Jae Dong Noh

Scale-free trees: the skeletons of complex networks.

We investigate the properties of the spanning trees of various real-world and model networks. The spanning tree representing the communication kernel of the original network is determined by maximizing the total weight of the edges, whose weights are given by the edge betweenness centralities. We find that a scale-free tree and shortcuts organize a complex network. Especially, in ubiquitous scale-free networks, it is found that the scale-free spanning tree shows very robust betweenness centrality distributions and the remaining shortcuts characterize the properties of the original network, such as the clustering coefficient and the classification of scale-free networks by the betweenness centrality distribution.

Model for correlations in stock markets

We propose a group model for correlations in stock markets. In the group model the markets are composed of several groups, within which the stock price fluctuations are correlated. The spectral properties of empirical correlation matrices reported recently are well understood from the model. It provides the connection between the spectral properties of the empirical correlation matrix and the structure of correlations in stock markets.

Random field Ising model and community structure in complex networks

Abstract. We propose a method to determine the community structure of a complex network. In this method the ground state problem of a ferromagnetic random field Ising model is considered on the network with the magnetic field Bs = +∞, Bt = -∞, and Bi≠s,t=0 for a node pair s and t. The ground state problem is equivalent to the so-called maximum flow problem, which can be solved exactly numerically with the help of a combinatorial optimization algorithm. The community structure is then identified from the ground state Ising spin domains for all pairs of s and t. Our method provides a criterion for the existence of the community structure, and is applicable equally well to unweighted and weighted networks. We demonstrate the performance of the method by applying it to the Barabási-Albert network, Zachary karate club network, the scientific collaboration network, and the stock price correlation network. (Ising, Potts, etc.)

Epidemic dynamics of two species of interacting particles on scale-free networks

We study the non-equilibrium phase transition in a model for epidemic spreading on scale-free networks. The model consists of two particle species

Load distribution in weighted complex networks

A

Percolation transition in networks with degree-degree correlation.

and

Epidemic threshold of the susceptible-infected-susceptible model on complex networks.

B

Stationary and dynamical properties of a zero-range process on scale-free networks

, and the coupling between them is taken to be asymmetric;

Universality class of absorbing transitions with continuously varying critical exponents

A

Nonequilibrium fluctuations for linear diffusion dynamics.

induces