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Soccer attracts the attention of many researchers and professionals in the sports industry. Therefore, the incorporation of science into the sport is constantly growing, with increasing investments in performance analysis and sports prediction industries. This study aims to (i) highlight the use of complex networks as an alternative tool for predicting soccer match outcomes, and (ii) show how the combination of structural analysis of passing networks with match statistical data can provide deeper insights into the game patterns and strategies used by teams. In order to do so, complex network metrics and match statistics were used to build machine learning models that predict the wins and losses of soccer teams in different leagues. The results showed that models based on passing networks were as effective as ``traditional'' models, which use general match statistics. Another finding was that by combining both approaches, more accurate models were obtained than when they were used separately, demonstrating that the fusion of such approaches can offer a deeper understanding of game patterns, allowing the comprehension of tactics employed by teams relationships between players, their positions, and interactions during matches. It is worth mentioning that both network metrics and match statistics were important and impactful for the mixed model. Furthermore, the use of networks with a lower granularity of temporal evolution (such as creating a network for each half of the match) performed better than a single network for the entire game., Comment: To appear in Journal of Complex Networks

To contain the propagation of emerging diseases that are transmissible from human to human, non-pharmaceutical interventions (NPIs) aimed at reducing the interactions between humans are usually implemented. One example of the latter kind of measures is social distancing, which can be either policy-driven or can arise endogenously in the population as a consequence of the fear of infection. However, if NPIs are lifted before the population reaches herd immunity, further re-introductions of the pathogen would lead to secondary infections. Here we study the effects of different social distancing schemes on the large scale spreading of diseases. Specifically, we generalize metapopulation models to include social distancing mechanisms at the subpopulation level and model short- and long-term strategies that are fed with local or global information about the epidemics. We show that different model ingredients might lead to very diverse outcomes in different subpopulations. Our results suggest that there is not a unique answer to the question of whether contention measures are more efficient if implemented and managed locally or globally and that model outcomes depends on how the full complexity of human interactions is taken into account., Comment: 14 pages, 11 figures

The purpose of this paper is to calculate the risk-dependent centrality (RDC) of the Brazilian stock market. We computed the RDC for assets traded on the Brazilian stock market between January 2008 to June 2020 at different levels of external risk. We observed that the ranking of assets based on the RDC depends on the external risk. Rankings' volatility is related to crisis events, capturing the recent Brazilian economic-political crisis. Moreover, we have found a negative correlation between the average volatility of assets' ranking based on the RDC and the average daily returns on the stock market. It goes in hand with the hypothesis that the rankings' volatility is higher in periods of crisis., Comment: 12 pages, 7 figures, 2 tables

As synchronized activity is associated with basic brain functions and pathological states, spike train synchrony has become an important measure to analyze experimental neuronal data. Many different measures of spike train synchrony have been proposed, but there is no gold standard allowing for comparison of results between different experiments. This work aims to provide guidance on which synchrony measure is best suitable to quantify the effect of epileptiform inducing substances (e.g. bicuculline (BIC)) in in vitro neuronal spike train data. Spike train data from recordings are likely to suffer from erroneous spike detection, such as missed spikes (false negative) or noise (false positive). Therefore, different time-scale dependent (cross-correlation, mutual information, spike time tiling coefficient) and time-scale independent (Spike-contrast, phase synchronization, A-SPIKE-synchronization, A-ISI-distance, ARI-SPIKE-distance) synchrony measures were compared in terms of their robustness to erroneous spike trains. As a result of the in silico manipulated data, Spike-contrast was the only measure being robust to false negative as well as false-positive spikes. Analyzing the experimental data set revealed that all measures were able to capture the effect of BIC in a statistically significant way, with Spike-contrast showing the highest statistical significance even at low spike detection thresholds. In summary, we suggest the usage of Spike-contrast to complement established synchrony measures, as it is time scale independent and robust to erroneous spike trains.

Centrality is a key property of complex networks that influences the behavior of dynamical processes, like synchronization and epidemic spreading, and can bring important information about the organization of complex systems, like our brain and society. There are many metrics to quantify the node centrality in networks. Here, we review the main centrality measures and discuss their main features and limitations. The influence of network centrality on epidemic spreading and synchronization is also pointed out in this chapter. Moreover, we present the application of centrality measures to understand the function of complex systems, including biological and cortical networks. Finally, we discuss some perspectives and challenges to generalize centrality measures for multilayer and temporal networks., Comment: Book Chapter in "From nonlinear dynamics to complex systems: A Mathematical modeling approach" by Springer

The identification of the minimal set of nodes that maximizes the propagation of information is one of the most relevant problems in network science. In this paper, we introduce a new method to find the set of initial spreaders to maximize the information propagation in complex networks. We evaluate this method in assortative networks and verify that degree-degree correlation plays a fundamental role in the spreading dynamics. Simulation results show that our algorithm is statistically similar, regarding the average size of outbreaks, to the greedy approach in real-world networks. However, our method is much less time consuming than the greedy algorithm.

