Structural controllability of temporal networks

The control of complex systems is an ongoing challenge of complexity research. Recent advances using concepts of structural control deduce a wide range of control related properties from the network representation of complex systems. Here, we examine the controllability of systems for which the timescale of the dynamics we control and the timescale of changes in the network are comparable. We provide analytical and computational tools to study controllability based on temporal network characteristics. We apply these results to investigate the controllable subnetwork using a single input. For a generic class of model networks, we witness a phase transition depending upon the density of the interactions, describing the emergence of a giant controllable subspace. We show the existence of the two phases in real-world networks. Using randomization procedures, we find that the overall activity and the degree distribution of the underlying network are the main features influencing controllability.Bundesministerium für Bildung und Forschung 10.13039/501100002347German Academic Exchange Service 10.13039/501100001655Peer Reviewe

Do the rich get richer? An empirical analysis of the BitCoin transaction network

The possibility to analyze everyday monetary transactions is limited by the scarcity of available data, as this kind of information is usually considered highly sensitive. Present econophysics models are usually employed on presumed random networks of interacting agents, and only macroscopic properties (e.g. the resulting wealth distribution) are compared to real-world data. In this paper, we analyze BitCoin, which is a novel digital currency system, where the complete list of transactions is publicly available. Using this dataset, we reconstruct the network of transactions, and extract the time and amount of each payment. We analyze the structure of the transaction network by measuring network characteristics over time, such as the degree distribution, degree correlations and clustering. We find that linear preferential attachment drives the growth of the network. We also study the dynamics taking place on the transaction network, i.e. the flow of money. We measure temporal patterns and the wealth accumulation. Investigating the microscopic statistics of money movement, we find that sublinear preferential attachment governs the evolution of the wealth distribution. We report a scaling relation between the degree and wealth associated to individual nodes.Comment: Project website: http://www.vo.elte.hu/bitcoin/; updated after publicatio

Core percolation on complex networks

As a fundamental structural transition in complex networks, core percolation is related to a wide range of important problems. Yet, previous theoretical studies of core percolation have been focusing on the classical Erd\H{o}s-R\'enyi random networks with Poisson degree distribution, which are quite unlike many real-world networks with scale-free or fat-tailed degree distributions. Here we show that core percolation can be analytically studied for complex networks with arbitrary degree distributions. We derive the condition for core percolation and find that purely scale-free networks have no core for any degree exponents. We show that for undirected networks if core percolation occurs then it is always continuous while for directed networks it becomes discontinuous when the in- and out-degree distributions are different. We also apply our theory to real-world directed networks and find, surprisingly, that they often have much larger core sizes as compared to random models. These findings would help us better understand the interesting interplay between the structural and dynamical properties of complex networks.Comment: 17 pages, 6 figure

Inferring the interplay of network structure and market effects in Bitcoin

A main focus in economics research is understanding the time series of prices of goods and assets. While statistical models using only the properties of the time series itself have been successful in many aspects, we expect to gain a better understanding of the phenomena involved if we can model the underlying system of interacting agents. In this article, we consider the history of Bitcoin, a novel digital currency system, for which the complete list of transactions is available for analysis. Using this dataset, we reconstruct the transaction network between users and analyze changes in the structure of the subgraph induced by the most active users. Our approach is based on the unsupervised identification of important features of the time variation of the network. Applying the widely used method of Principal Component Analysis to the matrix constructed from snapshots of the network at different times, we are able to show how structural changes in the network accompany significant changes in the exchange price of bitcoins.Comment: project website: http://www.vo.elte.hu/bitcoi

Shortest path discovery of complex networks

In this paper we present an analytic study of sampled networks in the case of some important shortest-path sampling models. We present analytic formulas for the probability of edge discovery in the case of an evolving and a static network model. We also show that the number of discovered edges in a finite network scales much slower than predicted by earlier mean field models. Finally, we calculate the degree distribution of sampled networks, and we demonstrate that they are analogous to a destructed network obtained by randomly removing edges from the original network.Comment: 10 pages, 4 figure