A method includes obtaining a matrix defining a topology of a multi-hop network, where the topology identifies nodes and links between the nodes in the multi-hop network. The method also includes identifying one or more Eigenvalues and/or one or more Eigenvectors of the matrix. The method further includes determining whether the topology of the multi-hop network defines a disconnected network using the one or more Eigenvalues and/or the one or more Eigenvectors. For example, one or more Eigenvalues of the matrix can be identified, and a determination can be made whether a second smallest Eigenvalue equals zero. As another example, Eigenvectors corresponding to two smallest Eigenvalues of the matrix can be identified, and a determination can be made whether the Eigenvectors have opposite zero and non-zero entries such that, for all entries in the Eigenvectors, an ith entry in one Eigenvector is zero while an ith entry in another Eigenvector is non-zero.