Hubs and Authorities on Japanese Inter-Firm Network: Characterization of Nodes in Very Large Directed Networks

Japanese inter-firm network which consists of about one million firms and four million directed links is analyzed by evaluating PageRank, and the authority and hub scores of HITS. We show scale-free degree distribution, power-law distribution of firm-size, fat-tailed distribution of growth rate, positive correlation between degree and firm-size, and similarities between degree and these scores. By comparing with randomized networks, we find that (i) the firm with large firm-size tends to have large PageRank, and small authority and hub scores, and (ii) PageRank correlates significantly with the growth rate which is hardly observed with other quantities.