Complex Networks Analysis with Transfer Entropy

Nowadays, data analysis has become more complicated.Agencies such as social media and online news sites cause rapid dissemination of information. This situation creates a lot of relevant and irrelevant data. It takes a lot of effort to make a meaningful analysis by extracting as many causal relational data as possible from the others. For example, from the diseases that trigger each other or the effects of the bankrupt company on other market players. In our thesis, we made a study to make these complex networks more understandable and readable.

We tried to apply Schreiber's transfer entropy on a complex network as a way to characterise interaction between data, in other words, information flow. We measures network similarity using Jensen-Shannon divergence and Kullback-Leibler divergence. With this, we wanted to compare the distribution of correlations between different networks. We explore how both weighted and unweighted representations derived from these characterisations perform on real-world time series data. We also use the transfer entropy to weight the edges of a graph where the nodes represent time series data and the edges represent the degree of commonality of pairs of time series. We also make a comparison between the graph characterisation calculated by von Neumann entropy and transfer entropy.

We also worked on smoothing the edge entropy by applying diffusion operation on how this information flow can be in multiplex graphs. We examined the causality of this information flow, especially in time-varying multiplex graph.