Vertexwise

Vertexwise is an adjective used across mathematics, computer science, and related fields to describe quantities or operations that are defined at the vertices of a graph, mesh, or polyhedral object, and often applied independently to each vertex. In graph theory, a vertexwise function or measurement assigns a value to every vertex; for example, a vertexwise degree sequence lists the degree of each vertex, or a vertexwise potential assigns a scalar to every vertex. In linear algebra and spectral graph theory, vertexwise operators such as the vertexwise Laplacian act on vertex-associated data to produce per-vertex results.

In computer graphics and numerical methods, vertexwise quantities include per-vertex normals, colors, or scalars on a triangulated surface, and vertexwise finite element techniques compute values at vertices. In neuroscience, particularly in neuroimaging, vertexwise analysis refers to statistical testing performed at each point (vertex) on a cortical surface model; results are subject to multiple comparison correction across vertices and are often contrasted with region-of-interest (ROI) or cluster-wise approaches.

The term emphasizes locality to individual vertices rather than global, edge-based, or region-based summaries. Its usage spans both theoretical contexts (per-vertex definitions) and applied contexts (per-vertex data analysis), serving as a concise descriptor for vertex-centric concepts and methods.