While PageRank has been extensively used to rank sport tournament participants (teams or individuals), its superiority over simpler ranking methods has been never clearly demonstrated. We use sports results from 18 major leagues to calibrate a state-of-art model for synthetic sports results. Model data are then used to assess the ranking performance of PageRank in a controlled setting. We find that PageRank outperforms the benchmark ranking by the number of wins only when a small fraction of all games have been played. Increased randomness in the data, such as intrinsic randomness of outcomes or advantage of home teams, further reduces the range of PageRank's superiority. We propose a new PageRank variant which outperforms PageRank in all evaluated settings, yet shares its sensitivity to increased randomness in the data. Our main findings are confirmed by evaluating the ranking algorithms on real data. Our work demonstrates the danger of using novel metrics and algorithms without considering their limits of applicability.
PageRank is arguably the most popular ranking algorithm which is being applied in real systems ranging from information to biological and infrastructure networks. Despite its outstanding popularity and broad use in different areas of science, the relation between the algorithm's efficacy and properties of the network on which it acts has not yet been fully understood. We study here PageRank's performance on a network model supported by real data, and show that realistic temporal effects make PageRank fail in individuating the most valuable nodes for a broad range of model parameters. Results o…
This paper describes our solution for WSDM Cup 2016. Ranking the query independent importance of scholarly articles is a critical and challenging task, due to the heterogeneity and dynamism of entities involved. Our approach is called Ensemble enabled Weighted PageRank (EWPR). To do this, we first propose Time-Weighted PageRank that extends PageRank by introducing a time decaying factor. We then develop an ensemble method to assemble the authorities of the heterogeneous entities involved in scholarly articles. We finally propose to use external data sources to further improve the ranking accur…
We study the time evolution of ranking and spectral properties of the Google matrix of English Wikipedia hyperlink network during years 2003 - 2011. The statistical properties of ranking of Wikipedia articles via PageRank and CheiRank probabilities, as well as the matrix spectrum, are shown to be stabilized for 2007 - 2011. A special emphasis is done on ranking of Wikipedia personalities and universities. We show that PageRank selection is dominated by politicians while 2DRank, which combines PageRank and CheiRank, gives more accent on personalities of arts. The Wikipedia PageRank of universit…
Connections among entities are everywhere. From social media interactions to web page hyperlinks, networks are frequently used to represent such complex systems. Node ranking is a fundamental task that provides the strategy to identify central entities according to multiple criteria. Popular node ranking metrics include degree, closeness or betweenness centralities, as well as HITS authority or PageRank. In this work, we propose a novel node ranking metric, where we combine PageRank and the idea of node fatigue, in order to model a random explorer who wants to optimize coverage - it gets fatig…
In network science, there is often the need to sort the graph nodes. While the sorting strategy may be different, in general sorting is performed by exploiting the network structure. In particular, the metric PageRank has been used in the past decade in different ways to produce a ranking based on how many neighbors point to a specific node. PageRank is simple, easy to compute and effective in many applications, however it comes with a price: as PageRank is an application of the random walker, the arc weights need to be normalized. This normalization, while necessary, introduces a series of un…
Ranking on large-scale graphs plays a fundamental role in many high-impact application domains, ranging from information retrieval, recommender systems, sports team management, biology to neuroscience and many more. PageRank, together with many of its random walk based variants, has become one of the most well-known and widely used algorithms, due to its mathematical elegance and the superior performance across a variety of application domains. Important as it might be, state-of-the-art lacks an intuitive way to explain the ranking results by PageRank (or its variants), e.g., why it thinks the…
The basic indicators of a researcher's productivity and impact are still the number of publications and their citation counts. These metrics are clear, straightforward, and easy to obtain. When a ranking of scholars is needed, for instance in grant, award, or promotion procedures, their use is the fastest and cheapest way of prioritizing some scientists over others. However, due to their nature, there is a danger of oversimplifying scientific achievements. Therefore, many other indicators have been proposed including the usage of the PageRank algorithm known for the ranking of webpages and its…
In this work we introduce and study a nonlocal version of the PageRank. In our approach, the random walker explores the graph using longer excursions than just moving between neighboring nodes. As a result, the corresponding ranking of the nodes, which takes into account a \textit{long-range interaction} between them, does not exhibit concentration phenomena typical of spectral rankings which take into account just local interactions. We show that the predictive value of the rankings obtained using our proposals is considerably improved on different real world problems.
