The analysis of dynamic systems provides insights into their time-dependent characteristics. This enables us to monitor, evaluate, and improve systems from various areas. They are often represented as graphs that model the system's components and their relations. The analysis of the resulting dynamic graphs yields great insights into the system's underlying structure, its characteristics, as well as properties of single components. The interpretation of these results can help us understand how a system works and how parameters influence its performance. This knowledge supports the design of new systems and the improvement of existing ones. The main issue in this scenario is the performance of analyzing the dynamic graph to obtain relevant properties. While various approaches have been developed to analyze dynamic graphs, it is not always clear which one performs best for the analysis of a specific graph. The runtime also depends on many other factors, including the size and topology of the graph, the frequency of changes, and the data structures used to represent the graph in memory. While the benefits and drawbacks of many data structures are well-known, their runtime is hard to predict when used for the representation of dynamic graphs. Hence, tools are required to benchmark and compare different algorithms for the computation of graph properties and data structures for the representation of dynamic graphs in memory. Based on deeper insights into their performance, new algorithms can be developed and efficient data structures can be selected. In this thesis, we present four contributions to tackle these problems: A benchmarking framework for dynamic graph analysis, novel algorithms for the efficient analysis of dynamic graphs, an approach for the parallelization of dynamic graph analysis, and a novel paradigm to select and adapt graph data structures. In addition, we present three use cases from the areas of social, computer, and biological networks to illustrate the great insights provided by their graph-based analysis. We present a new benchmarking framework for the analysis of dynamic graphs, the Dynamic Network Analyzer (DNA). It provides tools to benchmark and compare different algorithms for the analysis of dynamic graphs as well as the data structures used to represent them in memory. DNA supports the development of new algorithms and the automatic verification of their results. Its visualization component provides different ways to represent dynamic graphs and the results of their analysis. We introduce three new stream-based algorithms for the analysis of dynamic graphs. We evaluate their performance on synthetic as well as real-world dynamic graphs and compare their runtimes to snapshot-based algorithms. Our results show great performance gains for all three algorithms. The new stream-based algorithm StreaM_k, which counts the frequencies of k-vertex motifs, achieves speedups up to 19,043 x for synthetic and 2882 x for real-world datasets. We present a novel approach for the distributed processing of dynamic graphs, called parallel Dynamic Graph Analysis (pDNA). To analyze a dynamic graph, the work is distributed by a partitioner that creates subgraphs and assigns them to workers. They compute the properties of their respective subgraph using standard algorithms. Their results are used by the collator component to merge them to the properties of the original graph. We evaluate the performance of pDNA for the computation of five graph properties on two real-world dynamic graphs with up to 32 workers. Our approach achieves great speedups, especially for the analysis of complex graph measures. We introduce two novel approaches for the selection of efficient graph data structures. The compile-time approach estimates the workload of an analysis after an initial profiling phase and recommends efficient data structures based on benchmarking results. It achieves speedups of up to 5.4 x over baseline data structure configurations for the analysis of real-word dynamic graphs. The run-time approach monitors the workload during analysis and exchanges the graph representation if it finds a configuration that promises to be more efficient for the current workload. Compared to baseline configurations, it achieves speedups up to 7.3 x for the analysis of a synthetic workload. Our contributions provide novel approaches for the efficient analysis of dynamic graphs and tools to further investigate the trade-offs between different factors that influence the performance.

