\section{Conclusions}\label{conclusao}
We have extended a recently proposed method~\cite{radicchi_who_2011} that exploits complex network metrics to produce ranks in sport social networks. Our extensions cover issues related to the temporal aspects inherent to sports events, mainly when the goal is to generate rankings for specific points in time (e.g., current rankings). Our strategy applies a time-aware function to the weights of the edges of the network to capture the notion that the results of older confronts are not so important as newer ones to predict a more recent ranking (or rankings in a specific point in time). 

We applied our proposed time-aware ranking method to networks built based on results of confronts in two different sports, Mixed Martial Arts (MMA) and tennis. We compared the results produced by our method and the baseline's against a gold standard obtained from credible rankings and verified that ours outperformed the baseline in all situations, sometimes by very large margins. Moreover, for MMA the results obtained for the parameterization of the methods show that the best values are stable in a small range of values (between 0.20 and 0.30) and that the ranks we produced are very satisfactory, being very similar in some cases to the corresponding gold standard. For tennis, the produced rankings are also very close to the ATP ones, leading us to conclude that, as raised by~\citeN{radicchi_who_2011}, we need only to take into account a recent sequence of match results for establishing a ranking of players, without considering the actual tournaments and a complex punctuation system.

In this work, we chose to address a specific type of social network focused on sports. However, we argue that  our solutions can be applied to other contexts. The solution is based on the notion of temporal events between nodes that are characterized by some type of advantage of one node over the other. The events can be any type of dispute or conflict of interest between pairs of nodes that, when resolved, gives advantage to one of the nodes. Judicial disputes, for instance, could be one such an example in which nodes would represent the lawyers involved. Others could be easily thought. Moreover, the approach could also be easily adapted to win-win situations such as collaborations in which the weights are proportional to the level of collaboration but that may decay over time. Scientific social networks are an example of this type of network and the rank methods could be used, for instance, for recommending new collaborations.


As future work, besides applying our solutions to other contexts, as we just discussed, we intend to  experiment with alternative time-aware edge weighting functions, investigate better ways to determine the $\alpha$ parameter and perform a more thorough comparison of our method with others under several criteria.

%\section{Acknowledgements}\label{acknowledgements}
%This work was partially funded by InWeb - The Brazilian National Institute of Science and Technology
%for the Web (grant MCT/CNPq 573871/2008-6), and by the authors' individual grants from CNPq and FAPEMIG. The authors would also like to thank Filippo Radicchi for his assistance in their experiments.

%\section{Acknowledgments}\label{acknowledgements}
%This work was partially supported by InWeb - The Brazilian National Institute of Science and Technology for the Web, and by the authors' individual grants from CNPq and FAPEMIG.
