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 to rearrange 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.

本文提出一种基于排序算法的新方法，用于唯一地表示复杂网络的邻接矩阵，并使用此方法进行特征提取和机器学习分类，结果表明这种方法在合成和真实数据的分类上优于先前文献的结果。

在邻接矩阵中探索有序模式以提升复杂网络机器学习

Exploring ordered patterns in the adjacency matrix for improving machine learning on complex networks

We address the problem of learning a ranking by using adaptively chosen
pairwise comparisons. Our goal is to recover the ranking accurately but to
sample the comparisons sparingly. If all comparison outcomes are consistent
with the ranking, the optimal solution is to use an efficient sorting
algorithm, such as Quicksort. But how do sorting algorithms behave if some
comparison outcomes are inconsistent with the ranking? We give favorable
guarantees for Quicksort for the popular Bradley-Terry model, under natural
assumptions on the parameters. Furthermore, we empirically demonstrate that
sorting algorithms lead to a very simple and effective active learning
strategy: repeatedly sort the items. This strategy performs as well as
state-of-the-art methods (and much better than random sampling) at a minuscule
fraction of the computational cost.

通过使用自适应选择的成对比较来学习排名，我们的目标是准确地恢复排名但节省比较样本。对于使用快速排序算法等有效算法的所有比较结果一致的情况，最优解为使用有效排序算法。我们在 Bradley-Terry 模型下给出了 Quicksort 的优异保证，并通过实证证明了排序算法导致了非常简单有效的积极学习策略。