Image segmentation has many applications which range from machine learning to medical diagnosis. In this paper, we propose a framework for the segmentation of images based on super-pixels and algorithms for community identification in graphs. The super-pixel pre-segmentation step reduces the number of nodes in the graph, rendering the method the ability to process large images. Moreover, community detection algorithms provide more accurate segmentation than traditional approaches, such as those based on spectral graph partition. We also compare our method with two algorithms: a) the graph-based approach by Felzenszwalb and Huttenlocher and b) the contour-based method by Arbelaez. Results have shown that our method provides more precise segmentation and is faster than both of them., Comment: 20 pages, 12 figures

The identification of the most influential spreaders in networks is important to control and understand the spreading capabilities of the system as well as to ensure an efficient information diffusion such as in rumor-like dynamics. Recent works have suggested that the identification of influential spreaders is not independent of the dynamics being studied. For instance, the key disease spreaders might not necessarily be so when it comes to analyze social contagion or rumor propagation. Additionally, it has been shown that different metrics (degree, coreness, etc) might identify different influential nodes even for the same dynamical processes with diverse degree of accuracy. In this paper, we investigate how nine centrality measures correlate with the disease and rumor spreading capabilities of the nodes that made up different synthetic and real-world (both spatial and non-spatial) networks. We also propose a generalization of the random walk accessibility as a new centrality measure and derive analytical expressions for the latter measure for simple network configurations. Our results show that for non-spatial networks, the $k$-core and degree centralities are most correlated to epidemic spreading, whereas the average neighborhood degree, the closeness centrality and accessibility are most related to rumor dynamics. On the contrary, for spatial networks, the accessibility measure outperforms the rest of centrality metrics in almost all cases regardless of the kind of dynamics considered. Therefore, an important consequence of our analysis is that previous studies performed in synthetic random networks cannot be generalized to the case of spatial networks., Comment: 17 pages, 11 figures, 3 tables

In this paper we study synchronization of random clustered networks consisting of Kuramoto oscillators. More specifically, by developing a mean-field analysis, we find that the presence of cycles of order three does not play an important role on network synchronization, showing that the synchronization of random clustered networks can be described by tree-based theories, even for high values of clustering. In order to support our findings, we provide numerical simulations considering clustered and non-clustered networks, which are in good agreement with our theoretical results., Comment: 5 pages, 4 figures

Explosive synchronization can be observed in scale-free networks when Kuramoto oscillators have natural frequencies equal to their number of connections. In the current work, we took into account mean-field approximations to determine the critical coupling of such explosive synchronization. The obtained equation for the critical coupling has an inverse dependence with the network average degree. This expression differs from that calculated when the frequency distributions are unimodal and even. In this case, the critical coupling depends on the ratio between the first and second statistical moments of the degree distribution. We also conducted numerical simulations to verify our analytical results., Comment: 5 pages, 5 figures

There is an overall perception of increased interdisciplinarity in science, but this is difficult to confirm quantitatively owing to the lack of adequate methods to evaluate subjective phenomena. This is no different from the difficulties in establishing quantitative relationships in human and social sciences. In this paper we quantified the interdisciplinarity of scientific journals and science fields by using an entropy measurement based on the diversity of the subject categories of journals citing a specific journal. The methodology consisted in building citation networks using the Journal Citation Reports database, in which the nodes were journals and edges were established based on citations among journals. The overall network for the 11-year period (1999-2009) studied was small-world and scale free with regard to the in-strength. Upon visualizing the network topology an overall structure of the various science fields could be inferred, especially their interconnections. We confirmed quantitatively that science fields are becoming increasingly interdisciplinary, with the degree of interdisplinarity (i.e. entropy) correlating strongly with the in-strength of journals and with the impact factor., Comment: 23 pages, 6 figures

We study the emergence of synchronization in scale-free networks by considering the Kuramoto model of coupled phase oscillators. The natural frequencies of oscillators are assumed to be correlated with their degrees and a time delay is included in the system. This assumption allows enhancing the explosive transition to reach the synchronous state. We provide an analytical treatment developed in a star graph which reproduces results obtained in scale-free networks. Our findings have important implications in understanding the synchronization of complex networks, since the time delay is present in most systems due to the finite speed of the signal transmission over a distance., Comment: 5 pages, 7 figures

