2026ApJ...999..226A

In this work, we propose a graph-based method implemented on the pulsar timing residuals for stochastic gravitational-wave background (SGWB) detection within the nanohertz frequency regime and examining uncertainties of its parameters. We construct a correlation graph with pulsars as its nodes, and analyze the graph-based summary statistics, including structural characteristics of a complex network, for identifying an SGWB in real and synthetic datasets. The effect of the number of pulsars, the observation time span, and the strength of the SGWB on the graph-based feature vector is evaluated. Our results demonstrate that the discriminative summary statistics for common signal detection consist of the average clustering coefficient and the edge weight fluctuation. The SGWB detection conducted after the observation of a common signal and then exclusion of non-Hellings-Downs templates is performed by the second cumulant of edge weight for angular separation thresholds $\bar{\zeta }\gtrsim 4{0}^{\circ }$. The lowest detectable value of the SGWB strain amplitude utilizing our graph-based measures at the current pulsar timing array's sensitivity is A_SGWB ≳ 1.2 × 10^–15. Fisher forecasts confirmed that the uncertainty levels of ${\mathrm{log}}_{10}{A}_{{\rm{SGWB}}}$ and spectral index reach 1.5% and 19.5%, respectively, at the 2σ confidence interval. Weak evidence for an SGWB at an ∼2.3σ level is obtained by applying our graph-based method to the NANOGrav 15 yr dataset.