The author studies the canonical map \(\varphi\colon X\rightarrow {\mathbb P}(H^0(X,\,\Omega^1_X)^\ast)\) of a pointed curve \(X\) over an algebraically closed field with nodal singularities with the help of its dual modular graph \(\Gamma=\Gamma(X).\) In particular, it is proved that \(\varphi\) has no base points if and only if \(\text{th}(\Gamma) \geq 2;\) the canonical map is an embedding if and only if \(\text{th}(\Gamma) \geq 3,\) the dimension of \( H^0(X,\,\Omega^1_X)\) is at least 2, and the curve \(X\) is not a generalized hyperelliptic curve. Here the thickness of \(\Gamma\) is denoted by \(\text{th}(\Gamma)\) [A. N. Tyurin, “Quantization, classical and quantum field theory and theta functions”. CRM Monograph Series 21 (2003; Zbl 1083.14037)]. In fact, the author completes the results by F. Knudsen [Math. Scand. 52, 161–199 (1983; Zbl 0544.14020)] describing the multi-canonical map for Deligne-Mumford stable curves. He also remarks that analogous results for compact curves were earlier obtained by F. Catanese et al. [Nagoya Math. J. 154, 185–220 (1999; Zbl 0933.14003)].