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The SARS-CoV-2 coronavirus is the cause of the COVID-19 disease in humans. Like many coronaviruses, it can adapt to different hosts and evolve into different lineages. It is well-known that the major SARS-CoV-2 lineages are characterized by mutations that happen predominantly in the spike protein. Understanding the spike protein structure and how it can be perturbed is vital for understanding and determining if a lineage is of concern. These are crucial to identifying and controlling current outbreaks and preventing future pandemics. Machine learning (ML) methods are a viable solution to this effort, given the volume of available sequencing data, much of which is unaligned or even unassembled. However, such ML methods require fixed-length numerical feature vectors in Euclidean space to be applicable. Similarly, euclidean space is not considered the best choice when working with the classification and clustering tasks for biological sequences. For this purpose, we design a method that converts the protein (spike) sequences into the sequence similarity network (SSN). We can then use SSN as an input for the classical algorithms from the graph mining domain for the typical tasks such as classification and clustering to understand the data. We show that the proposed alignment-free method is able to outperform the current SOTA method in terms of clustering results. Similarly, we are able to achieve higher classification accuracy using well-known Node2Vec-based embedding compared to other baseline embedding approaches.