In the field of random walks, the mean first passage time matrix and the Kemeny's constant allow us to deepen into the study of networks. For a transition matrix $\mathsf{P}$, we can observe in the literature how the authors characterize mean first passage time using generalized inverses of $\mathsf{I}-\mathsf{P}$ and its associated group inverse. In this paper, we focus on obtaining expressions for the mentioned parameters in terms of generalized inverses of the combinatorial Laplacian. For that, we first analyse the structure and the relations between any generalized inverse and the group inverse of the combinatorial Laplacian. Then, we get closed-formulas for mean first passage matrix and Kemeny's constant based on the group inverse of the combinatorial Laplacian. As an example, we consider wheel networks.

在随机游走领域，平均首次通过时间矩阵和 Kemeny 常数使我们能够深入研究网络。对于转移矩阵$\mathsf{P}$，我们可以在文献中观察到作者如何使用广义逆来描述平均首次通过时间$\mathsf{我}-\mathsf{P}$及其关联的群逆。在本文中，我们专注于根据组合拉普拉斯算子的广义逆来获得上述参数的表达式。为此，我们首先分析了组合拉普拉斯算子的任何广义逆与群逆之间的结构和关系。然后，我们根据组合拉普拉斯算子的群逆得到平均首过矩阵和Kemeny常数的闭式。例如，我们考虑车轮网络。