\section{Related Work}

Within the area of Network Science, the problem of ranking nodes in a network is of 
fundamental importance due to its various applications in different contexts~\cite{DBLP:journals/sigkdd/GetoorD05a}. The problem 
consists in establishing an ordering or identifying a small set of nodes according to 
some predominant characteristic, for example, ranking individuals according to their 
social status within a social network, or ranking scientists according to their influence 
in a collaboration network~\cite{pires2011,newman2004}.%looseness=-1

Due to the availability of large relational data and increasingly powerful computational
resources, new challenging aspects naturally emerge, potentially harming the accuracy of current ranking
strategies. One such a challenge, considered here, has to do with the dynamic behavior
of the interactions found in the network, usually observed when data span long periods. 
PageRank and centrality metrics such as degree, closeness and betweenness are some of well known metrics for establishing an ordering of nodes in any given
network. However, when facing temporal dynamics, such common network properties may
change as time goes and various works have considered the time dimension when 
representing the network~\cite{barabasi2002,huang2008,kudelka2011,leskovec08,sharan07}. In fact, 
considering the entire data without regarding the temporal dimension may indeed lead to 
misleading conclusions about some characteristics of the network. Recently, \citeN{mourao09} 
have proposed a methodology to quantitatively characterize time-varying relational data. 
They show that neglecting the temporal dimension do indeed negatively impact the accuracy of 
prediction strategies.

This article focuses on a time-aware ranking method for sport social networks, which may also be applied 
to other networks that are subject to temporal factors, such as, for instance, collaboration networks. 
The idea of having time varying weights on network edges to capture the fact that intensity of 
relationships can increase and decrease over time has appeared in the literature~\cite{kudelka2011,sharan07}. 
However, these approaches have been applied to characterizing different types of social tie~\cite{kudelka2011} 
or addressing the problem of topic classification~\cite{sharan07}. 

\citeN{trank2004}, have proposed a method, T-Rank, that extends PageRank to improve node ranking by considering the activity and freshness of nodes to compute their importance, given a temporal window of interest. The quality of the method was assessed by comparing rankings produced by T-Rank with those produced by PageRank.

We focus explicitly on the \textit{network ranking problem} and propose an edge weight function specific for this purpose. Our proposed method does not restrict the importance of events to a given temporal interval of interest, but instead explicitly changes the importance of events according to time. We also focus on sport social networks and, unlike previous work, validate our method by quantitatively comparing its produced rankings to credible gold standards. Moreover,  there are significant conceptual differences between our approach and those discussed above, particularly T-Rank. They work on the algorithmic level and their solutions are hard-coded in the algorithm. We, otherwise, work on the data engineering level, modifying certain aspects of the data representation, which means that we are potentially much more flexible and adaptable to different domains and applications, by modifying for instance, the edge weight function.

%We focus explicitly on the \textit{network ranking problem} in face of temporal factors 
%and propose an edge weight function specific for this purpose. We also focus on sport social networks and validate our method using real datasets and comparing against very recent baseline rankings.
