Ces dernières années, les réseaux sont devenus une source importante d’informations dans différents domaines aussi variés que les sciences sociales, la physique ou les mathématiques. De plus, la taille de ces réseaux n’a cessé de grandir de manière conséquente. Ce constat a vu émerger de nouveaux défis, comme le besoin de mesures précises et intuitives pour caractériser et analyser ces réseaux de grandes tailles en un temps raisonnable. La première partie de cette thèse introduit une nouvelle mesure de similarité entre deux noeuds d’un réseau dirigé et pondéré : la covariance “sum-over-paths”. Celle-ci a une interprétation claire et précise : en dénombrant tous les chemins possibles deux noeuds sont considérés comme fortement corrélés s’ils apparaissent souvent sur un même chemin – de préférence court. Cette mesure dépend d’une distribution de probabilités, définie sur l’ensemble infini dénombrable des chemins dans le graphe, obtenue en minimisant l'espérance du coût total entre toutes les paires de noeuds du graphe sachant que l'entropie relative totale injectée dans le réseau est fixée à priori. Le paramètre d’entropie permet de biaiser la distribution de probabilité sur un large spectre : allant de marches aléatoires naturelles où tous les chemins sont équiprobables à des marches biaisées en faveur des plus courts chemins. Cette mesure est alors appliquée à des problèmes de classification semi-supervisée sur des réseaux de taille moyennes et comparée à l’état de l’art. La seconde partie de la thèse introduit trois nouveaux algorithmes de classification de noeuds en sein d’un large réseau dont les noeuds sont partiellement étiquetés. Ces algorithmes ont un temps de calcul linéaire en le nombre de noeuds, de classes et d’itérations, et peuvent dés lors être appliqués sur de larges réseaux. Ceux-ci ont obtenus des résultats compétitifs en comparaison à l’état de l’art sur le large réseaux de citations de brevets américains et sur huit autres jeux de données. De plus, durant la thèse, nous avons collecté un nouveau jeu de données, déjà mentionné : le réseau de citations de brevets américains. Ce jeu de données est maintenant disponible pour la communauté pour la réalisation de tests comparatifs. La partie finale de cette thèse concerne la combinaison d’un graphe de citations avec les informations présentes sur ses noeuds. De manière empirique, nous avons montré que des données basées sur des citations fournissent de meilleurs résultats de classification que des données basées sur des contenus textuels. Toujours de manière empirique, nous avons également montré que combiner les différentes sources d’informations (contenu et citations) doit être considéré lors d’une tâche de classification de textes. Par exemple, lorsqu’il s’agit de catégoriser des articles de revues, s’aider d’un graphe de citations extrait au préalable peut améliorer considérablement les performances. Par contre, dans un autre contexte, quand il s’agit de directement classer les noeuds du réseau de citations, s’aider des informations présentes sur les noeuds n’améliora pas nécessairement les performances. La théorie, les algorithmes et les applications présentés dans cette thèse fournissent des perspectives intéressantes dans différents domaines. In recent years, networks have become a major data source in various fields ranging from social sciences to mathematical and physical sciences. Moreover, the size of available networks has grow substantially as well. This has brought with it a number of new challenges, like the need for precise and intuitive measures to characterize and analyze large scale networks in a reasonable time. The first part of this thesis introduces a novel measure between two nodes of a weighted directed graph: The sum-over-paths covariance. It has a clear and intuitive interpretation: two nodes are considered as highly correlated if they often co-occur on the same -- preferably short -- paths. This measure depends on a probability distribution over the (usually infinite) countable set of paths through the graph which is obtained by minimizing the total expected cost between all pairs of nodes while fixing the total relative entropy spread in the graph. The entropy parameter allows to bias the probability distribution over a wide spectrum: going from natural random walks (where all paths are equiprobable) to walks biased towards shortest-paths. This measure is then applied to semi-supervised classification problems on medium-size networks and compared to state-of-the-art techniques. The second part introduces three novel algorithms for within-network classification in large-scale networks, i.e., classification of nodes in partially labeled graphs. The algorithms have a linear computing time in the number of edges, classes and steps and hence can be applied to large scale networks. They obtained competitive results in comparison to state-of-the-art technics on the large scale U.S.~patents citation network and on eight other data sets. Furthermore, during the thesis, we collected a novel benchmark data set: the U.S.~patents citation network. This data set is now available to the community for benchmarks purposes. The final part of the thesis concerns the combination of a citation graph with information on its nodes. We show that citation-based data provide better results for classification than content-based data. We also show empirically that combining both sources of information (content-based and citation-based) should be considered when facing a text categorization problem. For instance, while classifying journal papers, considering to extract an external citation graph may considerably boost the performance. However, in another context, when we have to directly classify the network citation nodes, then the help of features on nodes will not improve the results. The theory, algorithms and applications presented in this thesis provide interesting perspectives in various fields.

