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MATHEMATICAL REPRESENTATION

OF SONGKET PATTERNS USING GRAPH

THEORY AND ZERO-ONE MATRICES

SUPERVISOR: MADAM MASNIRA BINTI RAMLI

AHMAD RIDZWAN BIN ZAKI | 2022882386 | K242/16

Abstract

Traditional Malay songket textile are known for their complex and symmetric patterns, but people often forgot

to look at it from mathematical view. In this study, five songket pattern sketches has been chosen and transformed into the graph. This

study bridges the gap by transforming five different songket pattern sketches as simple and undirected graphs. Each patterns was

transformed into a graph by defining key elements in the graph which are vertices and edges. Then, vertex-degree sequences, connectivity

and transversal properties which are walk, trail and path has been analyzed to identify each patterns complexity. After that, every obtained

graph was encoded into both adjacency and incidence matrices. Then, each graph has been successfully reconstructed using ‘networkx’,

‘numpy’ and ‘matplotlib’ libraries in Python to ensure that each matrices were accurate. By capturing the graph and its properties within

songket pattern, it will help in pattern classification, digital preservation, cultural heritage and even generate new songket patterns.

Problem Statement Objectives

There is limited exploration on using graph

theory and zero-one matrices to mathematically represent songket patterns. 1 To transform songket pattern sketches into graphs

Most people recognize the cultural value of songket, but few understand its 2 To analyze the properties and classify the graphs

structural complexity from a mathematical perspective. This study addresses To represent the graphs using zero-one matrices and

the gap by applying graph-based models to analyze the patterns. 3 reconstruct them using Python

Method & Implementation Result & Discussion

Phase 1

Pattern-to-Graph Conversion

Phase 2

Structural Analysis & Classification

Vertex Degree Walk Trail & Path

Phase 3

Matrix Encoding & Python Reconstruction Five songket patterns were transformed into graphs and All graphs were successfully reconstructed from both

represented using adjacency and incidence matrices. adjacency and incidence matrices using Python.

Python reconstruction confirmed matrix accuracy. The outputs matched the original sketches,

Patterns II and V were most complex; Pattern IV confirming the accuracy of the mathematical

Tools moderately complex; Patterns I and III were the simplest. representation.

“Graphonline” All graphs are undirected, simple, and connected

Pattern V includes a cycle

No graphs are complete or regular

Adjacency Matrix
Key graph properties:

Degree, Walk, Trail, Path, and Connectivity were analyzed.

Walk:

All graphs showed valid walk sequences.

Pattern V included cycles with repeated vertices and edges.

Trail & Path:

Python Patterns I and III had identical sequences due to simplicity.
Incidence Matrix
Pattern V required careful edge selection to avoid

repetition.

Conclusions Recommendations

The study successfully transformed songket patterns into graphs Include more diverse songket Document cultural meanings of

and matrices, revealing structural features like symmetry, cycles, 1 patterns from various 3 each pattern alongside their graph

and complexity. All patterns were reconstructed accurately using regions. representations.

Python, proving the mathematical model's validity. The study Explore advanced Apply machine learning for

bridges traditional textile art and modern mathematical modeling. 2 mathematical tools. 4 pattern recognition and digital

design generation.