CT 2.6.4 Unified centrality measure of complex networks

For almost a decade, it has been found that many physical, biological, and social systems are properly described by complex networks in which a vertex represents each individual element and an edge denotes the interaction between a pair of vertices. These networks have been revealed that they share some non-trivial topological properties such as the scale-free degree distribution, P(k) ~k -γ . Moreover, many topological and dynamical properties have been known to be strongly affected by the topological properties of vertices and edges. The examples include the percolation, epidemic spreading, transmission of information and identifying the essential protein. This indicates that there are some important vertices or edges to characterize the dynamical properties on the networks. These are sometimes referred as dynamical “importance” or “centrality” of vertices and edges. One practical example for such importance can be found in the identification of the essential components of the biological systems. In developing a new drug it is crucial to target only the relevant components in a biological network without damaging the undesired components. Therefore, classifying the important vertices and edges is essential for both practical applications and deep understanding of dynamical phenomena on complex networks.