Analysis of the Adaptation of “Spar” Points in Tirana with Graph Theory and Elimination Algorithm

Mariana Nikolla¹, Albana Boçi¹*

¹Department of Mathematics and Informatics, Faculty of Economy and Agribusiness, Agricultural University of Tirana, Albania

*Corresponding author; E-mail: aboci@ubt.edu.al

 

Abstract

The network’s topological structure is an important determinant in analyzing the availability and efficiency of the network with respect to accessibility and service delivery in urban settings. In this study, the “Spar” retail network in Tirana was used to conduct a graph theory approach to model network availability and distribution. In graph theory representation, the “Spar” retail outlets are denoted by nodes while the connecting roads are represented by directed and weighted graphs determined using Google Maps. The output or result is presented through the critical matrix process called the elimination algorithm technique used in determining minimum paths represented in weighted graphs. By eliminating matrixes in sequence, the technique was used to calculate the minimum path between certain “Spar” retail networks and demonstrates how “Spar”-QTU and “Spar”- Bulevardi Kashar are related. The study demonstrates how using graph theory in retail distribution networks is an important technique in analyzing logistics and network availability. It is recommended that the technique has the ability to be used in analyzing retail and service networks operating in an urban setting.

Keywords: graph; algorithm; minimum distance; Spar points; networks; graph theory

JEL Codes: C61; C63; L81