In this work, we propose a graph-based method implemented on the pulsar timing residuals (PTRs) for stochastic gravitational wave background (SGWB) detection within the nano-Hertz 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 complex network, for identifying SGWB in the 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 consists 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 $\barζ\gtrsim 40^{\circ}$. The lowest detectable value of SGWB strain amplitude utilizing our graph-based measures at the current PTAs sensitivity is $A_{\rm SGWB}\gtrsim 1.2\times 10^{-15}$. Fisher forecasts confirmed that the uncertainty levels of $\log_{10} A_{\rm SGWB}$ and spectral index reach $1.5\%$ and $19.5\%$, respectively, at $2σ$ confidence interval. A weak evidence for an SGWB at $\sim 2.3σ$ level is obtained by applying our graph-based method to the NANOGrav 15-year dataset.

翻译：本文提出了一种基于图的方法，应用于脉冲星计时残差（PTRs），用于纳赫兹频率范围内随机引力波背景（SGWB）的探测及其参数不确定性的检验。我们构建了一个以脉冲星为节点的相关图，并分析了基于图的摘要统计量（包括复杂网络的结构特征），以识别真实和合成数据集中的SGWB。评估了脉冲星数量、观测时间跨度和SGWB强度对基于图的特征向量的影响。结果表明，用于常见信号探测的判别性摘要统计量由平均聚类系数和边权波动组成。在观测到常见信号并排除非Hellings & Downs模板后，基于角分离阈值$\barζ\gtrsim 40^{\circ}$的边权二阶累积量进行SGWB探测。在当前PTA灵敏度下，利用我们的基于图的方法可探测到的SGWB应变振幅最低值为$A_{\rm SGWB}\gtrsim 1.2\times 10^{-15}$。Fisher预测证实，在$2σ$置信区间内，$\log_{10} A_{\rm SGWB}$和谱指数的不确定度分别达到$1.5\%$和$19.5\%$。将我们的基于图的方法应用于NANOGrav 15年数据集，获得了约$2.3σ$水平的SGWB弱证据。