Dans cette thèse nous contribuons à répondre aux questions sur les processus dynamiques sur réseaux temporels. En particulier, nous etudions l'influence des représentations de données sur les simulations des processus épidémiques, le niveau de détail nécessaire pour la représentation des données et sa dépendance des paramètres de la propagation de l'épidémie. Avec l'introduction de la matrice de distributions du temps de contacts nous espérons pouvoir améliorer dans le futur la précision des prédictions des épidémies et des stratégies d'immunisation en intégrant cette représentation des données aux modèles d'épidémies multi-échelles. De plus nous montrons comment les processus épidémiques dynamiques sont influencés par les propriétés temporelles des données. / In this thesis we contribute to provide insights into questions concerning dynamic epidemic processes on data-driven, temporal networks. In particular, we investigate the influence of data representations on the outcome of epidemic processes, shedding some light on the question how much detail is necessary for the data representation and its dependence on the spreading parameters. By introducing an improvement to the contact matrix representation we provide a data representation that could in the future be integrated into multi-scale epidemic models in order to improve the accuracy of predictions and corresponding immunization strategies. We also point out some of the ways dynamic processes are influenced by temporal properties of the data.

The classical wavelet transform has been widely used in image and signal processing, where a signal is decomposed into a combination of basis signals. By analyzing the individual contribution of the basis signals, one can infer properties of the original signal. This dissertation presents an overview of the extension of the classical signal processing theory to graph domains. Specifically, we review the graph Fourier transform and graph wavelet transforms both of which based on the spectral graph theory, and explore their properties through illustrative examples. The main features of the spectral graph wavelet transforms are presented using synthetic and real-world data. Furthermore, we introduce in this dissertation a novel method for visual analysis of dynamic networks, which relies on the graph wavelet theory. Dynamic networks naturally appear in a multitude of applications from different domains. Analyzing and exploring dynamic networks in order to understand and detect patterns and phenomena is challenging, fostering the development of new methodologies, particularly in the field of visual analytics. Our method enables the automatic analysis of a signal defined on the nodes of a network, making viable the detection of network properties. Specifically, we use a fast approximation of the graph wavelet transform to derive a set of wavelet coefficients, which are then used to identify activity patterns on large networks, including their temporal recurrence. The wavelet coefficients naturally encode spatial and temporal variations of the signal, leading to an efficient and meaningful representation. This method allows for the exploration of the structural evolution of the network and their patterns over time. The effectiveness of our approach is demonstrated using different scenarios and comparisons involving real dynamic networks. / A transformada wavelet clássica tem sido amplamente usada no processamento de imagens e sinais, onde um sinal é decomposto em uma combinação de sinais de base. Analisando a contribuição individual dos sinais de base, pode-se inferir propriedades do sinal original. Esta tese apresenta uma visão geral da extensão da teoria clássica de processamento de sinais para grafos. Especificamente, revisamos a transformada de Fourier em grafo e as transformadas wavelet em grafo ambas fundamentadas na teoria espectral de grafos, e exploramos suas propriedades através de exemplos ilustrativos. As principais características das transformadas wavelet espectrais em grafo são apresentadas usando dados sintéticos e reais. Além disso, introduzimos nesta tese um método inovador para análise visual de redes dinâmicas, que utiliza a teoria de wavelets em grafo. Redes dinâmicas aparecem naturalmente em uma infinidade de aplicações de diferentes domínios. Analisar e explorar redes dinâmicas a fim de entender e detectar padrões e fenômenos é desafiador, fomentando o desenvolvimento de novas metodologias, particularmente no campo de análise visual. Nosso método permite a análise automática de um sinal definido nos vértices de uma rede, tornando possível a detecção de propriedades da rede. Especificamente, usamos uma aproximação da transformada wavelet em grafo para obter um conjunto de coeficientes wavelet, que são então usados para identificar padrões de atividade em redes de grande porte, incluindo a sua recorrência temporal. Os coeficientes wavelet naturalmente codificam variações espaciais e temporais do sinal, criando uma representação eficiente e com significado expressivo. Esse método permite explorar a evolução estrutural da rede e seus padrões ao longo do tempo. A eficácia da nossa abordagem é demonstrada usando diferentes cenários e comparações envolvendo redes dinâmicas reais.