Financial market is an example of complex system, which is characterized by a highly intricate organization and the emergence of collective behavior. In this paper, we quantify this emergent dynamics in the financial market by using concepts of network synchronization. We consider networks constructed by the correlation matrix of asset returns and study the time evolution of the phase coherence among stock prices. It is verified that during financial crisis a synchronous state emerges in the system, defining the market's direction. Furthermore, the paper proposes a statistical regression model able to identify the topological features that mostly influence such an emergence. The coefficients of the proposed model indicate that the average shortest path length is the measurement most related to network synchronization. Therefore, during economic crisis, the stock prices present a similar evolution, which tends to shorten the distances between stocks, indication a collective dynamics., Comment: 5 pages, 2 figures

A new complex network model is proposed which is founded on growth with new connections being established proportionally to the current dynamical activity of each node, which can be understood as a generalization of the Barabasi-Albert static model. By using several topological measurements, as well as optimal multivariate methods (canonical analysis and maximum likelihood decision), we show that this new model provides, among several other theoretical types of networks including Watts-Strogatz small-world networks, the greatest compatibility with three real-world cortical networks., Comment: A working manuscript, 5 pages, 3 figures, 1 table

This letter addresses the problem of modeling the highway systems of different countries by using complex networks formalism. More specifically, we compare two traditional geographical models with a modified geometrical network model where paths, rather than edges, are incorporated at each step between the origin and destination nodes. Optimal configurations of parameters are obtained for each model and used in the comparison. The highway networks of Brazil, the US and England are considered and shown to be properly modeled by the modified geographical model. The Brazilian highway network yielded small deviations that are potentially accountable by specific developing and sociogeographic features of that country., Comment: 5 pages, 3 figures, 1 table

This work addresses the intrinsic relationship between trees and networks (i.e. graphs). A complete (invertible) mapping is presented which allows trees to be mapped into weighted graphs and then backmapped into the original tree without loss of information. The extension of this methodology to more general networks, including unweighted structures, is also discussed and illustrated. It is shown that the identified duality between trees and graphs underlies several key concepts and issues of current interest in complex networks, including comprehensive characterization of trees and community detection. For instance, additional information about tree structures (e.g. phylogenetic trees) can be immediately obtained by taking into account several off-the-shelf network measurements -- such as the clustering coefficient, degree correlations and betweenness centrality. At the same time, the hierarchical structure of networks, including the respective communities, becomes clear when the network is represented in terms of the respective tree. Indeed, the network-tree mapping described in this work provides a simple and yet effective means of community detection., Comment: 4 pages, 4 figures. A working mansucript

This article focuses on the identification of the number of paths with different lengths between pairs of nodes in complex networks and how, by providing comprehensive information about the network topology, such an information can be effectively used for characterization of theoretical and real-world complex networks, as well as for identification of communities., Comment: 9 pages, 7 Figures, 1 Table. A working manuscript: comments and suggestions highly appreciated

Even more interesting than the intricate organization of complex networks are the dynamical behavior of systems which such structures underly. Among the many types of dynamics, one particularly interesting category involves the evolution of trails left by moving agents progressing through random walks and dilating processes in a complex network. The emergence of trails is present in many dynamical process, such as pedestrian traffic, information flow and metabolic pathways. Important problems related with trails include the reconstruction of the trail and the identification of its source, when complete knowledge of the trail is missing. In addition, the following of trails in multi-agent systems represent a particularly interesting situation related to pedestrian dynamics and swarming intelligence. The present work addresses these three issues while taking into account permanent and transient marks left in the visited nodes. Different topologies are considered for trail reconstruction and trail source identification, including four complex networks models and four real networks, namely the Internet, the US airlines network, an email network and the scientific collaboration network of complex network researchers. Our results show that the topology of the network influence in trail reconstruction, source identification and agent dynamics., Comment: 10 pages, 16 figures. A working manuscript, comments and criticisms welcomed

Protein-protein interactions can be properly modeled as scale-free complex networks, while the lethality of proteins has been correlated with the node degrees, therefore defining a lethality-centrality rule. In this work we revisit this relevant problem by focusing attention not on proteins as a whole, but on their functional domains, which are ultimately responsible for their binding potential. Four networks are considered: the original protein-protein interaction network, its randomized version, and two domain networks assuming different lethality hypotheses. By using formal statistical analysis, we show that the correlation between connectivity and essentiality is higher for domains than for proteins., Comment: 3 pages, 3 figures. Accepted for publication in Applied Physics Letters