edgelocalized

Edgelocalized is a descriptive term used across disciplines to denote phenomena, functions, or states that are concentrated near the boundary or edge of a domain, object, or system. It is often used when the edge plays a dominant role in the behavior being studied, compared with the interior.

In mathematics and physics, edgelocalization can refer to solutions or modes whose amplitude is strongest near boundaries. In partial differential equations, boundary layers or boundary-condition effects can lead to edgelocalized behavior where the influence of the boundary persists into the interior. In condensed matter and photonics, edge-localized states or modes occur at interfaces or surfaces and can govern transport, reflection, or confinement in finite systems.

In graph theory and network science, edgelocalization can describe patterns where activity or eigenvector components are larger on nodes or edges close to the network boundary or to a specified edge subset. Such localization can inform analyses of robustness, diffusion, or community structure, especially in finite or nonuniform networks.

Methods to assess edgelocalization typically involve localization measures such as participation ratios, boundary-to-volume ratios, or distance-weighted energy distributions, along with numerical experiments that contrast edge and interior contributions under different boundary conditions.

The term is used descriptively and its precise meaning varies by field and context. Related concepts include localization, edge states, boundary layers, and edge detection.