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===Characterization by network flows==

===Characterization by network flows==

A network can be considered a description of the paths along which something flows. This allows a characterization based on the type of flow and the type of path encoded by the centrality. A flow can be based on transfers, where each indivisible item goes from one node to another, like a package delivery going from the delivery site to the client's house. A second case is serial duplication, in which an item is replicated so that both the source and the target have it. An example is the propagation of information through gossip, with the information being propagated in a private way and with both the source and the target nodes being informed at the end of the process. The last case is parallel duplication, with the item being duplicated to several links at the same time, like a radio broadcast which provides the same information to many listeners at once.<ref name=Borgatti2005/>

A network can be considered a description of the paths along which something flows. This allows a characterization based on the type of flow and the type of path encoded by the centrality. A flow can be based on transfers, where each indivisible item goes from one node to another, like a package delivery going from the delivery site to the client's house. A second case is serial duplication, in which an item is replicated so that both the source and the target have it. An example is the propagation of information through gossip, with the information being propagated in a private way and with both the source and the target nodes being informed at the end of the process. The last case is parallel duplication, with the item being duplicated to several links at the same time, like a radio broadcast which provides the same information to many listeners at once.<ref name=Borgatti2005/>

Likewise, the type of path can be constrained to geodesics (shortest paths), paths  (no vertex is visited more than once), trails (vertices can be visited multiple times, no edge is traversed more than once), or walks (vertices and edges can be visited/traversed multiple times).

Likewise, the type of path can be constrained to geodesics (shortest paths), paths  (no vertex is visited more than once), trails (vertices can be visited multiple times, no edge is traversed more than once), or walks (vertices and edges can be visited/traversed multiple times).

同样，路径类型可以被限定为测地线(最短路径)、路径(对顶点的访问不超过一次)、轨迹(可以访问多次顶点，没有边被访问超过一次)或者步子(可以访问/遍历多次顶点和边)。

同样，路径类型可以被限定为测地线(最短路径)、路径(对顶点的访问不超过一次)、小径(可以访问多次顶点，没有边被访问超过一次)或者步子(可以访问/遍历多次顶点和边)。

===Characterization by walk structure===

===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 [[Centrality#Degree centrality|degree]] and [[Centrality#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 [[Centrality#Betweenness centrality|betweenness]] centrality, the number of shortest paths which pass through the given vertex.<ref name=Borgatti2006/>

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 [[Centrality#Degree centrality|degree]] and [[Centrality#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 [[Centrality#Betweenness centrality|betweenness]] centrality, the number of shortest paths which pass through the given vertex.<ref name=Borgatti2006/>