Recent research has highlighted limitations of studying complex systems with time-varying topologies from the perspective of static, time-aggregated networks. Non-Markovian characteristics resulting from the ordering of interactions in temporal networks were identified as one important mechanism that alters causality and affects dynamical processes. So far, an analytical explanation for this phenomenon and for the significant variations observed across different systems is missing. Here we introduce a methodology that allows to analytically predict causality-driven changes of diffusion speed in non-Markovian temporal networks. Validating our predictions in six data sets we show that compared with the time-aggregated network, non-Markovian characteristics can lead to both a slow-down or speed-up of diffusion, which can even outweigh the decelerating effect of community structures in the static topology. Thus, non-Markovian properties of temporal networks constitute an important additional dimension of complexity in time-varying complex systems.

We present a generalized method for calculating the k-shell structure of weighted networks. The method takes into account both the weight and the degree of a network, in such a way that in the absence of weights we resume the shell structure obtained by the classic k-shell decomposition. In the presence of weights, we show that the method is able to partition the network in a more refined way, without the need of any arbitrary threshold on the weight values. Furthermore, by simulating spreading processes using the susceptibleinfectious-recovered model in four different weighted real-world networks, we show that the weighted k-shell decomposition method ranks the nodes more accurately, by placing nodes with higher spreading potential into shells closer to the core. In addition, we demonstrate our new method on a real economic network and show that the core calculated using the weighted k-shell method is more meaningful from an economic perspective when compared with the unweighted one.

We model the spreading of a crisis by constructing a global economic network and applying the Susceptible-Infected-Recovered (SIR) epidemic model with a variable probability of infection. The probability of infection depends on the strength of economic relations between the pair of countries, and the strength of the target country.It is expected that a crisis which originates in a large country, such as the USA, has the potential to spread globally, like the recent crisis. Surprisingly we show that also countries with much lower GDP, such as Belgium, are able to initiate a global crisis. Using the k-shell decomposition method to quantify the spreading power (of a node), we obtain a measure of "centrality" as a spreader of each country in the economic network. We thus rank the different countries according to the shell they belong to, and find the 12 most central countries. These countries are the most likely to spread a crisis globally. Of these 12 only six are large economies, while the other six are medium/small ones, a result that could not have been otherwise anticipated.Furthermore, we use our model to predict the crisis spreading potential of countries belonging to different shells according to the crisis magnitude.

We study correlations in temporal networks and introduce the notion of betweenness preference. It allows to quantify to what extent paths, existing in time-aggregated representations of temporal networks, are actually realizable based on the sequence of interactions. We show that betweenness preference is present in empirical temporal network data and that it influences the length of shortest time-respecting paths. Using four different data sets, we further argue that neglecting betweenness preference leads to wrong conclusions about dynamical processes on temporal networks.Recent works have argued that properties of dynamical processes evolving on complex networks change profoundly when the dynamics of the network topology is taken into account. For a number of empirical temporal networks obtained from time-stamped contact data, simulations have shown that their topological dynamics can both slow down [5,1,6] or speed up spreading processes [17]. At the same time, it has been observed that, compared to time-aggregated topologies, the exploration dynamics of random walks in temporal networks is significantly slower [18]. Furthermore, it has been shown that network dynamics alone can give rise to collective phenomena like synchronization [19]. These observations have generated significant interest in the mechanism underlying these phenomena. A series of recent works focused on the influence of inter-event time distributions and temporal correlations in the time series of interactions [4,6,18,15,9]. Bursty activity patterns of nodes have been identified as one possible source that slows down spreading [6] and random walk processes [16]. Similarly, bursty node activities have been suggested to slow down information diffusion, particularly when the diffusion process is initiated in phases of low activity [13]. Furthermore, for a number of social contact networks, it has been shown that heterogeneous inter-event times increase the length of time-respecting paths [12]. Apart from inter-event time distributions, it has been argued that link appearance frequencies and their correlation with community structures are another characteristic of temporal networks that can slow down spreading dynamics [6]. Another line of research is concerned with the study of temporal motifs [8,20], i.e. whether there are classes of frequently occurring temporal contact patterns. It was shown that the presence of certain temporal motifs (like e.g. "chains" of consec-

We address the question to what extent the success of scientific articles is due to social influence. Analyzing a data set of over 100,000 publications from the field of Computer Science, we study how centrality in the coauthorship network differs between authors who have highly cited papers and those who do not. We further show that a Machine Learning classifier, based only on coauthorship network centrality metrics measured at the time of publication, is able to predict with high precision whether an article will be highly cited five years after publication. By this we provide quantitative insight into the social dimension of scientific publishingchallenging the perception of citations as an objective, socially unbiased measure of scientific success.