Atualmente, muitas redes com características dinâmicas estão em funcionamento (por exemplo MANETs, DTNs, redes oportunistas, etc). Neste trabalho, estudamos um modelo para estas redes chamado de Grafos Evolutivos, que permite expressar a dinamicidade das conexões entre nós por meio de uma simples extensão da estrutura comum de grafos. Esta modelagem é utilizada no arcabouço proposto por Casteigts et al. para definir algoritmos distribuídos em redes dinâmicas, que utiliza grafos evolutivos para representar a topologia da rede e renomeação de rótulos para expressar a comunicação entre os nós. Utilizamos esta abordagem para estudar o problema da exclusão mútua distribuída em redes dinâmicas e diversos algoritmos propostos para ele, a fim de definir e validar suas condições necessárias e suficientes de conectividade em redes dinâmicas. Além da formalização de algoritmos, o modelo de grafos evolutivos também pode ser utilizado para analisar redes dinâmicas. Rastros de redes dinâmicas reais são amplamente utilizados na literatura para estudos de algoritmos pois estes geram resultados mais realísticos do que redes simuladas com padrões de movimento. A partir dos detalhes de cada conexão entre nós de um destes rastros, é possível construir um grafo evolutivo, do qual se pode extrair dados como jornadas ótimas entre nós, variação da conectividade no tempo, estabilidade, e periodicidade. Com as informações mencionadas, um pesquisador pode observar com maior precisão as características do rastro, o que facilita na escolha da rede mais apropriada para sua necessidade. Além disso, o conhecimento prévio de tais características de uma rede auxilia no estudo do comportamento de algoritmos executados sobre ela e provém uma validação para suposições geralmente feitas pelos pesquisadores. Para fornecer estas informações, desenvolvemos uma ferramenta Web que analisa rastros de redes dinâmicas e agrega os dados em um formato de fácil visualização. Descrevemos, neste trabalho, a implementação e a utilidade de todos os serviços da ferramenta. / Lately, several networks with dynamic properties (for instance MANETs, DTNs, opportunistic networks, etc) are functioning. In this work, we studied a model for these networks called Evolving Graphs, which allows the expression of the dynamicity of the conections between nodes through a simple extension of the common graph structure. This model is used by the framework proposed by Casteigts et al. to define distributed algorithms in dynamic networks, which uses evolving graphs to represent the network topology and graph relabelling to express the communication between nodes. Using this approach, we study the distributed mutual exclusion problem in dynamic networks and several algorithms proposed to solve it, in order to define and validate their necessary and sufficient connectivity conditions. Apart from the formalization of algorithms, the evolving graphs model can also be used to analyze dynamic networks. Dynamic network traces are widely used in the literature in order to study algorithms, as they generate better results than simulated networks with movement patterns. From the details of every connection between nodes in a trace, it is possible to build an evolving graph, from which a large amount of information can be extracted, such as optimal journeys between nodes, variation of the conectivity over time, stability and periodicity. With the aforementioned information, a researcher might observe the characteristics of a trace more precisely, which facilitates the process of choosing the most appropriate trace for his needs. Furthermore, the early knowledge of such characteristics of a network helps in the study of the behavior of the algorithms exected over it and provides a validation for the assumptions usually made by the researchers. In order to provide this information, we developed a web tool which analyzes dynamic network traces and aggregates the data in an easily readable format. In this work, we describe the implementation and usefulness of every service in the tool.

