<p>Diversification is the cornerstone of risk-adjusted portfolio construction. Yet, despite being a well-established principle in finance, diversification has been overlooked in pairs trading strategies, which often focus solely on selecting the most cointegrated pairs in isolation from the broader market structure and without accounting for their combined behavior within a portfolio. Here, we address this gap by introducing a network science framework to construct diversified pairs trading portfolios with minimal risk exposure, using cryptocurrencies as a case study. Our approach builds the structural network of assets based on their cointegration and then applies the Planar Maximally Filtered Graph and Triangular Maximally Filtered Graph to extract an effective market representation, which provides the essential market map for constructing diversified, risk-optimized portfolios. We show that selecting pairs that bridge communities significantly increases portfolio risk and reduces the average returns, as these pairs exhibit less stable long-term relationships because they are influenced by different market dynamics. Conversely, selecting peripheral pairs enhances the overall portfolio performance, consistently outperforming the conventional pairs trading approach of selecting the top cointegrated pairs. Finally, we conclude that incorporating the market network structure where pairs are embedded is essential for building diversified portfolios that mitigate hidden risks and cascading failures.</p>