A comprehensive framework for solution space exploration in community detection

Community detection algorithms are essential tools for understanding complex networks, yet their results often vary between runs and are affected by node input order and the presence of outliers, undermining reproducibility and interpretation. This paper addresses these issues by introducing a framework for systematic exploration of the solution space, obtained through repeated runs of a given algorithm with permuted node orders. A Bayesian model assesses convergence, estimates solution probabilities, and provides a defensible stopping rule that balances accuracy and computational cost. Building on this process, we propose a taxonomy of solution spaces that offers clear diagnostics of partition reliability across algorithms and a shared vocabulary for interpretation. Applied to a real-world network, the approach shows that different algorithms produce various types of solution space, highlighting the importance of systematic exploration of the solutions before drawing scientific conclusions.