<ul data-eligibleForWebStory="true">The article delves into graph algorithms, transitioning from theory to optimization with examples in Rust.The research focuses on developing a 3D engine based on the ECS architecture, encountering challenges in scheduling systems efficiently.Understanding Big O notation is crucial as it describes the algorithm's performance relative to input size.Different representations of graphs like adjacency lists and matrices are discussed for memory efficiency and complexity.The concept of squared graphs (G²) and path lengths of 2 in graphs are explained.Bitwise operations and SIMD are introduced as optimizations for graph calculations, showcasing performance gains.The article explores parallelization in graph algorithms, highlighting the benefits and considerations.Various benchmarks and tests were conducted to compare different implementations, emphasizing the importance of simplicity and efficiency.The article concludes by providing a link to the complete code and resources on GitHub for further exploration.