1. Stronger statement than differentiability can be made regarding the resolvent map. 2. This uses the resolvent of the Feller semigroup, defined below. 3. The alpha centrality replaces the adjacency matrix with its resolvent . 4. The idea of a determinant was developed by Lagrange resolvents . 5. This subsection outlines properties of the resolvent map that are essential in this context. 6. The Klein group can be understood in terms of the Lagrange resolvents of the quartic. 7. It will be shown below that the resolvent mapping is holomorphic on the resolvent set. 8. It will be shown below that the resolvent mapping is holomorphic on the resolvent set. 9. As stated above, on such ?, the resolvent map admits a power series representation 10. The Laurent series of the resolvent mapping centered at " ? " shows that