Ces travaux de thèse portent sur l’élaboration et l’étude des propriétés thermomécaniques de polymères dynamiques incorporant des dérivés borés. Tout en appliquant ce concept sur une variété d’architectures macromoléculaires : copolymères fonctionnels, briques di- et tri-fonctionelles, deux réactivités distinctes du bore ont été étudiées et exploitées. Une large gamme de méthodes de caractérisation a été utilisée pour mener à bien ce projet : spectroscopies FTIR et RMN sous différents stimuli, ainsi que de nombreuses analyses thermiques et mécaniques. Dans un premier temps, nous avons considéré la formation de paires de Lewis frustrées entre des acides de Lewis (organoboranes) et des bases de Lewis (amines et phosphines) stériquement encombrés, cette interaction pouvant être fortement modulée par la participation d’un troisième composé tels que des molécules de gaz. Ainsi, nous avons été capables de former des réseaux dynamiques réticulables de façon réversible avec le dioxyde de carbone. Dans un second temps, nous avons mis en évidence une nouvelle réactivité dans les esters boroniques cycliques impliquant une ouverture de cycle à haute température, assistée par la présence de nucléophiles. Cette réaction a été mise à profit pour former des polymères réticulés dynamiquement, pouvant atteindre des températures de transition vitreuse jusqu’à 220°C et dé-réticulables par dilution avec un bon solvant du polymère (apolaire). Cette réactivité a été appliquée à une variété de polymères accessibles par copolymérisation radicalaire (styrène, éthylène, acétate de vinyle, acrylate de butyle) ou par post-fonctionnalisation de polymères commerciaux (polybutadiène) / This thesis focuses on the development and study of thermomechanical properties of dynamic polymers incorporating borylated derivatives. While applying this concept to a variety of macromolecular architectures: functional copolymers, di- and tri-functional bricks, two distinct reactivities of boron have been explored. A wide range of characterization methods has been used to carry out this project: FTIR and NMR spectroscopies under numerous stimuli, as well as many thermal and mechanical analyses. In a first step, we considered the formation of Frustrated Lewis Pairs between Lewis acids (organoboranes) and Lewis bases (amines and phosphines) sterically hindered, as this interaction can be strongly modulated by the participation of a third compound such as gas molecules. Thus, we have been able to form dynamic networks reversibly crosslinkable with carbon dioxide. In a second step, we demonstrated a new reactivity in cyclic boronic esters involving a ring-opening at high temperature, assisted by the presence of nucleophiles. This reaction has been used to form dynamically crosslinked polymers, which can reach glass transition temperatures up to 220°C and de-crosslinkable by dilution in a good (apolar) polymer solvent. This reactivity has been applied to a variety of polymers accessible by radical copolymerization (styrene, ethylene, vinyl acetate, butyl acrylate) or by post-functionalization of commercial polymers (polybutadiene)

Supporting emerging mobile applications in densely populated environments requires connecting mobile users and their devices with the surrounding digital landscape. Specifically, the volume of digitally-available data in such computing spaces presents an imminent need for expressive mechanisms that enable humans and applications to share and search for relevant information within their digitally accessible physical surroundings. Device-to-device communications will play a critical role in facilitating transparent access to proximate digital resources. A wide variety of approaches exist that support device-to-device dissemination and query-driven data access. Very few, however, capitalize on the contextual history of the shared data itself to distribute additional data or to guide queries. This dissertation presents Gander, an application substrate and mobile middleware designed to ease the burden associated with creating applications that require support for sharing and searching of hyper-localized data in situ. Gander employs a novel trajectory-driven model of spatiotemporal provenance that enriches shared data with its contextual history -- annotations that capture data's geospatial and causal history across a lifetime of device-to-device propagation. We demonstrate the value of spatiotemporal data provenance as both a tool for improving ad hoc routing performance and for driving complex application behavior. This dissertation discusses the design and implementation of Gander's middleware model, which abstracts away tedious implementation details by enabling developers to write high-level rules that govern when, where, and how data is distributed and to execute expressive queries across proximate digital resources. We evaluate Gander within several simulated large-scale environments and one real-world deployment on the UT Austin campus. The goal of this research is to provide formal constructs realized within a software framework that ease the software engineering challenges encountered during the design and deployment of several applications in emerging mobile environments. / text

