Chapter One focuses on investigational data on the fluorescence of DNA complexes inside neutrophils in flow cytometry with nanometre spatial resolution. Fluorescence visualises oxidative activity of all coding and non-coding DNA parts in the full set of chromosomes. Chapter Two studies real-world networks based on a centrality metric called the Leverage Centrality metric which has been recommended as a means of identifying neighbourhood hubs. The LevC of a node is a comparative measure of the connectivity of a node vis-a-vis its neighbours. In Chapter Three, the author goes on to examine neighbourhood overlap, bipartivity index, and algebraic connectivity as edge centrality metrics to measure the consistency of links for mobile sensor networks. For several instances of node density and mobility, the author observes the stability of the network-wide data gathering trees determined using the proposed three edge centrality metrics to be significantly larger than the stability of the LET-based data gathering trees. Chapter Four explores fractal dimensions for networks by reviewing theory and computation, including: the box counting dimension, the correlation dimension, the mass dimension, the transfinite fractal dimension, the information dimension, the generalised dimensions, and the sandbox method. Finally, Chapter Five proposes a fusion condition with the goal of preventing wrong fusions and alleviating the effect of the resolution limit. The suggested condition can also be used in other algorithms that make community fusions.