Due to the recent expansion of the Web 2.0 -based services, along with the widespread of smartphones, online social network services are being popularized among users. Online social network services are the online community services which enable users to communicate each other, share information and expand human relationships. In the social network services, each relation between users is represented by a graph consisting of nodes and links. As the users of online social network services are increasing rapidly, the SNS are actively utilized in enterprise marketing, analysis of social phenomenon and so on. Social Network Analysis (SNA) is the systematic way to analyze social relationships among the members of the social network using the network theory. In general social network theory consists of nodes and arcs, and it is often depicted in a social network diagram. In a social network diagram, nodes represent individual actors within the network and arcs represent relationships between the nodes. With SNA, we can measure relationships among the people such as degree of intimacy, intensity of connection and classification of the groups. Ever since Social Networking Services (SNS) have drawn increasing attention from millions of users, numerous researches have made to analyze their user relationships and messages. There are typical representative SNA methods: degree centrality, betweenness centrality and closeness centrality. In the degree of centrality analysis, the shortest path between nodes is not considered. However, it is used as a crucial factor in betweenness centrality, closeness centrality and other SNA methods. In previous researches in SNA, the computation time was not too expensive since the size of social network was small. Unfortunately, most SNA methods require significant time to process relevant data, and it makes difficult to apply the ever increasing SNS data in social network studies. For instance, if the number of nodes in online social network is n, the maximum number of link in social network is n(n-1)/2. It means that it is too expensive to analyze the social network, for example, if the number of nodes is 10,000 the number of links is 49,995,000. Therefore, we propose a heuristic-based method for finding the shortest path among users in the SNS user graph. Through the shortest path finding method, we will show how efficient our proposed approach may be by conducting betweenness centrality analysis and closeness centrality analysis, both of which are widely used in social network studies. Moreover, we devised an enhanced method with addition of best-first-search method and preprocessing step for the reduction of computation time and rapid search of the shortest paths in a huge size of online social network. Best-first-search method finds the shortest path heuristically, which generalizes human experiences. As large number of links is shared by only a few nodes in online social networks, most nods have relatively few connections. As a result, a node with multiple connections functions as a hub node. When searching for a particular node, looking for users with numerous links instead of searching all users indiscriminately has a better chance of finding the desired node more quickly. In this paper, we employ the degree of user node vn as heuristic evaluation function in a graph G = (N, E), where N is a set of vertices, and E is a set of links between two different nodes. As the heuristic evaluation function is used, the worst case could happen when the target node is situated in the bottom of skewed tree. In order to remove such a target node, the preprocessing step is conducted. Next, we find the shortest path between two nodes in social network efficiently and then analyze the social network. For the verification of the proposed method, we crawled 160,000 people from online and then constructed social network. Then we compared with previous methods, which are best-first-search and breath-first-search, in time for searching and analyzing. The suggested method takes 240 seconds to search nodes where breath-first-search based method takes 1,781 seconds (7.4 times faster). Moreover, for social network analysis, the suggested method is 6.8 times and 1.8 times faster than betweenness centrality analysis and closeness centrality analysis, respectively. The proposed method in this paper shows the possibility to analyze a large size of social network with the better performance in time. As a result, our method would improve the efficiency of social network analysis, making it particularly useful in studying social trends or phenomena.