While doing research work with Prof. Kishore Kothapalli, and Prof. Dip Sankar Banerjee.
Abstract — The Königsberg bridge problem, which was posed and answered in the negative by Euler in 1736 represents the beginning of graph theory. Graph is a generic data structure and is a superset of lists, and trees. Binary search on sorted lists can be interpreted as a balanced binary tree search. Database tables can be thought of as indexed lists, and table joins represent relations between columns. This can be modeled as graphs instead. Assignment of registers to variables (by compiler), and assignment of available channels to a radio transmitter are also graph problems. Neural networks are graphs too. Interaction between messenger molecules in the body, interaction between people on social media, and spreading of infectious diseases, are also modeled as graphs. Finding the shortest path between two points, and sorting web pages in order of importance are also graph problems. Graphs are indeed unifying abstractions that can leverage interconnectedness to represent, predict, and explain any phenomena.
Index terms — Temporal graph, Link analysis, Dynamic PageRank, Community detection, Dynamic Louvain.