Random matrix approach to shareholding networks

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, ρ(λ)∼|λ|-δ, in the tail part. It is also shown that the degree distribution of this network follows a power law distribution, p(k)∼k-γ, in the large degree range. The scaling law δ=2γ-1 is found in this network. The reason why this relation holds is attributed to the local tree-like structure of the shareholding network.