Network stylometry in complex systems: focused on the motif structures

Abstract

A complex system is a system in which numerous components interact strongly with each other. The emergence phenomenon refers to a collective phenomenon that cannot be explained only by understanding each component. The emergence phenomenon is a representative characteristic of the complex system. The complex system changes in size and interactions over time, which makes it difficult to understand the emergence. This system can be expressed as a network composed of nodes and links in terms of components and interactions among them. In this study, we try to understand the complex system by focusing on the basic structures of interactions that appear in the network. In the network, a motif is a pattern that appears more frequently observed than in randomized networks. Since the motif is a basic structure of interaction that builds up the network, we can measure the style of the system by looking at the change of the distribution of the motif structures over time. In other words, we are proposing a kind of Network Stylometry, which measures the network pattern by observing the dynamics of the motif, and studies them in various complex systems.

Language is used to record the events that happen among people living collectively, especially in civilized societies. Presidential speeches are archived as important records, and analyzing them helps to understand the cultural and historical background of the country. To analyze the speeches quantitatively, we convert words into vectors that can be understood by computers. Word2Vec, a machine learning method, has a tie-shaped artificial neural network structure, so each word is placed in appropriate word space. Converting into the word vectors, we can calculate the cosine similarity as the semantic relationship between the two words. If the artificial neural network learns speeches for each president, we can calculate and visualize the relationship between the words for the presidents. We organize a semantic network for each president and express the changes of the network stylometry over their terms. By observing the change of the unit structure in the semantic network period by period, we examine the policy changes and characteristics of each period. In particular, we confirm that the changes in the styles of presidential speeches reflect the continual increase of freedom and democracy in Korean society. This analysis can also be applied to sports data. In the sports data, events occur over time, and we can construct a semantic network using events as words. We investigate the network stylometry for the Korean national football team and confirm the strengths and weaknesses of the Korean national football team.

Biological, financial, and ecological systems consist of many individuals interacting with each other, showing their diversity. As one of the mechanisms to sustain this diversity, interaction structures have been extensively studied. A huge volume of work has focused only on static interactions. Recently, evolving open systems have drawn attention, in its importance in understanding the birth of new species and the extinction of existing species. We look at how interactions relate to diversity in an open evolving system. First of all, in the well-known network model, we analyze the growth process of the motif structure for the size of the system and confirm that positive feedback structures help the system grow. Using the friendship network data of freshmen in a university in the Netherlands, we look at the motif dynamics that can explain the structural characteristics of the social network. Furthermore, we implement a Lotka-Volterra type equation on a signed directional network, which describes interactions between species. By solving the equation numerically, we examine how the evolving interaction structure and strength affect the diversity of species.