Two Novel Network Measures and Their Applications with a Case Study on ADHD for Human Brain Networks

Complex networks have always been an integral part of our lives. From social networks keeping the world integrated in today’s scenario to the various complex biological networks operating within us, networks play an important and undeniable role everywhere which necessitates a better understanding and analysis of their structure and behavior. This makes it a common research practice to study the properties of these complex interconnected systems by representing them as heterogeneous networks and using various network theoretic tools for their analysis. In this thesis, I would be describing my work on the use of two novel network measures that use graph theoretic and computational tools to analyze heterogeneous complex networks and show how these algorithmic results and tools can be used for practical applications in both biological and social networks. I present the details of the theoretical and empirical results obtained in our case study wherein I studied the functional correlations between the different regions in the brains of patients suffering from Attention Deficit Hyperactivity Disorder (ADHD) while addressing the research question "Can Combinatorial Network Curvature be used to detect anomalies in the human brain due to the onset of ADHD?"
 I also show the relevance of the results obtained which are supported by previous neuroscience studies.