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We investigate the performance of analog network coding (ANC) for multi-hop networks in this paper. With the amplify-and-forward (AF) protocol, relays broadcast the sum of two colliding signals to neighboring nodes, while the source node can subtract its own signal from the colliding signal to obtain the received information. We first give the transmission scheme expressions for the n-node m-frame two-way multi-hop network. For this scheme, we derive the end-to-end signal-to-noise ratio (SNR) expression. Without loss of generality, the closed-form expression of the outage probability for the generalized multi-hop network is evaluated. Numerical results demonstrate that the outage performance with ANC is better than the traditional scheme without ANC.