Visibility Graph Analysis of Financial Time Series: A Comparative Study of Gas and Power Price Dynamics in the Italian Energy Market

This paper presents a comparative analysis of natural gas and electric power prices using visibility graph methodology, a technique from complex network theory that transforms temporal sequences into network representations. We analyze 1,826 daily observations from the Italian energy market (2019-2023), implementing a three-stage preprocessing pipeline (logarithmic transformation, LOESS detrending, and first differencing) before constructing visibility graphs. Our topological analysis reveals striking differences: gas exhibits substantially higher connectivity (6,202 versus 5,354 edges), heavier-tailed degree distributions (maximum degree 117 versus 54), and dramatically longer-range connections (average temporal distance 26.4 versus 11.0 days). Paradoxically, despite power displaying twice the raw volatility, gas generates more structured long-range correlations due to storage-enabled intertemporal linkages. Both series exhibit small-world properties with high clustering (≈0.76), short path lengths (4.59 and 5.36), and positive assortativity (≈0.17). Correlation analysis reveals moderate contemporaneous return correlation (Pearson r = 0.456) with substantial time variation (range 0.173– 0.696), no lead-lag relationships, and partial synchronization of topological properties. Node-level degree and clustering show positive correlations between markets, while closeness centrality exhibits strong negative correlation (r = −0.719), indicating fundamentally different global network organization. Structural similarity (Jaccard coefficient 0.404) confirms 40% shared visibility connections with 60% commodity-specific structure. These findings demonstrate that physical storability fundamentally shapes temporal correlation structure, with direct implications for risk management, forecasting model selection, and portfolio construction in energy markets.