Complicating Social Network Analysis: Toward a Multi-Order Ontology and Methodology

• In Event: Social Theory and Complexity Science: New Research Directions (Co-sponsored by Mathematical Sociology Section)

Abstract

This article argues that sociology’s relational turn remains methodologically incomplete insofar as most “relational analysis” still treats dyadic ties between pre-given units as the default ontological baseline, thereby pushing multi-actor interaction and relations among relations into informal interpretation. The paper proposes a multi-order ontology in which relations can be irreducibly polyadic, can link relations to higher-order structures such as triangles, cavities, and holes, and can also be compared across networks. The central explanatory unit thus shifts from nodes connected by edges to relations-of-relations, understood as structured constraints that relations impose on other relations and as topological features that enable or forbid collective modes of social change. Methodologically, the paper systematizes three higher-order pathways that respond to distinct empirical demands. First, hypergraphs treat multi-actor episodes as first-class objects rather than dyadic projections. Second, higher-order topological dynamics extends network dynamics beyond node states by placing state variables on edges and higher-dimensional cells and by treating topology as a constraint on possible collective patterns. Third, structural alignment treats networks themselves as comparable objects, enabling cross-actor comparison without assuming that categories and labels are already commensurable. Drawing on complexity science and consciousness research, the paper develops an interdisciplinary foundation for these moves and illustrates their sociological promise through three case studies, offering pragmatic criteria for when higher-order commitments are likely to yield explanatory surplus.

Authors

• Chuyin Zhang, Monash University

• Simon Yuan Xi, University of Virginia