Numerous network models have been investigated to gain insights into the origins of fractality. In this work, we introduce two novel network models, to better understand the growing mechanism and structural characteristics of fractal networks. The Repulsion Based Fractal Model (RBFM) is built on the well-known Song-Havlin-Makse (SHM) model, but in RBFM repulsion is always present among a specific group of nodes. The model resolves the contradiction between the SHM model and the Hub Attraction Dynamical Growth model, by showing that repulsion is the characteristic that induces fractality. The Lattice Small-world Transition Model (LSwTM) was motivated by the fact that repulsion directly influences the node distances. Through LSwTM we study the fractal-small-world transition. The model illustrates the transition on a fixed number of nodes and edges using a preferential-attachment-based edge rewiring process. It shows that a small average distance works against fractal scaling, and also demonstrates that fractality is not a dichotomous property, continuous transition can be observed between the pure fractal and non-fractal characteristics.Comment: 12 pages, 5 figures, to appear in: 978-3-031-17657-9, Pacheco et al (eds.): Complex Networks XII

Introduction to Complex Systems, Sustainability and Innovation

The technological innovations have always proved the impossible possible. Humans have all the time obliterated barriers and set records with astounding regularity. However, there are issues springing up in terms of complexity and sustainability in this context, which we were ignoring for long. Today, in every walk of life, we encounter complex systems, whether it is the Internet, communication systems, electrical power grids, or the financial markets. Due to its unpredictable behavior, any creative change in a complex system poses a threat of systemic risks. This is because an innovation is always introducing something new, introducing a change, possibly to solve an existing problem, the effect of which is nonlinear. Failure to predict the future states of the system due to the nonlinear nature makes any system unsustainable. This necessitates the need for any development to be sustainable by meeting the needs of people today without destroying the potential of future generations to meet their needs. This chapter, which studies systems that are complex due to intricateness in their connectivity, gives insights into their ways of emergence and the nonlinear cause and effects pattern the complex systems use to follow, effectively paving way for sustainable innovation