that the [edge]{} $(j^*,j^*)$ is also present, but not shown. (b) For the case [where]{} $C_{j^*}^{-} \geq 1/2$, we only focus on two-hop paths between $j^*$ and elements $i \in S^{-}$ obtained by taking $(i,j^*)$ as the first step and the self-edge $(j^*,j^*)$ as the second step. (c) For the case where $C_{j^*}^{+} \geq 1/2$, we only focus on two-hop paths between $i^*$ and elements $j\in S^{+}$ obtained by taking $(i^*,j^*)$ as the first step in $\E(A)$ and $(j^*,j)$ as the second step in $\E(A^T)$.](cplusbignew.eps "fig:"){width="4cm"} ![\[cdef\](a) Intuitively, $C_{j^*}^{+}$ measures how much weight $j^*$ assigns to nodes in $S^{+}$ (including itself), and $C_{j^*}^{-}$ measures how much weight $j^*$ assigns to nodes in $S^{-}$. Note that the [edge]{} $(j^*,j^*)$ is also present, but not shown. (b) For the case [where]{} $C_{j^*}^{-} \geq 1/2$, we only focus on two-hop paths between $j^*$ and elements $i \in S^{-}$ obtained by taking $(i,j^*)$ as the first step and the self-edge $(j^*,j^*)$ as the second step. (c) For the case where $C_{j^*}^{+} \geq 1/2$, we only focus on two-hop paths between $i^*$ and elements $j\in S^{+}$ obtained by taking $(i^*,j^*)$ as the first step in $\E(A)$ and $(j^*,j)$ as the second step in $\E(A^T)$.](c2bignew.eps "fig:"){width="4cm"} 