We propose a framework to construct statistical arbitrage portfolios with graph clustering algorithms. First, we use various clustering methods to partition the correlation matrix of market residual returns of stocks into clusters. Next, we construct and evaluate the performance of mean-reverting statistical arbitrage portfolios within each cluster. We explore five clustering algorithms and demonstrate that our proposed framework generates profitable trading strategies with over 10% annualized returns and statistically significant Sharpe ratios above one. The performance of our statistical arbitrage portfolios is neutral to the market and cannot be fully explained by intra-industry mean-reversion effects.