This paper analyzes the shortest path problem (SPP) in social networks, based on the investigation and implementation of different methods on a simulated example. The objectives of the paper include identification of the most commonly used methods for finding the shortest path in a social network as a strategic attempt to speed the search of network nodes, focusing on the application of the two most used SPP methods: the Dijkstra and Bellman-Ford algorithms. A comparative analysis is used as an investigation method for performance evaluation of different algorithms, based on their implementation and behavior, tested on a social network example. The research results indicate that the Dijkstra algorithm is faster, and therefore more suitable for searching the shortest connection in social networks.