Dynamic fuzzy paths and cycles in multi-level directed graphs

In this paper we propose improved algorithms for the discovery of significant paths and cycles that dynamically evolve through time in a series of multi-level directed graphs. First, we search for the most probable paths and combine them into clusters based on similar edges. We combine paths into dynamic fuzzy paths. We also detect cycles in different paths and combine them into dynamic fuzzy cycles. We obtain dynamic fuzzy structures using the hierarchical clustering of individual structures. For paths, the clustering distance depends on common edges, while for cycles we calculate the distance on the basis of common vertices. We apply the developed algorithms to a time series of multi-level directed graphs obtained from the results from the numerical model Mediterranean Ocean Forecasting System during the period 1999–2011. We compare the results with known structures from the oceanographic literature. With our approach we find a high similarity between the resulting dynamic fuzzy paths and cycles and structures found by oceanographic experts. When comparing the cycles, the expert sees our results as a convex hull of the average of individual cycles. On the other hand, the method reveals undiscovered paths and gyres, which can be verified through observation.