Local Alignment of Differential Causal Networks: A Methodological Framework for Detecting Recurrent Rewiring Motifs Across Multiple Systems

Differential Causal Networks (DCNs) were introduced to represent changes between two causal networks inferred under different conditions. In their original use, however, DCNs remain pairwise objects: each differential graph summarizes rewiring within a single system, while common differential structures shared across many systems remain implicit. We introduce a methodological framework for the local alignment of DCNs aimed at detecting recurrent rewiring motifs, that is, small directed differential subnetworks that reappear across multiple systems under the same contrast. The proposed framework transforms each system-specific comparison into a signed directed differential graph, preserves both edge direction and change type, and searches for approximate local correspondences rather than enforcing a full-network mapping. The method consists of four steps: construction of signed DCNs, extraction of differential seeds, pairwise local alignment by seed-and-extend, and progressive multiple alignment to build consensus motifs. We define a score that combines node compatibility, differential-edge conservation, directional consistency, and recurrence support, and we complement the alignment procedure with null-model testing and robustness analysis. The result is a collection of consensus local differential modules ranked by recurrence, confidence, and statistical significance. In this formulation, DCNs become comparable units in a higher-order analysis whose goal is not merely to describe pairwise causal change, but to identify the same local rewiring logic reused across multiple systems.