Bonacich's family of measures does not transform the adjacency matrix. [[Alpha centrality]] replaces the adjacency matrix with its [[resolvent formalism|resolvent]]. Subgraph centrality replaces the adjacency matrix with its trace. A startling conclusion is that regardless of the initial transformation of the adjacency matrix, all such approaches have common limiting behavior. As <math>\beta</math> approaches zero, the indices converge to [[Centrality#Degree centrality|degree centrality]]. As <math>\beta</math> approaches its maximal value, the indices converge to [[Centrality#Eigenvector centrality|eigenvalue centrality]].<ref name=Benzi2013/> | Bonacich's family of measures does not transform the adjacency matrix. [[Alpha centrality]] replaces the adjacency matrix with its [[resolvent formalism|resolvent]]. Subgraph centrality replaces the adjacency matrix with its trace. A startling conclusion is that regardless of the initial transformation of the adjacency matrix, all such approaches have common limiting behavior. As <math>\beta</math> approaches zero, the indices converge to [[Centrality#Degree centrality|degree centrality]]. As <math>\beta</math> approaches its maximal value, the indices converge to [[Centrality#Eigenvector centrality|eigenvalue centrality]].<ref name=Benzi2013/> |