The $k$-center problem is one of the most fundamental clustering problems and has applications in a wide range of areas, including facility location, network design, data mining, and machine learning. Given a set of objects together with a distance measure, the goal is to select $k$ centers such that the maximum distance from any object to its closest center is minimized. The $k$-center problem has been studied extensively from a theoretical perspective, both in metric spaces and on graphs. While there have been experimental studies for $k$-center clustering in metric spaces, a comprehensive experimental comparison of graph-based $k$-center algorithms on large-scale graphs is still lacking. In this paper, we bridge this gap by evaluating a set of algorithms ranging from classical approaches such as Gonzalez's greedy algorithm [TCS 1985], an algorithm based on the framework established by Hochbaum and Shmoys [Math. Oper. Res. 1985], to more recent methods, including algorithms by Thorup [SICOMP 2001] and Abboud et al. [SOSA 2023]. Our study considers both running time, solution quality and the effects of parallelism on a variety of synthetic and real-world datasets. Our goal is to provide a comprehensive comparison of state-of-the-art $k$-center algorithms on graphs and identify the strengths and weaknesses of different approaches in practice.

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