Os motores de busca utilizam o WebGraph formado pelas páginas e seus links para atribuir reputação às páginas Web. Essa reputação é utilizada para montar o ranking de resultados retornados ao usuário. No entanto, novas versões de páginas com uma boa reputação acabam por distribuir os votos de reputação entre todas as versões, trazendo prejuízo à página original e também as suas versões. O objetivo deste trabalho é especificar novos escores que considerem todas as versões de uma página Web para atribuir reputação para as mesmas. Para atingir esse objetivo, foram propostos quatro escores que utilizam a detecção de versões para atribuir uma reputação mais homogênea às páginas que são versões de um mesmo documento. Os quatro escores propostos podem ser classificados em duas categorias: os que realizam mudanças estruturais no WebGraph (VersionRank e VersionPageRank) e os que realizam operações aritméticas sobre os escores obtidos pelo algoritmo de PageRank (VersionSumRank e VersionAverageRank). Os experimentos demonstram que o VersionRank tem desempenho 26,55% superior ao PageRank para consultas navegacionais sobre a WBR03 em termos de MRR, e em termos de P@10, o VersionRank tem um ganho de 9,84% para consultas informacionais da WBR99. Já o escore VersionAverageRank, apresentou melhores resultados na métrica P@10 para consultas informacionais na WBR99 e WBR03. Na WBR99, os ganhos foram de 6,74% sobre o PageRank. Na WBR03, para consultas informacionais aleatórias o escore VersionAverageRank obteve um ganho de 35,29% em relação ao PageRank. / Search engines use WebGraph formed by the pages and their links to assign reputation to Web pages. This reputation is used for ranking show for the user. However, new versions of pages with a good reputation distribute your votes of reputation among all versions, damaging the reputation of original page and also their versions. The objective of this work is to specify the new scores to consider all versions of a Web page to assign reputation to them. To achieve this goal, four scores were proposed using the version detection to assign a more homogeneous reputation to the pages that are versions of the same document. The four scores proposed can be classified into two categories: those who perform structural changes in WebGraph (VersionRank and VersionPageRank) and those who performs arithmetic operations on the scores obtained by the PageRank algorithm (VersionSumRank and VersionAverageRank). The experiments show that the performance VersionRank is 26.55% higher than the PageRank for navigational queries on WBR03 in terms of MRR, and in terms of P@10, the VersionRank has a gain of 9.84% for the WBR99 informational queries. The score VersionAverageRank showed better results in the metric P@10 for WBR99 and WBR03 information queries. In WBR99, it had a gain of 6.74% compared to PageRank. In WBR03 for random informational queries, VersionAverageRank showed an increase of 35.29% compared to PageRank.

Denna rapport är resultatet av ett tio veckors långt examensarbete med fokus på området sökmotoroptimering. Arbetet utgörs av en kombination av litteraturstudier och praktisk tillämpning. Syftet var att undersöka om det är möjligt att påverka en webbsidas ranking på Google positivt med enbart on page-metoder, det vill säga genom förändringar på den aktuella webbplatsen. Det praktiska arbetet har utförts på Rabble Communications AB, där fem av deras webbsidor utgör undersökningsobjekt. De teorier och riktlinjer som samlats in under litteraturstudien har applicerats på dessa sidor för att verifiera dess effektivitet samt för att se om det går att se resultat snabbare än vad tidigare forskning säger. Resultaten pekar på att det går att nå högre placeringar på Google genom enbart on page-metoder, dessutom inom tidsramen för detta examensarbete.

The thesis describes a search engine of Google company and its method of web pages evaluating, which is used for sorting them on the search engine result page. In addition to the description of how search engines work in general, the thesis targets on differencies between Google and other search engines, as well as it mentions characteristics and principles designed by its founders, Larry Page and Sergey Brin, which make it unique. In the second part there are outlined some of many signals which are rated for every single web page. The most concerned signal is PageRank as the leading idea of pages evaluating, based on their link scheme which is founded on principles of citation analysis. Factors for evaluating are analysed using particular examples, and the topic is ended by the description of Google search engines changes from its beginning in 1998 until present.