An urban environment can be abstracted in form of a street network in order to be further analysed structurally. The urban street network can be represented in various ways by taking different principles and constraints into account. Therefore the aim of this work is to investigate human behaviour and communication in emerged urban phenomena, namely traffic flow and wayfinding, by structural characterization of an appropriate representation of an urban street network and modifying the conventional methods. / In order to characterize the depicted urban street network, centrality measure and specifically betweenness centrality is utilized. This analysis is then implemented to characterize the studied urban phenomena with respect to their structural, temporal and dynamic properties. In case of studying only the structural properties of the phenomena such as route description or self localization the conventional betweenness centrality is performed. But in case of studying the dynamic and temporal properties of a phenomenon such as traffic flow a modified version of betweenness centrality is proposed which considers dynamic and temporal aspects of human travel behaviour. / Experiments are designed to test the implementation of the suggested methods in the studied urban phenomena. The results of experiments demonstrate the efficiency of the proposed model in characterization of the studied urban phenomena in this thesis and then mention some of the problems and potential areas for future works.

In the last few years, large-scale experiments have generated genome-wide protein interaction networks for many organisms including Saccharomyces cerevisiae (baker's yeast), Caenorhabditis elegans (worm) and Drosophila melanogaster (fruit fly). In this thesis, we examine the vertex and edge betweenness centrality measures of these graphs. These measures capture how "central" a vertex or an edge is in the graph by considering the fraction of shortest paths that pass through that vertex or edge. Our primary observation is that the distribution of the vertex betweenness centrality follows a power law, but the distribution of the edge betweenness centrality has a Poisson-like distribution with a very sharp spike. To investigate this phenomenon, we generated random networks with degree distribution identical to those of the protein interaction networks. To our surprise, we found out that the random networks and the protein interaction networks had almost identical distribution of edge betweenness. We conjecture that the "Poisson-like" distribution of the edge betweenness centrality is the property of any graph whose degree distribution satisfies power law. / Master of Science

Esse trabalho consiste em um estudo sobre a aplicabilidade da medida de centralidade de intermediação (betweenness centrality) combinada com demandas de tráfego em redes viárias com o objetivo de identificar os principais pontos dessas redes. Como principais pontos refere-se aqui aos que aparecem com maior frequência entre os caminhos utilizados pelos motoristas que se deslocam pela rede viária. Trata-se de um estudo exploratório, que se inicia com a aplicação da centralidade de intermediação sobre redes simples, estendendo-se até simulações sobre redes baseadas em mapas reais. Nesse trabalho é analisado o comportamento da medida de centralidade sobre a topologia da rede - i.e. tanto sem considerar uma demanda, como considerando demandas de diversas magnitudes. Para ilustrar a proposta, os resultados são confrontados com valores de centralidade de intermediação calculados sobre as taxas de ocupação das vias extraídas de simulação microscópica. Ao final, foram apresentadas evidências de que o método proposto consegue explicar os fluxos de tráfego com melhor desempenho do que a centralidade de intermediação original. No entanto, o método mostrou-se muito sensível à função de custo utilizada na atribuição da demanda de tráfego ao grafo da rede. Os melhores resultados demonstrados pela abordagem proposta foram obtidos em experimentos sobre redes não regulares e com demandas de tráfego não uniformes. No caso de redes regulares com demanda uniforme, o melhor desempenho foi obtido pelo cálculo da centralidade sem considerar a demanda, mas atribuindo-se o custo unitário às arestas do grafo representativo da rede. / This work consists of a study of applicability of betweenness centrality combined with traffic demands in road networks with the objective of identifying their central points. By central points we refer to those which appear with high frequency among the paths used by drivers that move along the road network. It is an exploratory study, which begins with the application of the betweenness centrality on simple networks, extending to simulations on networks based on real maps. In this study we have analyzed the behavior of the metric over the network topology - i.e. without considering demand, as well as experiments considering demands with several magnitudes. To illustrate the proposed method, the results are compared with betweenness centrality values calculated over roadways occupation rates extracted from microscopic simulation. At the end, evidence that the proposed method can explain traffic flows with better performance than the original betweenness centrality were presented. However, the proposed method was shown to be very sensitive to the cost function used in the allocation of the graph network traffic demand. The best results demonstrated by the proposed approach were obtained in experiments on nonregular networks and non-uniform traffic demands. In the case of regular networks with uniform demand, the best performance was obtained by calculating the betweenness centrality without considering the demand, but assigning the unitary cost to the edges of the network graph.

