Graph theory is a sophisticated mathematical framework for studying the characteristics and connections of graphs, which are collections of nodes and edges. Significant advancements have been made in graph theory and its applications in recent years, leading to novel techniques and real-world implementations. This abstract provides an overview of these recent advances. One notable development is the emergence of Graph Neural Networks (GNNs), which enable learning graph-structured data representations. GNNs have been successfully applied in various domains, including node classification and link prediction.Community detection algorithms have also improved accuracy and efficiency, benefiting social network analysis and other related fields. Graph embedding techniques have also progressed, facilitating learning low-dimensional vector representations for nodes or subgraphs. This advancement has enhanced tasks such as link prediction and node classification. Furthermore, temporal graph analysis has gained attention for studying dynamic graphs, allowing for predicting future states and anomaly detection. The application of graph theory in social networks has yielded valuable insights into sentiment dynamics, influence maximization, and information diffusion. These findings aid in understanding social behaviour and designing effective interventions. Network alignment and graph matching techniques have been developed to integrate and analyze data from multiple sources, finding applications in diverse fields, including biological networks and cross-domain data analysis. Graph theory has significantly contributed to transportation and urban planning, addressing challenges like traffic flow optimization, route planning, and public transportation design.Furthermore, the application of graph theory in bioinformatics and drug discovery has led to advancements in drug-target interaction and protein function prediction. Recent advances in graph theory have opened up new avenues for research and practical applications. The growing availability of large-scale graph data and the need to extract insights from complex interconnected systems continue to drive the evolution of this field. These advancements hold great potential for addressing real-world challenges across diverse domains.