In this chapter, several quantitative indices involving the spectrum of the matrix-weighted adjacency and matrix-weighted Laplacian matrices will be presented. First, the energy of a matrix-weighted graph, which involves the spectrum of the matrix-weighted adjacency matrix, will be studied. The energy of scalar graphs has been, for instance, conceptualized by the total energy of electrons in hydrocarbons. Although the initial connections with chemistry have faded, graph energy has become a theoretical research topic in spectral graph theory. The Laplacian energy of matrix-weighted graph is then similarly defined. Second, the effective resistance and resistance matrices associated with a matrix-weighted graph are then revisited. As ubiquitous applications of resistance distance can be found, e.g., in DC circuit theory, chemistry, or robustness analysis of a consensus network, a corresponding result for matrix-weighted graph will be of interest. Specifically, the connections between the Moore–Penrose pseudo-inverse of the matrix-weighted Laplacian and the effective resistance, the Kron reduction, the computation of equivalent simple matrix-weighted networks, and several properties of the resistance matrix will be explored. Third, the notions of node and edge importance are then defined. The node and edge importance indices are then generalized so that they could be applied to various network systems. Several inequalities relating to the edge- and vertex-cutset indices with the connectivity index are also provided.