A Study on Graph-Theoretic-Based Classification to Explore Geometric Consistency in Tissue Architecture of Colon Histopathology

Dr. M. Siva Parvathi
Assistant Professor, Dept. of Applied Mathematics, Sri Padmavati Mahila Visvavidyalayam, Tirupati, Andhra Pradesh, India

Prof. T. Sudha
Professor, Dept. of Computer Science, Sri Padmavati Mahila Visvavidyalayam, Tirupati, Andhra Pradesh, India

Dr. Shaheen Begum
Associate Professor, Institute of Pharmaceutical Technology, Sri Padmavati Mahila Visvavidyalayam, Tirupati, Andhra Pradesh, India

Dr. N.V. Muttu Lakshmi
Assistant Professor, Dept. of Computer Science, Sri Padmavati Mahila Visvavidyalayam, Tirupati, Andhra Pradesh, India

Mrs. T. Sukeerthi
Academic Consultant, Dept. of Statistics, Sri Padmavati Mahila Visvavidyalayam, Tirupati, Andhra Pradesh, India

G. Keerthi
Research Assistant, Dept. of Applied Mathematics, Sri Padmavati Mahila Visvavidyalayam, Tirupati, Andhra Pradesh, India

P.V. Anand Krishna
Student, Government Polytechnic, Pilaripattu, Andhra Pradesh, India

Abstract

This pilot study investigates conventional characterization of spatial organization in colon histopathology using graph theory which represents complex tissue images as networks of interconnected elements. It explores the potential of graph theory-based transformations in histopathological images of colon tissue to support medical image interpretation. Using a dataset of 40 images (20 benign and 20 adenocarcinoma), the research adopts five different graph modeling approaches such as proximity graph representation, Voronoi diagram, Delaunay triangulation, Minimum Spanning Tree (MST), and K-Nearest Neighbor (KNN) graph. These methods convert visual information into a spatially measurable network to improve on manual microscopic inspection, where superimposed structures often obscure diagnostic clarity. In the results, the Graph Convolution Network (GCN) shows 90% test accuracy, compared with Delaunay Triangulation and Minimum Spanning Tree models, which reveal perfect identification, thereby demonstrating that graph-theoretic thought captures related features effectively in tissue organisation.

Keywords: Voronoi Diagram, Delaunay Triangulation, Minimum Spanning Tree (MST), K-Nearest Neighbor (KNN)