In a time when information and opinions are to a large extent shared via social media, it is important to find a way to determine how credible the content is. The purpose of this study is to investigate whether PageRank based algorithms can be used to deter- mine how credible a Twitter user is based on how much the user’s posts are retweeted by other users. Two different algorithms based on PageRank have rated the credibility of Twitter users in a network. This ranking has been compared with a manual credibil- ity check on the users to determine how close to reality the credibility distribution from the algorithms is. The results show that the algorithms can be said to preform better than random, but they still assign inaccurate credibility scores to many users. The simplicity of the algorithms is an advantage compared to other methods used in previous research. The conclusion is that the algorithms in their current states are not suitable for determin- ing the credibility of Twitter users. / I en tid då information och åsikter till stor del delas via sociala medier är det viktigt att finna ett sätt att avgöra hur trovärdig detta innehåll är. Syftet med denna studie är att utreda om det med hjälp av algoritmer baserade på PageRank-algoritmen går att avgö- ra hur trovärdig en Twitteranvändare är, baserat på hur mycket användarens inlägg bli- vit delade av andra användare. Två olika algoritmer baserade på PageRank har rankat trovärdigheten hos Twitteranvändare i ett nätverk. Denna rankning har sedan jämförts med en manuell trovärighetstilldelning av användarna för att avgöra hur nära verklighe- ten algoritmernas trovärdighetsfördelning är. Resultaten visar att algoritmerna kan anses prestera bättre än slumpen, men att de trots detta tilldelar en fleaktig trovärdighet till många användare i nätverket. Algoritmernas triviala natur ger dem en fördel gentemot algoritmer som använts i tidigare studier. Slutsatsen är att algoritmerna i deras nuvaran- de form inte är lämpade för att fastställa trovärdighet hos Twitteranvändare.

Uppsatsen behandlar sökmotoroptimering gällande Google. En litteraturstudiegörs för att besvara vilka metoder som är de mest effektiva för ett så braträffresultat som möjligt samt vilka metoder som Google inte anser följer derasriktlinjer. En empirisk studie görs även genom att skicka ut ett antal frågor omsökmotoroptimering till SEO-konsulter i Sverige. Ett antal ”on-page”-metoder och”off-page”-metoder redovisas samt även ett antal tveksamma metoder. Vilkametoder som är mest effektiva gällande sökmotoroptimering skiljer sig en del vaddet gäller litteratur från några år tillbaka och vad SEO-konsulterna idag anser.Resultaten från litteraturstudien visar att nyckelord är den viktigaste metodenmedan SEO-konsulterna menar att länkbygge är det man ska prioritera. Vilkametoder som är mest effektiva förändras och kommer att förändras eftersomwebben växer och fler webbsidor skapas vilket resulterar i en högre konkurrens. / The essay treats search engine optimization for Google. A literature study is doneto answer which methods are the most efficient to achieve as good result aspossible and which methods Google does not consider follow their guidelines. Anempirical study is also performed by sending out several questions about searchengine optimization to consultants in SEO in Sweden. Several “on-page”-methodsand “off-page”-methods are presented and also a few methods which are againstthe guidelines of Google. The methods which are the most efficient when it comesto search engine optimization are different if you compare the literature from acouple of years ago and what the consultants in SEO use today. The results fromthe literature study indicate that keywords is the most important method whilethe consultants in SEO say that links should be prioritised. The methods whichare the most efficient change and will be continued to change since the web isgrowing and more web pages are created which results in a higher degree ofcompetition.

The purpose of this activity is to investigate how the PageRank algorithm behaves in relation to the damping factor when applied to small graphs and certain special graph types. The PageRank algorithm involves the calculation of eigenvalues and eigenvectors of the Google matrix for both directed and undirected graphs. This discussion will focus on all directed graphs with up to four vertices and select special graphs. Our primary objective is to observe how the damping factor influences the dominant eigenvector for each graph and, consequently, how it impacts PageRank. We have calculated PageRank for all the graphs and conducted an analysis, particularly focusing on the effect of the damping factor, denoted as "c," in our discussions. To compute the PageRank algorithm, we constructed a probability matrix for all the graphs and performed the calculations using MATLAB. This process yielded eigenvalues and eigenvectors associated with the Google matrix. The theoretical section of this thesis encompasses the PageRank theory, including essential proofs, theorems, and definitions that serve as foundational elements throughout the thesis. Additionally, we delve into the historical context and practical applications of PageRank. In our study, we present a comparative analysis of the results, specifically examining the impact of a damping factor on the dominant PageRank eigenvector.

