PageRank is a centrality algorithm that measures the transitive influence of nodes in a graph, considering not only direct connections but also the importance of neighboring nodes. It calculates an estimation of how important a page is based on the number and quality of links to it, with higher-quality links indicating greater importance. PageRank can be applied across various domains, including social media platforms like Twitter, traffic flow prediction, and anomaly detection in healthcare and insurance industries. When using PageRank, it's essential to consider potential issues such as spider traps, rank sinks, and dead-ends to ensure accurate results. The algorithm has been used in real-world applications to personalize recommendations, predict traffic flow, and detect anomalies, demonstrating its effectiveness in understanding the influence of nodes within a graph.