As a widely adopted deep learning (DL) framework, TensorFlow’s vulnerabilities have the potential to affect a substantial number of DL applications throughout the software supply chain (SSC). However, Existing research lacks a comprehensive exploration of the characterization of TensorFlow vulnerabilities and the propagation of vulnerabilities on SSC. To help TensorFlow-based developers and security specialists in understanding the security risks, we construct an empirical study on 429 vulnerabilities of TensorFlow across a TensorFlow-based vulnerability SSC comprising 5790 versions across 691 affected packages constructed through the GitHub dependency graph. We observe that: 1) A predominant share (79.6%) of vulnerabilities occur in the TensorFlow’s Core modules (e.g., kernels, and ops), featuring prevalent vulnerabilities such as Reachable Assertion, Out-of-bounds Read, Improper Input Validation, and NULL Pointer Dereference. Notably, Divide By Zero vulnerabilities pose significant risks in the Lite module; 2) Vulnerability co-occurrence is observed in 20 pairs involving 50 vulnerabilities, with Heap-based Buffer Overflow vulnerabilities particularly likely to coexist with other types of vulnerabilities; 3) Packages within the Large Language Models (LLM) domain, often distributed across the third and fourth layers of the SSC, are vulnerable to TensorFlow’s security issues; 4) Many commonly utilized APIs (i.e. \emph{tf.constant, tf.concat}, and \emph{tf.range}), are implicated in TensorFlow vulnerabilities, affecting over half of all packages and, by extension, a significant portion of software within the SSC. Our findings suggest that: i)It would be better for Tensorflow developers take input validation, bounds checking, and assertion and exception handling before performing tensor operations, division operations, and pointer accesses to avoid Reachable Assertion, Divide By Zero, and memory-related vulnerabilities. ii) TensorFlow developers would be better to scrutinize the presence of memory-related vulnerabilities when encountering a vulnerability stemming from improper input validation. iii)TensorFlow-based Developers would be better to be aware of some widely used APIs that affected by vulnerabilities, such as \emph{tf.constant, tf.range, tf.concat}, and \emph{tf.reshape}.