The concept of connectivity is crucial for understanding information propagation, functional coupling, and the robustness of complex adaptive systems, such as the coupled ocean-climate system. However, existing metrics—such as shortest paths, effective resistance, and minimum cut—belong to distinct theoretical frameworks and lack a unified perspective to fully capture multiscale complexity. In this presentation, we propose a unified framework based on the random cluster (RC) model. By tuning the cluster weight (q) and edge probability (p), this framework can continuously characterize diverse connectivity patterns, ranging from a "single optimal pathway" to "multiple redundant pathways," uncovering hidden structural properties. Furthermore, we define a universal RC connectivity metric. Compared to traditional methods, this emergent notion of connectivity more accurately captures dynamic correlations between components in complex dynamical settings, as demonstrated in epidemic spreading (SIR model) and neurodynamics (FitzHugh-Nagumo model). By linking structural and dynamical perspectives into an interpretable and physically consistent foundation, RC connectivity offers a powerful new tool for complex networks with broad potential for investigating spatio-temporal connections, teleconnections, and cross-scale interactions in the ocean-climate system.

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