Where does edge collide?

In a graph, an edge is a connection joining two vertices, the abstract pairing that records a relationship between two items: an edge may be directed or undirected, and it may carry a weight that quantifies the strength of the tie. Newman's 2003 review The Structure and Function of Complex Networks treats vertices and edges as the two primitives from which every network is built, and shows how counting and arranging edges yields measures like degree, path length, and clustering. The referent here is a purely relational object, a line in a mathematical structure with no physical extent, and it is unrelated to a boundary between habitats, a change of brightness in a picture, or a firm's advantage over rivals.[1]

Unit

One vertex-to-vertex link, optionally directed and weighted

Recovery means

Not applicable

Measured by

Recorded in the adjacency matrix and analysed through graph statistics such as degree, edge weight, and path length

In landscape ecology, an edge is the boundary where two different habitat types meet, such as the margin between a forest and a field, and the distinctive conditions found there are called the edge effect: light, moisture, temperature, and the mix of species often differ sharply from the interior of either habitat. Ries, Fletcher, Battin, and Sisk's 2004 review Ecological Responses to Habitat Edges gathered the mechanisms and models that explain why organisms concentrate at, avoid, or change their behaviour near such boundaries. The referent is a physical zone of transition on the land, measured in metres of penetration into a habitat, and it has nothing in common with a link in a network, a step of intensity in an image, or a competitive advantage.[2]

Unit

A transition zone between habitats, by depth of edge influence in metres

Recovery means

The edge influence fades with distance inward, until interior habitat conditions return

Measured by

Mapped from the habitat boundary and quantified by how microclimate and species abundance change with distance from the edge

In image processing, an edge is a location in a picture where brightness changes abruptly, typically at the outline of an object or a change of surface or lighting: finding these points, called edge detection, is an early step in extracting the shapes and features an image contains. Canny's 1986 paper A Computational Approach to Edge Detection defined an edge by the steepness of the intensity gradient and derived an operator that marks such points while suppressing noise, still a standard detector today. The referent is a place of steep contrast in a two-dimensional signal, located to the pixel, and it is not a link between nodes, a boundary between habitats, or a business advantage.[3]

Unit

A pixel location of steep intensity gradient in an image

Recovery means

Not applicable

Measured by

Found by computing the intensity gradient and marking its maxima, as in the Canny detector, then thresholding

In business strategy, a competitive edge, more formally a competitive advantage, is whatever lets a firm create more value than its rivals and so outperform them, whether through lower costs, a better product, or a resource competitors cannot easily copy. Barney's 1991 paper Firm Resources and Sustained Competitive Advantage argued that such an advantage endures when it rests on resources that are valuable, rare, hard to imitate, and hard to substitute. The referent is an economic and organisational position held relative to competitors, judged by profitability and market share, and it bears no relation to a link in a graph, a habitat boundary, or a change of brightness in an image.[4]

Unit

A firm's margin of advantage over its competitors

Recovery means

Not applicable

Measured by

Inferred from sustained above-average profitability, market share, and returns relative to competitors

In urban design, edge refers to a linear boundary such as a shore or rail cut that people perceive as breaking the city's continuity, one of five elements of a city's image. This meaning comes from Lynch (1960) in The Image of the City.[5]

Unit

Recovery means

Measured by