Network Theory Overview

This is an introductory book where we present topics in a non-mathematical and intuitive form that should not require any specific prior knowledge of science as the book is designed to be accessible to anyone with an interest in the subject. During the book, we will explore all the major topics in this area. The study of network theory is a highly interdisciplinary field, which has emerged as a major topic of interest in various disciplines ranging from physics and mathematics, to biology and computer science to almost all areas of social science. From the metabolic networks that fuel the cells in our body, to the social networks that shape our lives, networks are everywhere, we see them in the rise of the Internet, the flow of global air traffic and in the spread of financial crises, learning to model and design these networks is central to 21st Century science and engineering.

Networks Overview: In this first section of the book, we are going to give an overview of network theory that will also work as an overview of the structure of the book and the content we will be covering. We talk about what we called the network paradigm that is the whole new perspective that network theory offers when we look at the world through the lenses of connectivity.

Graph Theory: In this second section, we lay down the basics of our language for talking about graphs by giving an introduction to graph theory, we talk about a node’s degree of connectivity and different metrics for analyzing a node’s degree of centrality and significance within a network.

Network Structure: In the third section, we explore the overall topology to a network by talking about connectivity, which is how connected the whole network is, diameter, density, and clustering all key factors in defining the overall structure to a network.

Types Of Networks: In this section, we will be looking at different models to networks by starting out with a randomly generated network we will see how most networks are in fact not random but have some distinct structure, here we will be talking about a number of different models such as centralized scale-free networks and the small world phenomena.

Network Diffusion: In the last section of the book, we touch upon how networks change over time, in particular looking at the different parameter effecting the generation of a network, how something spreads or fails to spread across it and finally wrap-up by talking about network robustness and resilience.

By the end of taking this book, I hope that you will have a solid grasp of the formal language of network theory, the standardized language used to model networks within a wide variety of domains. You should also have a solid conceptual background required to approach a more advanced book in the mathematical analysis of networks. Being an introductory book, it has been designed to be accessible to a broad group of people but will be of particular relevance to those in engineering, the natural and social sciences, mathematics or IT.