Opsomming Daar bestaan 'n behoefte aan 'n objektiewe maatstaf om die gehalte van akademiese publikasies te bepaal en te vergelyk. Hierdie navorsing het die invloed of reaksie wat deur 'n publikasie gegenereer is uit verwysingsdata bepaal. Daar is van 'n iteratiewe algoritme gebruik gemaak wat gewigte aan verwysings toeken. In die Internetomgewing word hierdie benadering reeds met groot sukses toegepas deur onder andere die PageRank-algoritme van die Google soekenjin. Hierdie en ander algoritmes in die Internetomgewing is bestudeer om 'n algoritme vir akademiese artikels te ontwerp. Daar is op 'n variasie van die PageRank-algoritme besluit wat 'n Invloedwaarde bepaal. Die algoritme is op gevallestudies getoets. Die empiriese studie dui daarop dat hierdie variasie spesialisnavorsers se intu¨ıtiewe gevoel beter weergee as net die blote tel van verwysings. Abstract Ranking of journals are often used as an indicator of quality, and is extensively used as a mechanism for determining promotion and funding. This research studied ways of extracting the impact, or influence, of a journal from citation data, using an iterative process that allocates a weight to the source of a citation. After evaluating and discussing the characteristics that influence quality and importance of research with specialist researchers, a measure called the Influence factor was introduced, emulating the PageRankalgorithm used by Google to rank web pages. The Influence factor can be seen as a measure of the reaction that was generated by a publication, based on the number of scientists who read and cited itA good correlation between the rankings produced by the Influence factor and that given by specialist researchers were found. / Mathematical Sciences / M.Sc. (Operasionele Navorsing)

Cette thèse s’intéresse à l’analyse du réseau dirigé extrait de la structure des hyperliens de Wikipédia. Notre objectif est de mesurer les interactions liant un sous-ensemble de pages du réseau Wikipédia. Par conséquent, nous proposons de tirer parti d’une nouvelle représentation matricielle appelée matrice réduite de Google ou "reduced Google Matrix". Cette matrice réduite de Google (GR) est définie pour un sous-ensemble de pages donné (c-à-d un réseau réduit).Comme pour la matrice de Google standard, un composant de GR capture la probabilité que deux noeuds du réseau réduit soient directement connectés dans le réseau complet. Une des particularités de GR est l’existence d’un autre composant qui explique la probabilité d’avoir deux noeuds indirectement connectés à travers tous les chemins possibles du réseau entier. Dans cette thèse, les résultats de notre étude de cas nous montrent que GR offre une représentation fiable des liens directs et indirects (cachés). Nous montrons que l’analyse de GR est complémentaire à l’analyse de "PageRank" et peut être exploitée pour étudier l’influence d’une variation de lien sur le reste de la structure du réseau. Les études de cas sont basées sur des réseaux Wikipédia provenant de différentes éditions linguistiques. Les interactions entre plusieurs groupes d’intérêt ont été étudiées en détail : peintres, pays et groupes terroristes. Pour chaque étude, un réseau réduit a été construit. Les interactions directes et indirectes ont été analysées et confrontées à des faits historiques, géopolitiques ou scientifiques. Une analyse de sensibilité est réalisée afin de comprendre l’influence des liens dans chaque groupe sur d’autres noeuds (ex : les pays dans notre cas). Notre analyse montre qu’il est possible d’extraire des interactions précieuses entre les peintres, les pays et les groupes terroristes. On retrouve par exemple, dans le réseau de peintre sissu de GR, un regroupement des artistes par grand mouvement de l’histoire de la peinture. Les interactions bien connues entre les grands pays de l’UE ou dans le monde entier sont également soulignées/mentionnées dans nos résultats. De même, le réseau de groupes terroristes présente des liens pertinents en ligne avec leur idéologie ou leurs relations historiques ou géopolitiques.Nous concluons cette étude en montrant que l’analyse réduite de la matrice de Google est une nouvelle méthode d’analyse puissante pour les grands réseaux dirigés. Nous affirmons que cette approche pourra aussi bien s’appliquer à des données représentées sous la forme de graphes dynamiques. Cette approche offre de nouvelles possibilités permettant une analyse efficace des interactions d’un groupe de noeuds enfoui dans un grand réseau dirigé / This thesis concentrates on the analysis of the large directed network representation of Wikipedia.Wikipedia stores valuable fine-grained dependencies among articles by linking webpages togetherfor diverse types of interactions. Our focus is to capture fine-grained and realistic interactionsbetween a subset of webpages in this Wikipedia network. Therefore, we propose to leverage anovel Google matrix representation of the network called the reduced Google matrix. This reducedGoogle matrix (GR) is derived for the subset of webpages of interest (i.e. the reduced network). Asfor the regular Google matrix, one component of GR captures the probability of two nodes of thereduced network to be directly connected in the full network. But unique to GR, anothercomponent accounts for the probability of having both nodes indirectly connected through allpossible paths in the full network. In this thesis, we demonstrate with several case studies that GRoffers a reliable and meaningful representation of direct and indirect (hidden) links of the reducednetwork. We show that GR analysis is complementary to the well-known PageRank analysis andcan be leveraged to study the influence of a link variation on the rest of the network structure.Case studies are based on Wikipedia networks originating from different language editions.Interactions between several groups of interest are studied in details: painters, countries andterrorist groups. For each study, a reduced network is built, direct and indirect interactions areanalyzed and confronted to historical, geopolitical or scientific facts. A sensitivity analysis isconducted to understand the influence of the ties in each group on other nodes (e.g. countries inour case). From our analysis, we show that it is possible to extract valuable interactions betweenpainters, countries or terrorist groups. Network of painters with GR capture art historical fact sucha painting movement classification. Well-known interactions of countries between major EUcountries or worldwide are underlined as well in our results. Similarly, networks of terrorist groupsshow relevant ties in line with their objective or their historical or geopolitical relationships. Weconclude this study by showing that the reduced Google matrix analysis is a novel powerfulanalysis method for large directed networks. We argue that this approach can find as well usefulapplication for different types of datasets constituted by the exchange of dynamic content. Thisapproach offers new possibilities to analyze effective interactions in a group of nodes embedded ina large directed network.

