Yi-Er-San topics in network science: centrality, bicycle, triplet
Creators: name: Chen, Bingsheng
Publisher: name: Imperial College London
Year: 2022

description: Network science studies interactions between different entities. This thesis covers three different topics in network science: higher-order network structures, human mobility and network centralities. Higher-order network is an emerging field in recent years and combinatorial models use multi-body interactions to describe the structures beyond pairwise. In chapter two, I focus on studying the evolution of the links in temporal networks using three nodes motif-- triplets. In specific, I develop a method that use a transition matrix to describe the evolution of triplets in temporal networks. To identify the importance of higher-order interactions in the evolution of networks, we compare both artificial and real-world network data to a model based on pairwise interactions only. The differences between the transition matrix and the calculated matrix from the fitted parameters demonstrate that non-pairwise interactions exist for various real-world systems in space and time. Furthermore, this also reveals that different patterns of higher-order interaction are involved in different real-world situations. To test my approach, I used the transition matrix to design a link prediction method-- Triplet Transition score. I investigate the performance of the methods on four temporal networks, comparing my approach against ten other link prediction methods. My results show that higher-order interactions in both space and time play a crucial role in the evolution of networks as I find Triplet Transaction method, along with two other methods based on non-local interactions, gives the best overall performance. The results also confirm the concept that the higher-order interaction patterns, i.e., triplet dynamics, can help us understand and predict the evolution of different real-world systems. In chapter three, I investigate the behaviours of human mobility in different cities using gravity models. Due to previous technical challenges in collecting data on riding behaviours, there have been only a few studies focusing on patterns and regularities of biking traffic. To extend the research, I use the data from mobike and apply the gravity model to study the mobility of dockless bicycles. I validate the effectiveness of the general gravity model on predicting biking traffic at fine spatial resolutions of locations. I then further study the impacts of spatial scale on the gravity model and reveal that the distance-related parameter grows in a similar way as population-related parameters when the spatial scale of locations increases. The result reveals the emergence of the scaling can be explained by the gravity models. Measuring the importance of nodes in networks via centrality measures is an important task in many network systems. There are many centrality measures available and it is speculated that many encode similar information but the reason behind them is rarely studied. In chapter four, I give an explicit non-linear relationship between two of the most popular measures of node centrality: degree and closeness. Based on a shortest-path tree approximation, I give an analytic derivation that shows the inverse of closeness is linearly dependent on the logarithm of degree. I show that the hypothesis works well for a range of networks produced from stochastic network models and for networks derived from many real-world data sets. I connect our results with previous results for other network distance scales such as average distance. My results imply that measuring closeness is broadly redundant unless our relationship is used to remove the dependence on degree from closeness. The success of our relationship suggests that most networks can be approximated by shortest-path spanning trees which are all statistically similar two or more steps away from their root nodes.