We present Rusty-Cracker, a high-performance Rust library that implements a parallel version of the Cracker algorithm for efficiently identifying connected components in large-scale graphs. Designed to address the growing demands of graph analytics in fields such as social network analysis, bioinformatics, and infrastructure modeling, Rusty-Cracker leverages Rust's concurrency and memory safety features to ensure both speed and reliability. The adapted Cracker algorithm capitalizes on modern multi-core architectures through parallel processing, effectively minimizing synchronization overhead and optimizing workload distribution. This design significantly reduces computational time while maintaining accuracy. We present the implementation details and evaluate its performance on a real-world dataset of undirected graphs.

Abstract Graphlets of order k in a graph G are connected subgraphs induced by k nodes (called k-graphlets) or by k edges (called edge k-graphlets). They are among the interesting subgraphs in network analysis to get insights on both the local and global structure of a network. While several algorithms exist for discovering and enumerating graphlets, the amortized time complexity of such algorithms typically depends on the size of the graph G, or its maximum degree. In real networks, even the latter can be in the order of millions, whereas k is typically required to be a small value. In this paper we provide the first algorithm to list all graphlets of order k in a graph $$G=(V,E)$$ G = ( V , E ) with an amortized time complexity depending solely on the order k, contrarily to previous approaches where the cost depends also on the size of G or its maximum degree. Specifically, we show that it is possible to list k-graphlets in $$O(k^2)$$ O ( k 2 ) time per solution, and to list edge k-graphlets in O(k) time per solution. Furthermore we show that, if the input graph has bounded degree, then the amortized time for listing k-graphlets is reduced to O(k). Whenever $$k = O(1)$$ k = O ( 1 ) , as it is often the case in practical settings, these algorithms are the first to achieve constant time per solution.