从随机游走轨迹重构未知图结构，既见于天体物理学中的空间相关性网络，也见于网络科学中的连通性推断。我们提出一种重构流程：其可观测量为随机游走共访问矩阵，建模基础为成对边权重基，拟合器为带节点组权重与自校准边读出的帧平衡Levenberg-Marquardt（fbLM）算法。与边缘占据率不同，共访问矩阵在行求和前保留了有序对信息；而成对基可表征加性节点势模型无法表达的结构；二者任一单独改变均不足以实现该优势。我们将该流程应用于电子邮件通信子图、由COSMOS天区星表构建的Delaunay与Voronoi网络，以及两个受控的12顶点测试图（一为单环图，一为树），分别在解析噪声与有限步长游走两种情形下进行实验。重构结果以真实邻接矩阵（未参与拟合过程）为基准，通过真/假阳性率及Matthews相关系数（MCC）进行评估。所有测试场景在全图规模下均实现高保真重构：在有限步长游走数据上，COSMOS Delaunay与Voronoi图分别在N=119与N=223（即完整图而非局部截取）下达到MCC > 0.98；经验性电子邮件Eu-core图（N=240，417条边）亦被完整重构。在完整Delaunay图上，图形Lasso基线方法MCC为0.540，而fbLM达0.988。每条重构边均附带Fisher传播不确定性，残差遗漏几乎全部集中于随机游走从未遍历的边上。在有限步长游走情形下，制约因素在于游走覆盖度而非拟合精度：游走实际访问的边几乎全部被成功重构。

Reconstructing an unknown graph from the trajectory of a random walk arises both for spatial correlation networks in astrophysics and for connectivity inference in network science. We present a reconstruction pipeline whose observable is the random-walk co-visitation matrix, whose model is a pairwise edge-weight basis, and whose fitter is a frame-balanced Levenberg-Marquardt (fbLM) scheme with per-node group weights and a self-calibrated edge readout. Unlike the marginal occupation, the co-visitation retains the ordered pair before the row sum is taken, and the pairwise basis can represent structure that an additive node-potential model cannot; neither change suffices alone. We apply the pipeline to an email communication subgraph, to Delaunay and Voronoi networks built from a COSMOS sky catalogue, and to two controlled 12-vertex test graphs, one unicyclic and one a tree, under both analytic-noise and finite-walk regimes. Reconstructions are scored against the ground-truth adjacency, which enters nowhere in the fit, by true/false positives and the Matthews correlation coefficient (MCC). All test-beds are reconstructed with high fidelity at full graph size: on finite-walk data we recover the COSMOS Delaunay and Voronoi graphs at MCC above 0.98 up to their full extent, N=119 and N=223, the whole graph rather than a cut-out of it, and the empirical email-Eu-core graph at N=240 (417 edges). On the full Delaunay graph a graphical-lasso reference returns MCC 0.540 against 0.988 for fbLM. Each reconstructed edge carries a Fisher-propagated uncertainty, and the residual misses are almost entirely confined to edges the walk never traverses. In the finite-walk regime the limiting factor is therefore walk coverage rather than the fit: essentially every edge the walk visits is recovered, so reconstructibility is governed by the sampling of the graph rather than by the estimator.