Opsomming Daar bestaan 'n behoefte aan 'n objektiewe maatstaf om die gehalte van akademiese publikasies te bepaal en te vergelyk. Hierdie navorsing het die invloed of reaksie wat deur 'n publikasie gegenereer is uit verwysingsdata bepaal. Daar is van 'n iteratiewe algoritme gebruik gemaak wat gewigte aan verwysings toeken. In die Internetomgewing word hierdie benadering reeds met groot sukses toegepas deur onder andere die PageRank-algoritme van die Google soekenjin. Hierdie en ander algoritmes in die Internetomgewing is bestudeer om 'n algoritme vir akademiese artikels te ontwerp. Daar is op 'n variasie van die PageRank-algoritme besluit wat 'n Invloedwaarde bepaal. Die algoritme is op gevallestudies getoets. Die empiriese studie dui daarop dat hierdie variasie spesialisnavorsers se intu¨ıtiewe gevoel beter weergee as net die blote tel van verwysings. Abstract Ranking of journals are often used as an indicator of quality, and is extensively used as a mechanism for determining promotion and funding. This research studied ways of extracting the impact, or influence, of a journal from citation data, using an iterative process that allocates a weight to the source of a citation. After evaluating and discussing the characteristics that influence quality and importance of research with specialist researchers, a measure called the Influence factor was introduced, emulating the PageRankalgorithm used by Google to rank web pages. The Influence factor can be seen as a measure of the reaction that was generated by a publication, based on the number of scientists who read and cited itA good correlation between the rankings produced by the Influence factor and that given by specialist researchers were found. / Mathematical Sciences / M.Sc. (Operasionele Navorsing)

Les graphes, ou réseaux, sont des structures mathématiques représentant des relations entre des éléments. Ces systèmes peuvent être analysés dans le but d’extraire des informations sur la structure globale ou sur des composants individuels. L'analyse de graphe conduit souvent à des problèmes hautement complexes à résoudre. À grande échelle, le coût de calcul de la solution exacte est prohibitif. Heureusement, il est possible d’utiliser des méthodes d’approximations itératives pour parvenir à des estimations précises. Lesméthodes historiques adaptées à un petit nombre de variables ne conviennent pas aux matrices creuses de grande taille provenant des graphes. Par conséquent, la conception de solveurs fiables, évolutifs, et efficaces demeure un problème essentiel. L’émergence d'architectures parallèles telles que le GPU ouvre également de nouvelles perspectives avec des progrès concernant à la fois la puissance de calcul et l'efficacité énergétique. Nos travaux ciblent la résolution de problèmes de valeurs propres de grande taille provenant des méthodes d’analyse de graphe dans le but d'utiliser efficacement les architectures parallèles. Nous présentons le domaine de l'analyse spectrale de grands réseaux puis proposons de nouveaux algorithmes et implémentations parallèles. Les résultats expérimentaux indiquent des améliorations conséquentes dans des applications réelles comme la détection de communautés et les indicateurs de popularité / Graphs, or networks, are mathematical structures to represent relations between elements. These systems can be analyzed to extract information upon the comprehensive structure or the nature of individual components. The analysis of networks often results in problems of high complexity. At large scale, the exact solution is prohibitively expensive to compute. Fortunately, this is an area where iterative approximation methods can be employed to find accurate estimations. Historical methods suitable for a small number of variables could not scale to large and sparse matrices arising in graph applications. Therefore, the design of scalable and efficient solvers remains an essential problem. Simultaneously, the emergence of parallel architecture such as GPU revealed remarkable ameliorations regarding performances and power efficiency. In this dissertation, we focus on solving large eigenvalue problems a rising in network analytics with the goal of efficiently utilizing parallel architectures. We revisit the spectral graph analysis theory and propose novel parallel algorithms and implementations. Experimental results indicate improvements on real and large applications in the context of ranking and clustering problems