Graphoglyptids are biogenic structures commonly found in deep-sea flysch deposits and occasionally detected on the modern deep-sea floor. They extend principally horizontally and take a variety of geometric patterns, whose functional morphology remains an enigma in ichnology and paleoceanography. Based on published materials from 1850 to 2017 (79 ichnotaxa from 28 ichnogenera of graphoglyptids) and systematic observations of one of the largest deep-sea trace fossil collections in the world, this paper proposes that topological analysis is an important ingredient in the taxonomy and functional interpretation of graphoglyptids. Accordingly, graphoglyptids are classified into line, tree, and net forms by their key topological architecture, and are further attributed to 19 topological prototypes by detailed secondary topological features. Line graphoglyptids are single-connected structures with uniform tunnel width, representing primarily the feeding patterns of solitary animals. Tree graphoglyptids, the most diverse architectural group of graphoglyptids, are ascribed to 11 topological prototypes according to the connectivity features of burrow segments and the number and distributional pattern of the branching points. Net graphoglyptids are subdivided into three topological prototypes on the basis of the connectivity features and/or the regularity of the meshes. Multiconnected net forms are considered as a continuous morphological spectrum with different levels of complexity in the net formation. The various connected components in multiconnected tree and net graphoglyptids generally exhibit small and uniform tunnel diameter in a given structure (suggesting a tiny trace maker[s]). The whole structure shows relatively extensive linear or surface coverage and overall good preservation, indicating sustained processes of burrow construction. It is highly probable that certain multiconnected tree and net graphoglyptids represent some emergent patterns from self-organized collective behaviors of conspecific animals. Graphoglyptids thus provide us with a new perspective on the study of solitary and collective behaviors of macrobenthos in the deep-sea environment.

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