Recently, physically unclonable functions (PUFs) have received considerable attention from the research community due to their potential use in security mechanisms for applications such as the Internet of things (IoT). The concept generally employs the fabrication variability and naturally embedded randomness of object characteristics for secure identification. This approach complements and improves upon the conventional cryptographic security algorithms by covering their vulnerability against counterfeiting, cloning attacks, and physical hijacking. In this work, we propose a new identification/authentication mechanism based on a specific implementation of optical PUFs based on electrochemically formed dendritic patterns. Dendritic tags are built by growing unique, complex and unclonable nano-scaled metallic patterns on substrates. Dendritic patterns with 3D surfaces are technically impossible to reproduce, hence can be used as the fingerprints of objects. Current optical PUF-based identification mechanisms rely on image processing methods that require high-complexity computations and massive storage and communication capacity to store and exchange high-resolution image databases in large-scale networks. To address these issues, we propose a light-weight identification algorithm that converts the images of dendritic patterns into representative graphs and uses a graph-matching approach for device identification. More specifically, we develop a probabilistic graph matching algorithm that makes linkages between the similar feature points in the test and reference graphs while considering the consistency of their local subgraphs. The proposed method demonstrates a high level of accuracy in the presence of imaging artifacts, noise, and skew compared to existing image-based algorithms. The computational complexity of the algorithm grows linearly with the number of extracted feature points and is therefore suitable for large-scale networks.