A position detecting apparatus and a library apparatus that have a flag and a sensor for detecting the flag can shorten time required to perform a position detecting process. Transactions of a service provided by each of a plurality of computers to another computer are collected, a matrix of correlations between nodes in the system is calculated from the transactions, and a feature vector representing a node activity balance is obtained from the matrix. According to the invention, this is brought about in that the polymer is applied to the top side of the granulate.