PageRank has been widely used to measure the authority or the influence of a user in social networks. However, conventional PageRank only makes use of edge-based relations, which represent first-order relations between two connected nodes. It ignores higher-order relations that may exist between nodes. In this paper, we propose a novel framework, motif-based PageRank (MPR), to incorporate higher-order relations into the conventional PageRank computation. Motifs are subgraphs consisting of a small number of nodes. We use motifs to capture higher-order relations between nodes in a network and in…
From the viewpoint of networks, a ranking system for players or teams in sports is equivalent to a centrality measure for sports networks, whereby a directed link represents the result of a single game. Previously proposed network-based ranking systems are derived from static networks, i.e., aggregation of the results of games over time. However, the score of a player (or team) fluctuates over time. Defeating a renowned player in the peak performance is intuitively more rewarding than defeating the same player in other periods. To account for this factor, we propose a dynamic variant of such a…
The Football World Cup as world's favorite sporting event is a source of both entertainment and overwhelming amount of data about the games played. In this paper we analyse the available data on football world championships since 1930 until today. Our goal is to rank the national teams based on all matches during the championships. For this purpose, we apply the PageRank with restarts algorithm to a graph built from the games played during the tournaments. Several statistics such as matches won and goals scored are combined in different metrics that assign weights to the links in the graph. Fi…
In the light of the need to achieve a ranking which is understood by all tennis supporters, the ATP ranking is exposed to constant complaints from players and at the same time exposes new players to be benefited with a good tournament to be able to start progressing in their careers. Moreover, the ATP ranking is not powerful enough to predict with certainty who will be the winner of a match if we are based solely on the positions. In order to combat these problems, the idea of creating a new ranking that can indicate what are the real chances of victory of a player before the start of a new to…
Methods for ranking the importance of nodes in a network have a rich history in machine learning and across domains that analyze structured data. Recent work has evaluated these methods though the seed set expansion problem: given a subset $S$ of nodes from a community of interest in an underlying graph, can we reliably identify the rest of the community? We start from the observation that the most widely used techniques for this problem, personalized PageRank and heat kernel methods, operate in the space of landing probabilities of a random walk rooted at the seed set, ranking nodes according…
The objective assessment of the prestige of an academic institution is a difficult and hotly debated task. In the last few years, different types of University Rankings have been proposed to quantify the excellence of different research institutions in the world. Albeit met with criticism in some cases, the relevance of university rankings is being increasingly acknowledged: indeed, rankings are having a major impact on the design of research policies, both at the institutional and governmental level. Yet, the debate on what rankings are {\em exactly} measuring is enduring. Here, we address th…
Many complex systems can be described as multiplex networks in which the same nodes can interact with one another in different layers, thus forming a set of interacting and co-evolving networks. Examples of such multiplex systems are social networks where people are involved in different types of relationships and interact through various forms of communication media. The ranking of nodes in multiplex networks is one of the most pressing and challenging tasks that research on complex networks is currently facing. When pairs of nodes can be connected through multiple links and in multiple layer…
Statistical Properties of Rankings in Sports and Games
Instituto de Física, Universidad Nacional Autónoma de México（墨西哥国立自治大学物理研究所）；Instituto de Investigaciones en Matemáticas Aplicadas y Sistemas, Universidad Nacional Autónoma de México（墨西哥国立自治大学应用数学与系统研究所）；Centro de Ciencias de la Complejidad, Universidad Nacional Autónoma de México（墨西哥国立自治大学复杂性科学中心）；Lakeside Labs GmbH（Lakeside Labs有限公司）
Higher-order networks are efficient representations of sequential data. Unlike the classic first-order network approach, they capture indirect dependencies between items composing the input sequences by the use of \textit{memory-nodes}. We focus in this study on the variable-order network model introduced in [Xu et al. (2016);Saebi et al. (2020)]. Authors suggested that random-walk-based mining tools can be directly applied to these networks. We discuss the case of the PageRank measure. We show the existence of a bias due to the distribution of the number of representations of the items. We pr…
Hiring a head coach of a college sports team is vital which will definitely have a great influence on the later development of the team. However, a lot of attention has been focused on each coach's individual features. A systematic and quantitative analysis of the whole coach hiring market is lacking. In a coach hiring network, the coaches are actually voting with their feet. It is interesting to analyze what factors are affecting the "footprint" left by those head coaches. In this paper, we collect more than 12,000 head coach hiring records in two different popular sports from the NCAA. Using…
We study the problem of score and rank monotonicity for spectral ranking methods, such as eigenvector centrality and PageRank, in the case of undirected networks. Score monotonicity means that adding an edge increases the score at both ends of the edge. Rank monotonicity means that adding an edge improves the relative position of both ends of the edge with respect to the remaining nodes. It is known that common spectral rankings are both score and rank monotone on directed, strongly connected graphs. We show that, surprisingly, the situation is very different for undirected graphs, and in part…
Identifying the importance of nodes of complex networks is of interest to the research of Social Networks, Biological Networks etc.. Current researchers have proposed several measures or algorithms, such as betweenness, PageRank and HITS etc., to identify the node importance. However, these measures are based on different aspects of properties of nodes, and often conflict with the others. A reasonable, fair standard is needed for evaluating and comparing these algorithms. This paper develops a framework as the standard for ranking the importance of nodes. Four intuitive rules are suggested to …
In this paper we show a new technique to analyze families of rankings. In particular we focus on sports rankings and, more precisely, on soccer leagues. We consider that two teams compete when they change their relative positions in consecutive rankings. This allows to define a graph by linking teams that compete. We show how to use some structural properties of this competitivity graph to measure to what extend the teams in a league compete. These structural properties are the mean degree, the mean strength and the clustering coefficient. We give a generalization of the Kendall's correlation …
This paper describes the first results obtained by implementing a novel approach to rank vertices in a heterogeneous graph, based on the PageRank family of algorithms and applied here to the bipartite graph of papers and authors as a first evaluation of its relevance on real data samples. With this approach to evaluate research activities, the ranking of a paper/author depends on that of the papers/authors citing it/him or her. We compare the results against existing ranking methods (including methods which simply apply PageRank to the graph of papers or the graph of authors) through the analy…
The massive presence of silent members in online communities, the so-called lurkers, has long attracted the attention of researchers in social science, cognitive psychology, and computer-human interaction. However, the study of lurking phenomena represents an unexplored opportunity of research in data mining, information retrieval and related fields. In this paper, we take a first step towards the formal specification and analysis of lurking in social networks. We address the new problem of lurker ranking and propose the first centrality methods specifically conceived for ranking lurkers in so…
Despite the increasing use of citation-based metrics for research evaluation purposes, we do not know yet which metrics best deliver on their promise to gauge the significance of a scientific paper or a patent. We assess 17 network-based metrics by their ability to identify milestone papers and patents in three large citation datasets. We find that traditional information-retrieval evaluation metrics are strongly affected by the interplay between the age distribution of the milestone items and age biases of the evaluated metrics. Outcomes of these metrics are therefore not representative of th…