Networks are models that help us understanding and thinking about relationships between entities in the real world. Many of these networks are dynamic, i.e. connectivity changes over time. Understanding changes in connectivity means to understand interactions between elements of complex systems; how people create and break up friendship relations, how signals get passed in the brain, how business collaborations evolve, or how food-webs restructure after environmental changes. However, understanding static networks is already difficult, due to size, density, attributes and particular motifs; changes over time very much increase this complexity. Quantification of change is often insufficient, but beyond an analysis that is driven by technology and algorithms, humans dispose a unique capability of understanding and interpreting information in data, based on vision and cognition. This dissertation explores ways to interactively explore dynamic networks by means of visualization. I develop and evaluate techniques to unfold the complexity of dynamic networks, making them understandable by looking at them from different angles, decomposing them into their parts and relating the parts in novel ways. While most techniques for dynamic network visualization rely on one particular type of view on the data, complementary visualizations allow for higher-level exploration and analysis. Covering three aspects Tasks, Visualization Design and Evaluation, I develop and evaluate the following unfolding techniques: (i) temporal navigation between individual time steps of a network and improved animated transitions to better understand changes, (ii) designs for the comparison of weighted graphs, (iii) the Matrix Cube, a space-time cube based on adjacency matrices, allowing to visualize dense dynamic networks by, as well as GraphCuisine, a system to (iv) generate synthetic networks with the primary focus on evaluating visualizations in user studies. In order to inform the design and evaluation of visualizations, we (v) provide a task taxonomy capturing users' tasks when exploring dynamic networks. Finally, (vi) the idea of unfolding networks with Matrix Cubes is generalized to other data sets that can be represented in space-time cubes (videos, geographical data, etc.). Visualizations in these domains can inspire visualizations for dynamic networks, and vice-versa. We propose a taxonomy of operations, describing how 3D space-time cubes are decomposed into a large variety of 2D visualizations. These operations help us exploring the design space for visualizing and interactively unfolding dynamic networks and other spatio-temporal data, as well as may serve users as a mental model of the data.

Networks are models that help us understanding and thinking about relationships between entities in the real world. Many of these networks are dynamic, i.e. connectivity changes over time. Understanding changes in connectivity means to understand interactions between elements of complex systems; how people create and break up friendship relations, how signals get passed in the brain, how business collaborations evolve, or how food-webs restructure after environmental changes. However, understanding static networks is already difficult, due to size, density, attributes and particular motifs; changes over time very much increase this complexity. Quantification of change is often insufficient, but beyond an analysis that is driven by technology and algorithms, humans dispose a unique capability of understanding and interpreting information in data, based on vision and cognition. This dissertation explores ways to interactively explore dynamic networks by means of visualization. I develop and evaluate techniques to unfold the complexity of dynamic networks, making them understandable by looking at them from different angles, decomposing them into their parts and relating the parts in novel ways. While most techniques for dynamic network visualization rely on one particular type of view on the data, complementary visualizations allow for higher-level exploration and analysis. Covering three aspects Tasks, Visualization Design and Evaluation, I develop and evaluate the following unfolding techniques: (i) temporal navigation between individual time steps of a network and improved animated transitions to better understand changes, (ii) designs for the comparison of weighted graphs, (iii) the Matrix Cube, a space-time cube based on adjacency matrices, allowing to visualize dense dynamic networks by, as well as GraphCuisine, a system to (iv) generate synthetic networks with the primary focus on evaluating visualizations in user studies. In order to inform the design and evaluation of visualizations, we (v) provide a task taxonomy capturing users' tasks when exploring dynamic networks. Finally, (vi) the idea of unfolding networks with Matrix Cubes is generalized to other data sets that can be represented in space-time cubes (videos, geographical data, etc.). Visualizations in these domains can inspire visualizations for dynamic networks, and vice-versa. We propose a taxonomy of operations, describing how 3D space-time cubes are decomposed into a large variety of 2D visualizations. These operations help us exploring the design space for visualizing and interactively unfolding dynamic networks and other spatio-temporal data, as well as may serve users as a mental model of the data.

