Exploring Ordered Patterns in the Adjacency Matrix - for Improving Machine Learning on Complex Networks

Aug 5, 2026

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The study investigates how representing complex networks through adjacency matrices can improve machine learning–based network classification. Since row and column permutations yield the same underlying graph, the work introduces a sorting approach to rearrange the adjacency matrix into a consistent order. The sorted matrix then supports feature extraction and machine learning algorithms for identifying synthetic and real-world networks. Experimental results show higher classification performance than prior methods on both data types.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages12

Reading Time30 min

AccessFree to download

Introduction

Pattern recognition in complex networks

Motivation for using the adjacency matrix

Proposed methodology and evaluation

arXiv :2301 .08364v 1 [ cs . SI] 20 Jan 2023 EXPLORING ORDERED PATTERNS IN THE ADJACENCY MATRIX FOR IMPROVING MACHINE LEARNING ON COMPLEX NETWORKS Mariane B. Neiva, Odemir M. Bruno *Scientiﬁc Computing Group Institute of Physics of Sao Carlos University of Sao Paulo [marianeneiva@usp.br](marianeneiva@usp.br) , bruno@ifsc.usp.br ABSTRACT The use of complex networks as a modern approach to understanding the world and its dynamics is well-established in literature. The adjacency matrix, which provides a one-to-one representation of a complex network, can also yield several metrics of the graph. However, it is not always clear that this representation is unique, as the permutation of lines and rows in the matrix can represent the same graph. To address this issue, the proposed methodology employs a sorting algorithm torearrange the elements of the adjacency matrix of a complex graph in a speciﬁc order. The resulting sorted adjacency matrix is then used as input for feature extraction and machine learning algorithms to classify the networks. The results indicate that the proposed methodology outperforms previous literature results on synthetic and real-world data. Keywords Adjacency matrix 􀀁 Pattern recognition 􀀁 Complex networks 􀀁 Deep learning 1 Introduction The emergence of Big Data has sparked an interest in structuring data as closely as possible to reality and evaluating it to extract knowledge. Traditional data analysis often reduces complex phenomena to a simpliﬁed object. However, technological advances and the ability to gather, process, and store larger amounts of data allow us to explore information from various viewpoints. Complex networks, systems that can connect elements based on a speciﬁc aspect, ﬁll a gap left by classical science. The capability to create a system with elements and relationships shifts the reductionist approach to an integrative one. In addition, pattern recognition has been a prominent branch of data science in understanding the world through the perspective of technology. If one were to think of a method that could evolve the beneﬁts of artiﬁcial intelligence techniques and integrative data analysis, complex networks would be a natural choice. Pattern recognition in complex networks includes a range of algorithms, such as classiﬁcation and clustering. Although clustering plays a signiﬁcant role in the ﬁeld, classiﬁcation enables us to recognize diseases, species, structures, and cities, among others. This task is crucial nowadays due to the large amount of data generated that would be too time-consuming and costly to analyze manually. Furthermore, complex networks have a signiﬁcant advantage for pattern recognition in the era of Big Data, as they can be used to model a wide variety of data, from images to biological systems. It has been demonstrated over the years that most real systems exhibit characteristics of small-world and scale-free networks. The former refers to structures in which elements are connected, on average, by short minimum paths, similar to what occurs in social networks where there is a high probability that a person's friend is also a friend of the person in question. The latter refers to the knowledge that there are frequently reached elements in a network, such as prominent researchers in a ﬁeldor inﬂuential articles in a text. The latter example illustrates the importance of using graphs to analyze the patterns and structures of a given organization. Therefore, this work's quantitative analysis focuses on classifying synthetic and realnetworks. Based on the advantages mentioned above, researchers have successfully used the model for pattern recognition in various applications, such as the classiﬁcation of static and dynamic texture [1], shapes [2], authorship [3], and others. Exploring ordered patterns in the adjacency matrix for improving machine learning on complex networks Recently, some works such as the use of cellular automata in [4]

FAQs

Why can adjacency matrices cause ambiguity in complex network representation?

Adjacency matrices represent graphs one-to-one, but permuting rows and columns can describe the same underlying graph while producing different matrix layouts.

What does the proposed methodology do with the adjacency matrix?

It uses a sorting/ordination algorithm to rearrange rows into a specific order, making patterns more consistent for downstream learning tasks.

How is the sorted adjacency matrix used to improve classification?

The method applies feature extraction techniques and machine learning algorithms to the sorted adjacency matrix, including approaches such as projection and deep learning feature extraction, to classify networks.

Aug 5, 2026

Upload by Jiven