Structure, dynamics and applications of complex networks

Abstract

The newly developed complex network theory is extremely essential to describe the various real world phenomena within the extended scope of the statistical physics. Because there exists huge complexity in patterns of interactions between enormous number of individuals in the real world systems, these interactions cannot be considered as the bonds on the regular lattice which have been used to deal with to understand magnetism in materials. Instead, they have to be considered as complex connections on a generalized lattice called the complex network. Since the pioneering works observing scale-free networks in abundant real-world systems, the studies of complex network has been accelerated in recent years because of its promising application to prediction of phenomena occurring in real world. This thesis addresses our recent studies on the structural and dynamical characteristics of complex networks and their applications to modeling of fracture cascade and clustering of stocks in the stock market. First we find out the universal skeleton structure of complex networks that plays a very important role in communications between vertices. The skeleton of a complex network is defined as the special spanning tree maximizing the total weight, given by an edgebetweenness centrality (edge-BC), an average traffic, on each edges. For various scale-free networks, it turns out that the skeleton shows the characteristics of the scale-free tree and can be regarded as the communication kernel handling a large part of the communication traffics. Moreover, in scale-free networks, while the skeleton structure has the universality of the power-law BC distribution with the exponent 2.0, we find that either the fast decaying or the bell-shaped length distribution of the additional shortcuts on the skeleton discriminates the known two different categories classified by the BC exponent, which gives very intuitive explanation for the difference of the two. In homogeneous networks, altho...