Le maintien de la morphologie et la production des forces par les cellules sont possibles grâce au cytosquelette, constitué de trois types de polymères protéiques dont les microfilaments d’actine. Les filaments d’actine s’organisent en différentes architectures, dont l’assemblage et le désassemblage sont étroitement contrôlés dans le temps et l’espace. En effet, une des caractéristiques d’un filament d’actine est son vieillissement, par l’hydrolyse progressive de l’ATP au sein des sous-unités. Pour assurer un renouvellement continu de l’ actine celle-ci doit donc être recyclée. Lorsque l’assemblage et désassemblage se compensent, les architectures d’actine sont alors dans un état stationnaire dynamique, dans lequel la concentration demonomères d’actine est perpétuellement renouvelée. Le désassemblage permet également de maintenir un réservoir important d’actine monomérique polymérisable, pour répondre rapidement aux besoins cellulaires. Le lamellipode, organe moteur de la cellule, est essentiellement composé d’unfeuillet fin mais très dense d’actine dendritique ainsi que de protéines régulatrices. Une protéine essentielle dans le turnover rapide du lamellipode est l’ADF/Cofiline. Elle est responsable du désassemblage des filaments âgés par fragmentation et pardébranchement. Jusqu’à présent, les études portaient le plus souvent sur les mécanismes microscopiques, à l’échelle du filament individuel. Or, pour comprendre la dynamique des réseaux branchés notamment au cours de la motilité cellulaire, il nous faut comprendre le désassemblage collectif et macroscopique du réseau d’actine dendritique. En combinant des milieux de motilité reconstitués à partir de protéinespurifiées à une nouvelle technique de micro-structuration de surfaces, j’ai pu reconstituer in vitro des réseaux dendritiques semblables au lamellipode. Ainsi, j’ai exploré au cours de ma thèse les paramètres qui contrôlent leur désassemblage macroscopique. Il en ressort que le désassemblage des réseaux dépend de leur architecture (densité) et de leur géométrie (taille) : les réseaux denses ou étendus sont moins efficacement désassemblés et restent cohésifs plus longtemps. Des modélisations montrent que c’est la déplétion locale en ADF/Cofiline autour du réseau d’actine qui semble responsable des effets observés. De plus, les réseaux constitués de densités d’actine hétérogènes acquièrent une directionnalité, qui peut être modulée par le désassemblage sélectif par ADF/Cofiline. Parallèlement, ces études ont permis de déterminer que pour avoir un réseau à l’état dynamiquestationnaire (ou à l’équilibre), il fallait atteindre un certain ratio d’ADF/Cofiline par actine. Ce travail a permis d’aller plus loin que les études fondamentales sur la fragmentation de filaments d’actine individuels, à l’échelle microscopique, et d’établir deux nouveaux paramètres qui contrôlent le désassemblage de réseaux d’actine dendritique à l’échelle macroscopique / Cells maintain their morphology and produce forces thanks to the cytoskeleton, which is composed of three types of protein polymers, amongst which the actin microfilaments. Actin filaments assemble into diverse architectures, which assembly and disassembly is tightly controlled in space and time. Indeed, the progressive hydrolysis of ATP in the monomers causes the actin filaments to age. Thus, actin needs to be recycled. When assembly and disassembly compensate, different actin architectures are in a dynamic steady state, in which the pool of actin monomers is renewed. Disassembly of actin structures also maintains a large reservoir of polymerization-ready monomers ready to assemble when needed by the cell.The lamellipodium is the locomotory organelle of the cell, and is made of a thin yet very dense sheet of dendritic actin network, with regulatory proteins. A pivotal protein is ADF/Cofilin, which is responsible of the disassembly of old actin filaments by fragmentation and debranching. To date, there have been extensive studies about the microscopic mechanisms, but if one wants to understand cell motility, one must decipher the collective and macroscopic disassembly of the dendritic actin network.By combining motility media reconstituted from purified proteins, and a new surface micro-patterning technique, I was able to reconstitute lamellipodium-like dendritic networks in vitro. During this thesis I explored the parameters that control the macroscopic disassembly of these networks. This work shows that the disassembly of dendritic actin networks depends on their architecture (density) and geometry (size): dense or extended networks are less efficiently disassembled and remain cohesive longer. Simulations show that these effects can be explains by a local depletion of ADF/Cofilin in the volume surrounding the network. Besides, networks of heterogeneous densities acquire directionality. This steering is modulated by selective disassembly of the networks by ADF/Cofilin. In parallel, these studies established a ratio at which networks are at a dynamic steady state.This work goes further than the fundamentally important studies about fragmentation of individual actin filaments, and establishes new parameters that control the disassembly of dendritic actin at the macroscopic scale.