Esse trabalho consiste em um estudo sobre a aplicabilidade da medida de centralidade de intermediação (betweenness centrality) combinada com demandas de tráfego em redes viárias com o objetivo de identificar os principais pontos dessas redes. Como principais pontos refere-se aqui aos que aparecem com maior frequência entre os caminhos utilizados pelos motoristas que se deslocam pela rede viária. Trata-se de um estudo exploratório, que se inicia com a aplicação da centralidade de intermediação sobre redes simples, estendendo-se até simulações sobre redes baseadas em mapas reais. Nesse trabalho é analisado o comportamento da medida de centralidade sobre a topologia da rede - i.e. tanto sem considerar uma demanda, como considerando demandas de diversas magnitudes. Para ilustrar a proposta, os resultados são confrontados com valores de centralidade de intermediação calculados sobre as taxas de ocupação das vias extraídas de simulação microscópica. Ao final, foram apresentadas evidências de que o método proposto consegue explicar os fluxos de tráfego com melhor desempenho do que a centralidade de intermediação original. No entanto, o método mostrou-se muito sensível à função de custo utilizada na atribuição da demanda de tráfego ao grafo da rede. Os melhores resultados demonstrados pela abordagem proposta foram obtidos em experimentos sobre redes não regulares e com demandas de tráfego não uniformes. No caso de redes regulares com demanda uniforme, o melhor desempenho foi obtido pelo cálculo da centralidade sem considerar a demanda, mas atribuindo-se o custo unitário às arestas do grafo representativo da rede. / This work consists of a study of applicability of betweenness centrality combined with traffic demands in road networks with the objective of identifying their central points. By central points we refer to those which appear with high frequency among the paths used by drivers that move along the road network. It is an exploratory study, which begins with the application of the betweenness centrality on simple networks, extending to simulations on networks based on real maps. In this study we have analyzed the behavior of the metric over the network topology - i.e. without considering demand, as well as experiments considering demands with several magnitudes. To illustrate the proposed method, the results are compared with betweenness centrality values calculated over roadways occupation rates extracted from microscopic simulation. At the end, evidence that the proposed method can explain traffic flows with better performance than the original betweenness centrality were presented. However, the proposed method was shown to be very sensitive to the cost function used in the allocation of the graph network traffic demand. The best results demonstrated by the proposed approach were obtained in experiments on nonregular networks and non-uniform traffic demands. In the case of regular networks with uniform demand, the best performance was obtained by calculating the betweenness centrality without considering the demand, but assigning the unitary cost to the edges of the network graph.

Esse trabalho consiste em um estudo sobre a aplicabilidade da medida de centralidade de intermediação (betweenness centrality) combinada com demandas de tráfego em redes viárias com o objetivo de identificar os principais pontos dessas redes. Como principais pontos refere-se aqui aos que aparecem com maior frequência entre os caminhos utilizados pelos motoristas que se deslocam pela rede viária. Trata-se de um estudo exploratório, que se inicia com a aplicação da centralidade de intermediação sobre redes simples, estendendo-se até simulações sobre redes baseadas em mapas reais. Nesse trabalho é analisado o comportamento da medida de centralidade sobre a topologia da rede - i.e. tanto sem considerar uma demanda, como considerando demandas de diversas magnitudes. Para ilustrar a proposta, os resultados são confrontados com valores de centralidade de intermediação calculados sobre as taxas de ocupação das vias extraídas de simulação microscópica. Ao final, foram apresentadas evidências de que o método proposto consegue explicar os fluxos de tráfego com melhor desempenho do que a centralidade de intermediação original. No entanto, o método mostrou-se muito sensível à função de custo utilizada na atribuição da demanda de tráfego ao grafo da rede. Os melhores resultados demonstrados pela abordagem proposta foram obtidos em experimentos sobre redes não regulares e com demandas de tráfego não uniformes. No caso de redes regulares com demanda uniforme, o melhor desempenho foi obtido pelo cálculo da centralidade sem considerar a demanda, mas atribuindo-se o custo unitário às arestas do grafo representativo da rede. / This work consists of a study of applicability of betweenness centrality combined with traffic demands in road networks with the objective of identifying their central points. By central points we refer to those which appear with high frequency among the paths used by drivers that move along the road network. It is an exploratory study, which begins with the application of the betweenness centrality on simple networks, extending to simulations on networks based on real maps. In this study we have analyzed the behavior of the metric over the network topology - i.e. without considering demand, as well as experiments considering demands with several magnitudes. To illustrate the proposed method, the results are compared with betweenness centrality values calculated over roadways occupation rates extracted from microscopic simulation. At the end, evidence that the proposed method can explain traffic flows with better performance than the original betweenness centrality were presented. However, the proposed method was shown to be very sensitive to the cost function used in the allocation of the graph network traffic demand. The best results demonstrated by the proposed approach were obtained in experiments on nonregular networks and non-uniform traffic demands. In the case of regular networks with uniform demand, the best performance was obtained by calculating the betweenness centrality without considering the demand, but assigning the unitary cost to the edges of the network graph.

