Random matrix approach to shareholding networks

✍ Scribed by Wataru Souma; Yoshi Fujiwara; Hideaki Aoyama

• Book ID: 103881517
• Publisher: Elsevier Science
• Year: 2004
• Tongue: English
• Weight: 598 KB
• Volume: 344
• Category: Article
• ISSN: 0378-4371
• DOI: 10.1016/j.physa.2004.06.090

✦ Synopsis

A shareholding network is represented by a symmetrical adjacency matrix. The random matrix theoretical approach to this matrix shows that the spectrum follows a power law distribution, rðlÞ $ jlj Àd , in the tail part. It is also shown that the degree distribution of this network follows a power law distribution, pðkÞ $ k Àg , in the large degree range. The scaling law d ¼ 2g À 1 is found in this network. The reason why this relation holds is attributed to the local tree-like structure of the shareholding network.