图拓扑识别（GTI）是网络化系统中的核心挑战，其底层结构通常不可观测，但节点数据可得。传统方法常依赖概率模型或复杂的优化公式，普遍存在非凸性问题，或需对无环性或正定性等施加严格假设。本文提出一种新颖的协方差匹配（CovMatch）框架，直接将观测数据的经验协方差与由潜在图结构所导出的理论协方差对齐。我们证明：只要数据生成过程允许显式协方差表达式，CovMatch 即可为拓扑推断提供统一路径。我们在线性结构方程模型（SEM）上验证该方法，表明 CovMatch 可自然处理无向图及一般稀疏有向图——无论其是否无环或边权是否为正——且无需显式知晓这些结构性约束。通过适当的重参数化，CovMatch 将图学习问题简化为：对无向图采用锥混合整数规划，对有向图则转化为正交矩阵优化。数值实验表明，即使对于相对大规模图，该方法亦能高效恢复真实拓扑，并在准确性上优于标准基线方法。这些结果凸显 CovMatch 作为 GTI 领域中对数行列式法或贝叶斯方法的一种有力替代方案，为在极简假设下学习复杂网络拓扑开辟了更广阔的研究路径。

Graph topology identification (GTI) is a central challenge in networked systems, where the underlying structure is often hidden, yet nodal data are available. Conventional solutions to address these challenges rely on probabilistic models or complex optimization formulations, commonly suffering from non-convexity or requiring restrictive assumptions on acyclicity or positivity. In this paper, we propose a novel covariance matching (CovMatch) framework that directly aligns the empirical covariance of the observed data with the theoretical covariance implied by an underlying graph. We show that as long as the data-generating process permits an explicit covariance expression, CovMatch offers a unified route to topology inference. We showcase our methodology on linear structural equation models (SEMs), showing that CovMatch naturally handles both undirected and general sparse directed graphs - whether acyclic or positively weighted - without explicit knowledge of these structural constraints. Through appropriate reparameterizations, CovMatch simplifies the graph learning problem to either a conic mixed integer program for undirected graphs or an orthogonal matrix optimization for directed graphs. Numerical results confirm that, even for relatively large graphs, our approach efficiently recovers the true topology and outperforms standard baselines in accuracy. These findings highlight CovMatch as a powerful alternative to log-determinant or Bayesian methods for GTI, paving the way for broader research on learning complex network topologies with minimal assumptions.