## 1 Introduction  
In several areas, such as government, industry, and science, knowledge derived from data is of great importance. Therefore, it is important to develop methods for extracting useful information and knowledge [1, 2, 3, 4]. This problem is studied in pattern mining, a data mining technique that aims to discover interesting, unexpected, and useful patterns [5]. A trend in pattern mining is the development of algorithms designed to analyze complex data such as graphs [6, 7]. Graphs have become popular due to their flexibility and simplicity in representing relationships between objects [8, 9] and are widely used in science and technology to describe and visualize data [10]. These characteristics have led to the use of graphs in many applications, such as medicine [11, 12], chemistry [13, 14], bioinformatics [15, 16], social networks [17, 18, 19], linguistics [20, 21], computer vision [22, 23, 24], and image classification [25, 26], among others. Despite their advantages, data mining algorithms for pattern mining cannot be directly applied to graphs due to their complex structure. Consequently, it is necessary to develop algorithms capable of mining patterns in graphs [27]. Mining patterns in graphs refers to the mining of frequent subgraphs in a single graph or graph collection. Frequent subgraph mining (FSM) involves discovering subgraphs that repeat no less than a user-specified threshold [28; 29; 30] in a single graph or graph collection. FSM can be performed exactly or approximately. Frequent exact subgraph mining aims to mine subgraphs with one-to-one correspondence (isomorphism). Several algorithms have been developed to mine exact frequent subgraphs [31; 32; 33; 34; 35; 36; 37; 38; 39; 40]. In contrast, frequent approximate subgraph mining aims to mine subgraphs allowing variations in their structure or labels. Therefore, approximate FSM allows dealing with distortions found in real-world applications, such as noisy data, data diversity, and uncertain data [41; 42; 43]. However, despite its usefulness in real-world applications, approximate FSM introduces significant computational challenges. The problem is inherently more complex than frequent exact subgraph mining, as it requires approximate matching techniques that are more computationally expensive. Although approximate FSM has already addressed structural variations, most algorithms reported in the literature address frequent approximate subgraph mining with structural variations in a single graph [44; 45; 46]. While the literature mentions that the algorithms for mining subgraphs in a single graph can be extended to mine subgraphs in graph collections [47], it is not an easy task because subgraphs obtained by an algorithm for a single graph differ from those obtained by an algorithm for a graph collection. The literature describes only one algorithm, REAFUM [48], for mining frequent approximate subgraphs in an undirected graph collection. This algorithm can handle structural and label variations in edges and nodes. Nevertheless, it mines the subgraphs from a small subset of representative graphs in the collection. Therefore, this paper addresses the problem of mining all frequent approximate subgraphs in graph collections, allowing structural and label variations in nodes and edges. The contribution of this paper is the AGCM-SLV (Approximate Graph Collection Miner with Structural and Label Variations) algorithm (see Section 4), which is designed to mine all frequent approximate subgraphs within an undirected labeled graph collection, allowing variations in both node and edge labels as well as in the structure of the graphs. For handling label variations, the proposed algorithm allows defining partial similarities between the labels of nodes and edges. For handling structural variations, AGCM-SLV stores all the occurrences of a frequent subgraph and its corresponding dissimilarity.