Dans le contexte des réseaux complexes, la structure communautaire du réseau devient un sujet important pour plusieurs domaines de recherche. Les communautés sont en général vues comme des groupes intérieurement denses. La détection de tels groupes offre un éclairage intéressant sur la structure du réseau. Par exemple, une communauté de pages web regroupe des pages traitant du même sujet. La définition de communautés est en général limitée à une partition de l’ensemble des nœds. Cela exclut par définition qu’un nœd puisse appartenir à plusieurs communautés, ce qui pourtant est naturel dans de nombreux (cas des réseaux sociaux par exemple). Une autre question importante et sans réponse est l’étude des réseaux et de leur structure communautaire en tenant compte de leur dynamique. Cette thèse porte sur l’étude de réseaux dynamiques et la détection de communautés recouvrantes. Nous proposons deux méthodes différentes pour la détection de communautés recouvrantes. La première méthode est appelée optimisation de clique. L'optimisation de clique vise à détecter les nœds recouvrants granulaires. La méthode de l'optimisation de clique est une approche à grain fin. La seconde méthode est nommée détection floue (fuzzy detection). Cette méthode est à grain plus grossier et vise à identifier les groupes recouvrants. Nous appliquons ces deux méthodes à des réseaux synthétiques et réels. Les résultats obtenus indiquent que les deux méthodes peuvent être utilisées pour caractériser les nœds recouvrants. Les deux approches apportent des points de vue distincts et complémentaires. Dans le cas des graphes dynamiques, nous donnons une définition sur la relation entre les communautés à deux pas de temps consécutif. Cette technique permet de représenter le changement de la structure en fonction du temps. Pour mettre en évidence cette relation, nous proposons des diagrammes de lignage pour la visualisation de la dynamique des communautés. Ces diagrammes qui connectent des communautés à des pas de temps successifs montrent l’évolution de la structure et l'évolution des groupes recouvrantes., Nous avons également appliquer ces outils à des cas concrets. / In complex networks, the notion of community structure refers to the presence of groups of nodes in a network. These groups are more densely connected internally than with the rest of the network. The presence of communities inside a network gives an insight on network structural properties. For example, in social networks, communities are based on common interests, location, hobbies.... Generally, a community structure is described by a partition of the network nodes, where each node belongs to a unique community. A more reasonable description seems to be overlapping community structure, where nodes are allowed to be shared by several communities. Moreover, when considering dynamic networks whose interactions between nodes evolve in time, it appears crucial to consider also the evolution of the intrinsic community structure. This thesis focus on mining dynamic community evolution and overlapping community detection. We have proposed two distinct methods for overlapping community detection. The first one named clique optimization and the second one called fuzzy detection. Our clique optimization aims to identify granular overlaps and it is a fine grain scale approach. Our fuzzy detection is at a coarser grain scale with the strategy of identifying modular overlaps. Their applications in synthetic and real networks indicate that both methods can be used for characterizing overlapping nodes but in distinct and complementary views. We also propose the definition of predecessor and successor in mining community evolution. Such definition describes the relationship between communities at different time steps. We use it to detect community evolution in dynamic networks and show how modular overlaps evolve over time. A visualization tool called lineage diagrams is used to show community evolution by connecting communities in relationship of predecessor and successor. Several cases are studied.