The thesis focuses on the social web and on the analysis of social networks with particular emphasis on their temporal aspects. Social networks are represented here by Time Varying Graphs (TVG), a general model for dynamic graphs borrowed from distributed computing. In the first part of the thesis we focus on the temporal aspects of social networks. We develop various temporal centrality measures for TVGs including betweenness, closeness, and eigenvector centralities, which are well known in the context of static graphs. Unfortunately the computational complexities of these temporal centrality metrics are not comparable with their static counterparts. For example, the computation of betweenness becomes intractable in the dynamic setting. For this reason, approximation techniques will also be considered. We apply these temporal measures to two very different datasets, one in the context of knowledge mobilization in a small community of university researchers, the other in the context of Facebook commenting activities among a large number of web users. In both settings, we perform a temporal analysis so to understand the importance of the temporal factors in the dynamics of those networks and to detect nodes that act as “accelerators”. In the second part of the thesis, we focus on a more standard static graph representation. We conduct a propagation study on YouTube datasets to understand and compare the propagation dynamics of two different types of users: subscribers and friends. Finally, we conclude the thesis with the proposal of a general framework to present, in a comprehensive model, the influence of the social web on e-commerce decision making.

In network analysis, it is useful to identify important vertices in a network. Based on the varying notions of importance of vertices, a number of centrality measures are defined and studied in the literature. Some popular centrality measures, such as betweenness centrality, are computationally prohibitive for large-scale networks. In this thesis, we propose a new centrality measure called k-path centrality and experimentally compare this measure with betweenness centrality. We present a polynomial-time randomized algorithm for distinguishing high k-path centrality vertices from low k-path centrality vertices in any given (unweighted or weighted) graph. Specifically, for any graph G = (V, E) with n vertices and for every choice of parameters α ∈ (0, 1), ε ∈ (0, 1/2), and integer k ∈ [1, n], with probability at least 1 − 1/n2 our randomized algorithm distinguishes all vertices v ∈ V that have k-path centrality Ck(v) more than nα(1 + 2ε) from all vertices v ∈ V that have k-path centrality Ck(v) less than nα(1 − 2ε). The running time of the algorithm is O(k2ε −2n1−α ln n). Theoretically and experimentally, our algorithms are (for suitable choices of parameters) significantly faster than the best known deterministic algorithm for computing exact betweenness centrality values (Brandes’ algorithm). Through experimentations on both real and randomly generated networks, we demonstrate that vertices that have high betweenness centrality values also have high k-path centrality values.

<p>The cyber-attacks have increased, and with everything going digital, data theft has become a significant issue. This raises an alarm on the security of the source code. Sometimes, to release products early, the security of the code is compromised. Static analysis tools can help in finding possible security issues. Identifying and fixing the security issues may overwhelm the software developers. This process of "fixing" the errors or securing the code may take a lot of time, and the product may be released before all the errors are fixed. But these vulnerabilities in the source code may cost millions of dollars in case of a data breach. It is important to fix the security issues in the source code before releasing the product. This leads to the question of how to fix errors quickly so products can be rolled out with fewer security issues? A possible solution is to use temporal networks to find the influencer nodes in the source code. If these influencer variables are fixed, the connected security issues depending on the influencer in the community (functions) will also get fixed. The research question of the study: Can we identify the influencer node of the buggy site in the source code using temporal networks (K-tool) if the buggy sites present in the source code are identified using static analysis? The study also aims to know if it is faster to find the influencer node using the K-tool than the betweenness centrality algorithm. This research is an "Applied research" and will target the code written in C programming language. Possible vulnerabilities that can be fixed include "Integer Overflow", "Out of bounds", and "Buffer overflow." In the future, we plan to extend to other errors such as "Improper input validation." In this research, we will discuss how we can find the influencer node of the vulnerability (buggy site) in the source code after running the static analysis. Fixing this influencer node will fix the remaining errors pointed out by the static analysis. This will help in reducing the number of fixes to be done in the source code so that the product can be rolled out faster with less security issues.</p> <p><br></p>

Centrality measures in network analysis have become a popular measurement tool for identifying coherent nodes within a network. In the context of stock markets, the centrality measure helps to identify key performing ele- ments and strengths for specific stocks and determine their impact on disrupting market value and performance. Multiple studies presented practical implementations of centrality measures for determining trends and perform- ance of a particular market. However, fewer studies applied centrality measures to predict trends in the stock market.