Transit functions in weighted graphs

Abstract

The visualization of complex conceptual structures is a key component of sup- newlineport tools for many applications in science and technology. A graph is an abstract newline newlinestructure that is used to model information. Graphs are used to represent infor- newlinemation that can be modeled as objects and connections between those objects. newline newlineHence, many information visualization systems require graphs to be drawn so newlinethat they are easy to read and understand. In connection with such real-world newline newlinescenario, the signiand#57346;cance of graph theory and related domains have raised tremen- newlinedously in the recent times. Applications in quickly developing networks like social newline newlinenetworks and internet are some examples. newline newlineRelations can be eand#57345;ectively represented as weighted graphs. Various challeng- newlineing problems in discrete mathematics, especially in graph Theory captivate the newline newlineattention of researchers from diand#57345;erent sectors like chemistry, computer science, newlinephysics, and engineering. newlineThe notion of distance has an inevitable role in the history of mathematics. It newlineis also a very essential geometrical notion in graph theory. It contains numerous newlinedeep and beautiful results and has various applications also. Nowadays, and#57346;nite newlinedistance metrics have become an essential tool in many areas of Mathematics. In newlinethe classical study of distances in graph theory, the main focus has been on the newlinestudy of the two main graph parameters concerned with distance, the diameter newlineand the radius. newline