Editing Centrality (section)

===Characterization by walk structure===
An alternative classification can be derived from how the centrality is constructed. This again splits into two classes. Centralities are either ''radial'' or ''medial.'' Radial centralities count walks which start/end from the given vertex. The [[#Degree centrality|degree]] and [[#Eigenvector centrality|eigenvalue]] centralities are examples of radial centralities, counting the number of walks of length one or length infinity. Medial centralities count walks which pass through the given vertex. The canonical example is Freeman's [[#Betweenness centrality|betweenness]] centrality, the number of shortest paths which pass through the given vertex.<ref name=Borgatti2006/>

Likewise, the counting can capture either the ''volume'' or the ''length'' of walks. Volume is the total number of walks of the given type. The three examples from the previous paragraph fall into this category. Length captures the distance from the given vertex to the remaining vertices in the graph. [[#Closeness centrality|Closeness]] centrality, the total geodesic distance from a given vertex to all other vertices, is the best known example.<ref name=Borgatti2006/> Note that this classification is independent of the type of walk counted (i.e. walk, trail, path, geodesic).

Borgatti and Everett propose that this typology provides insight into how best to compare centrality measures. Centralities placed in the same box in this 2×2  classification are similar enough to make plausible alternatives; one can reasonably compare which is better for a given application. Measures from different boxes, however, are categorically distinct. Any evaluation of relative fitness can only occur within the context of predetermining which category is more applicable, rendering the comparison moot.<ref name=Borgatti2006/>