Directed Graph Influence Analysis

Origin. Graph-theoretic methods in Soviet sociology (Gvishiani, Kovalyov) and organizational cybernetics; influence network analysis.

Mechanism. Represent agents or components as nodes and influence as directed edges. An edge from A to B means A influences B's state or decision. Influence propagates through the graph: A influences C directly via edge A→C, and indirectly via paths A→B→C. The power of a node is a function of its out-degree (how many it influences) and its position (how many paths pass through it). Cycles indicate feedback, and the cycle polarity determines stability.

Procedure. Enumerate entities and influence relations. Draw the directed graph. Identify high-out-degree nodes (influencers), high-in-degree nodes (influenced), and high-betweenness nodes (bridges). To change system behavior, intervene at high-betweenness nodes, where intervention affects the most paths. Identify cycles and label polarity: reinforcing (positive) or balancing (negative). Reinforcing cycles produce growth or collapse; balancing cycles produce homeostasis.

Applies to. Stakeholder analysis, social network analysis, organizational diagnosis, and identifying leverage points in complex systems.

Limitations. Influence strength is often non-quantifiable, so edge weights are ordinal at best. The analysis is structural and says nothing about dynamics' time constants; a high-betweenness node that acts slowly is not a leverage point. Also: the graph is a snapshot, and influence networks change over time.