We investigate graph-based representations of astronomical light curves for transient classification on a quality-controlled, class-balanced subset of the MANTRA benchmark (minimum coverage N min = 100 epochs; N = 1 , 705 objects after filtering and Non–Tr. subsampling). Each series is mapped to three visibility-graph views—horizontal (HVG), directed (DHVG), and weighted (W-HVG)—from which we extract compact, length-aware network descriptors (degree/strength moments, clustering and motifs, assortativity, path/efficiency, and spectral summaries). Using {object-level} stratified five-fold validation and tree-based learners, the best configuration (LightGBM with HVG+DHVG+W-HVG features) attains a macro–F1 of 0.622 ± 0.010 and accuracy of 0.661 ± 0.010 on this subset. For context, the published MANTRA baseline reports F 1 m a c r o = 0.528 on the full dataset; because class priors differ after quality control, this reference is not a like-for-like comparison. Ablations show that weighted contrasts and directed asymmetry contribute complementary gains to undirected topology. Per-class analysis highlights strong performance for CV, HPM, and Non–Tr., with residual confusions concentrated in the AGN–Blazar–SN block. These results indicate that visibility graphs offer a simple, survey-agnostic bridge between irregular photometric time series and standard classifiers, yielding competitive multiclass performance without bespoke deep architectures. We release code and feature definitions together with the list of object IDs used in the evaluation subset to facilitate reproducibility and future extensions.