Topological data analysis (TDA) is a collection of powerful tools that can quantify shape and structure in data in order to answer questions from the data's domain. This is done by representing some aspect of the structure of the data in a simplified topological signature. In this article, we introduce two of the most commonly used topological…

This article is essentially devoted to a brief historical introduction to Euler's formula for polyhedra, topology, theory of graphs and networks with many examples from the real-world. Celebrated Konigsberg seven-bridge problem and some of the basic properties of graphs and networks for some understanding of the macroscopic behaviour of real…

This tricentennial tribute commemorates Euler's major contributions to mathematical and physical sciences. A brief biographical sketch is presented with his major contributions to certain selected areas of number theory, differential and integral calculus, differential equations, solid and fluid mechanics, topology and graph theory, infinite…

Presents a model for representing and storing binary topological and directional relationships between 2-dimensional objects that is used to provide a basis for fuzzy querying capabilities. A data structure called an abstract spatial graph (ASG) is defined for the binary relationships that maintains all necessary information regarding topology and…

Reports on a continuing investigation of intertextual networks. Describes how intertextual networks can be modeled as directed graphs and extends this to matrix representations. Discusses topological index values of these networks and speculates how topological index values might be used in the estimation of retrieval values in information…

Explores graph theory and use of topological indices to predict boiling points. Lists three indices: Wiener Number, Randic Branching Index and Molecular Connectivity, and Molecular Identification numbers. Warns of inadequacies with stereochemistry. (ML)