Leicht, Holme, and Newman (LHN) similarity is defined as: $\mathbf{S}_{LHN} [u,v]=\mathbf{I}[u,v]+\frac{2m}{d_ud_v}\sum_{i=1}^{\infty}\beta^i \lambda_1^{1-i} \mathbf{A}^i [u,v]$ where $d_u$ and $d_v$ are the degrees of nodes $u$ and $v$, $\lambda_1$ is the largest eigenvalue, and $m$ is the total number of edges in the graph. It can be proved that: $\mathbf{S}_{LHN}=2\alpha m\lambda_1\mathbf{D}^{-1}(\mathbf{I}-\frac{\beta}{\lambda_1} \mathbf{A})^{-1}\mathbf{D}$ The idea of LHN is that because Katz similarity gives much higher scores for high degree nodes, LHN similarity solves this issue by normalizing the actual number of observed paths using the expected number of paths, which is $\frac{\mathbf{A}^i}{\mathbb{E}[\mathbf{A}^i]}$. The expected value $\mathbb{E}[\mathbf{A}^i]$ can be estimated through $d_u$, $d_v$, and $\lambda_1$.