Date of Award

23-8-2024

Document Type

Thesis

School

School of Arts, Sciences, Humanities & Education

Programme

Ph.D.-Doctoral of Philosophy

First Advisor

Dr.V.Swaminathan

Keywords

Hypergraph, Centrality Measures, Strong and Weak Ties, Genetic Algorithm, Unimodular Hypergraph

Abstract

Network analysis explores the connections between nodes and evaluates their characteristics across diverse fields such as biological, chemical, social networks and so on. Identifying key nodes within a network is crucial for grasping how information spreads, which has significant applications across multiple fields. This includes studying disease transmission, managing rumours, understanding social leadership, enhancing viral marketing strategies, and monitoring public opinion. Influential nodes play a pivotal role in effectively distributing information throughout the network. The centrality measures are paramount in network analysis that uses various metrics to evaluate the importance of the node. The centrality predicts the characteristics and significance of the nodes in the network.

Initially, this thesis reviewed different centrality measures alongside their respective implementations to illustrate how different centrality metrics comprehensively characterize and predict the significance of nodes in the network. First the chemical network was chosen for analysis using centrality measures of graphs. The combined centrality index (CCI) is proposed to rank isomers of alkanes without degeneracy which shows strong inter-correlation with existing indices EE, J, RVa, and RVb. Similarly, in social and biological network analysis, the relationships between individuals and proteins are modeled using graphs.

However, social and biological interactions often involve complex, multi-way relationships that simple graphs cannot easily capture. To capture these intricate interactions, hypergraphs, xiv the generalization of graphs is employed, that allows edges to connect multiple nodes. Directed hypergraph is constructed for the football network, where hyperedges are the ball passes between players, while in the Wikipedia network, they could represent user votes on specific topics. The upper and lower bounds on the number of hyperedges in directed hypergraphs are determined using degree and betweenness centrality. The influential nodes are identified based on these results, yielding the minimum number of influential nodes required for maximum spreading.

Next, the biological network is analyzed by constructing a directed hypergraph. Initially, a degree centrality-based weight assignment is proposed for the nodes in the biological network, and these weights are then optimized using a genetic algorithm (GA). The proposed method is applied to ten biological and COVID-19 protein-protein interaction (PPI) networks, and obtains the influential proteins that act as critical ones in the biological activities. The identified critical human proteins have a considerable role in viral infections.

Hence, the obtained proteins may help in the discovery of a drug for COVID-19. The pathway interaction analysis in biological networks impacts many functional features of biological entities. So, we have analyzed the pathway interactions of certain diseases, like Parkinson’s, COVID-19, and diabetes PPI’s, and predicted the critical proteins using modified depth-first search and unimodular property of directed hypergraph. The property of unimodular hypergraph clusters the related essential proteins and enzymes, thereby providing potential avenues for disease treatment.

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