The classical wavelet transform has been widely used in image and signal processing, where a signal is decomposed into a combination of basis signals. By analyzing the individual contribution of the basis signals, one can infer properties of the original signal. This dissertation presents an overview of the extension of the classical signal processing theory to graph domains. Specifically, we review the graph Fourier transform and graph wavelet transforms both of which based on the spectral graph theory, and explore their properties through illustrative examples. The main features of the spectral graph wavelet transforms are presented using synthetic and real-world data. Furthermore, we introduce in this dissertation a novel method for visual analysis of dynamic networks, which relies on the graph wavelet theory. Dynamic networks naturally appear in a multitude of applications from different domains. Analyzing and exploring dynamic networks in order to understand and detect patterns and phenomena is challenging, fostering the development of new methodologies, particularly in the field of visual analytics. Our method enables the automatic analysis of a signal defined on the nodes of a network, making viable the detection of network properties. Specifically, we use a fast approximation of the graph wavelet transform to derive a set of wavelet coefficients, which are then used to identify activity patterns on large networks, including their temporal recurrence. The wavelet coefficients naturally encode spatial and temporal variations of the signal, leading to an efficient and meaningful representation. This method allows for the exploration of the structural evolution of the network and their patterns over time. The effectiveness of our approach is demonstrated using different scenarios and comparisons involving real dynamic networks. / A transformada wavelet clássica tem sido amplamente usada no processamento de imagens e sinais, onde um sinal é decomposto em uma combinação de sinais de base. Analisando a contribuição individual dos sinais de base, pode-se inferir propriedades do sinal original. Esta tese apresenta uma visão geral da extensão da teoria clássica de processamento de sinais para grafos. Especificamente, revisamos a transformada de Fourier em grafo e as transformadas wavelet em grafo ambas fundamentadas na teoria espectral de grafos, e exploramos suas propriedades através de exemplos ilustrativos. As principais características das transformadas wavelet espectrais em grafo são apresentadas usando dados sintéticos e reais. Além disso, introduzimos nesta tese um método inovador para análise visual de redes dinâmicas, que utiliza a teoria de wavelets em grafo. Redes dinâmicas aparecem naturalmente em uma infinidade de aplicações de diferentes domínios. Analisar e explorar redes dinâmicas a fim de entender e detectar padrões e fenômenos é desafiador, fomentando o desenvolvimento de novas metodologias, particularmente no campo de análise visual. Nosso método permite a análise automática de um sinal definido nos vértices de uma rede, tornando possível a detecção de propriedades da rede. Especificamente, usamos uma aproximação da transformada wavelet em grafo para obter um conjunto de coeficientes wavelet, que são então usados para identificar padrões de atividade em redes de grande porte, incluindo a sua recorrência temporal. Os coeficientes wavelet naturalmente codificam variações espaciais e temporais do sinal, criando uma representação eficiente e com significado expressivo. Esse método permite explorar a evolução estrutural da rede e seus padrões ao longo do tempo. A eficácia da nossa abordagem é demonstrada usando diferentes cenários e comparações envolvendo redes dinâmicas reais.