A Study on Dynamics of Network Properties in Scientific Phenomena

Abstract

In recent years, research on complex systems are actively conducted across several disciplines including physics, biology, earth science, economy, and social science, etc. A complex system is made up of numerous components with complex interactions among them, which results in a macroscopic phenomenon of the whole system more than the sum of the parts. In order to understand the complex system as holistic perspectives, researchers usually take a network or graph theory. The network is a set constituted of nodes and their links, and use the adjacency matrix to descript the links of nodes. Network theory in discrete mathematics has acted as a wonderful language to express a complex system since the 1960s. Starting from the study of random network by Erdös and Rény (ER) in 1961, Watts and Strogatz (WS) clarified the actor network, C. elegans network, and electrical power network have small-worldness using clustering coefficient in 1998. Also, Barabási and Albert (BA) investigated the scale-free properties of complex networks in 1999. Thereafter, researches on complex networks have evolved explosively by a variety of methods and data. In this paper, we construct several networks in biology, earth science, economics, and social science in various methods. Analyzing the network properties in multiple ways, we derived the dynamics of network properties. First, we investigate the interacting amino acids in protein structures as an example of biological system. It is shown from our result that protein networks have a small-world feature regardless of their structural class (alpha, beta, alpha+beta, and alpha/beta). Also, proteins are particularly found to have the positive assortative coefficient that applied to the topological property described as a tendency of connectivity of high-degree nodes. The modularity of the proteins in our case is significantly large as an increasing function of the number of amino acids in each protein. Second, we study the seismic network of California in USA as an example of geological system. We performed the computer simulation from seismic time series data taken in southern California. After simulating a seismic network against spatial shifts and scales in a volume, we treat the feature of the topological properties more briefly via various statistical quantities such as the probability distribution of degree, characteristic path length, mean clustering coefficient, small-worldness, cost efficiency, global efficiency, modularity, and assortative coefficient. Third, we study the seismic network more profound using Japan earthquake time series. Seismic network is investigated by considering the volume resolution and the temporal causality. A computer simulation of seismic networks is performed from seismic time series data taken in Japan. For our case, the universal and irregular properties of statistical quantities in seismic network do not find unambiguously, but it may be inferred that these topological properties improve by implementing the method and its technique from registered data of seismic networks. Forth, we investigate the visibility network in a time series of the KOSPI and the KOSDAQ indices converting by the visibility algorithm. As a data, we extract the indices from the KOSPI and KOSDAQ that are exchanged on the Korean stock market during a period 1996–2014. The KOSPI and the KOSDAQ by adopting the visibility algorithm is proportional to a power law rather than the Poisson distribution. We mainly simulate and analyze the network metrics from the nodes and its links in the financial networks. The universal and irregular properties of statistical quantities in financial network do not find unambiguously, but it may be inferred that these topological properties improve by implementing the statistical method and its technique from registered data of financial networks. Lastly, we study the microscopic community structure of the Korean meteorological society in the author network. Through oscillator networks, we simulate and analyze the averaged communicability functions such as the G_p^EA, G_p^RA, G_p^EL, and 1/G_p^D. After constructing networks triggered an equally contributed weight between the first author and other authors in one published paper, we mainly treat these structures of communicability from these averaged communicability functions. The function G_p^EL has a commutative relation stronger than the other three, and our results support the development of the adaptability and the stability of social organization for an individual.