Com base em três modelos de mobilidade MapBasedMovement, RandomWayPoint e RandomWalk presentes no simulador The One, sugerimos e discutimos vários modelos es- tocásticos para mobilidade. Primeiramente, a dinâmica das unidades móveis é reduzida a um processo chamado grafo dinâmico, de forma que a configuração espacial das unidades móveis em cada instante de tempo está resumida em um grafo. Os vértices desse grafo são unidades móveis e não mudam conforme o tempo: consideramos um sistema fechado, as unidades não desaparecem e não aparecem novas. O elo entre duas unidades (vértices) em um instante de tempo significa um contato neste instante (a distância entre as unidades é menor que um raio de contato), assim o conjunto de elos muda durante a evolução do sistema. Em seguida, modelamos a evolução do grafo dinâmico como um conjunto de pro- cessos aleatórios binários de forma que cada componente do processo está associada com um par de unidades móveis indicando presença ou ausência de contato entre elas. Três componentes principais constroem o processo: (i) distribuição de tempo de intercontato, (ii) distribuição de tempo de contato, e (iii) independência/interação entre as unidades. Nesta Tese mostramos teoricamente e através de simulações como escolher todos os três componentes para três modelos de mobilidade mencionados acima na situação de baixa densidade de unidades móveis, chamado DTNs (Delay Tolerant Networks). Considerar a modelagem da mobilidade desse ponto de vista é novo e não existe na literatura, até onde sabemos. Existe uma discussão na literatura sobre o tempo de intercontato, mas não conhecemos os resultados e discussão sobre a distribuição do tempo de contato e a interdependência de processos de contatos. / Based on three mobility models MapBasedMovement, RandomWayPoint and Ran- domWalk present on The One Simulator we suggest and discuss various stochastic mo- dels for mobility. First the dynamics of mobile units is reduced to process called dynamic graph, so that the spatial configuration of mobile units in every moment of time is sum- med up in a graph. The vertices of this graph are mobile units and do not change with the time: consider a closed system, the units dont disappear and not appear new. The link between two units (vertices) in an instant of time means a contact right now (dis- tance between the units is less that the radius contact). So the set of links changes during the system evolution. As a second step, the evolution of dynamic graph model as a set of random processes. Each process component is associated with a pair of mobile units indicating presence or absence of contact between them. Three major components build process: (i) distribution of intercontact time , (ii) distribution of contact time, and (iii) Independence interaction between units. In this work we show theoretically and by si- mulation how to choose all three components for three mobility models mentioned above on the situation of low density of mobile units, called DTNs (Delay Tolerant Networks). Consider the mobility modeling from that point of view is new and does not exist in the literature for our knowledge. There is a discussion in the literature about the intercontact time, but we dont know the results and discussion on the distribution of contact time and the interdependence of contact process.

The analysis of dynamic systems provides insights into their time-dependent characteristics. This enables us to monitor, evaluate, and improve systems from various areas. They are often represented as graphs that model the system's components and their relations. The analysis of the resulting dynamic graphs yields great insights into the system's underlying structure, its characteristics, as well as properties of single components. The interpretation of these results can help us understand how a system works and how parameters influence its performance. This knowledge supports the design of new systems and the improvement of existing ones. The main issue in this scenario is the performance of analyzing the dynamic graph to obtain relevant properties. While various approaches have been developed to analyze dynamic graphs, it is not always clear which one performs best for the analysis of a specific graph. The runtime also depends on many other factors, including the size and topology of the graph, the frequency of changes, and the data structures used to represent the graph in memory. While the benefits and drawbacks of many data structures are well-known, their runtime is hard to predict when used for the representation of dynamic graphs. Hence, tools are required to benchmark and compare different algorithms for the computation of graph properties and data structures for the representation of dynamic graphs in memory. Based on deeper insights into their performance, new algorithms can be developed and efficient data structures can be selected. In this thesis, we present four contributions to tackle these problems: A benchmarking framework for dynamic graph analysis, novel algorithms for the efficient analysis of dynamic graphs, an approach for the parallelization of dynamic graph analysis, and a novel paradigm to select and adapt graph data structures. In addition, we present three use cases from the areas of social, computer, and biological networks to illustrate the great insights provided by their graph-based analysis. We present a new benchmarking framework for the analysis of dynamic graphs, the Dynamic Network Analyzer (DNA). It provides tools to benchmark and compare different algorithms for the analysis of dynamic graphs as well as the data structures used to represent them in memory. DNA supports the development of new algorithms and the automatic verification of their results. Its visualization component provides different ways to represent dynamic graphs and the results of their analysis. We introduce three new stream-based algorithms for the analysis of dynamic graphs. We evaluate their performance on synthetic as well as real-world dynamic graphs and compare their runtimes to snapshot-based algorithms. Our results show great performance gains for all three algorithms. The new stream-based algorithm StreaM_k, which counts the frequencies of k-vertex motifs, achieves speedups up to 19,043 x for synthetic and 2882 x for real-world datasets. We present a novel approach for the distributed processing of dynamic graphs, called parallel Dynamic Graph Analysis (pDNA). To analyze a dynamic graph, the work is distributed by a partitioner that creates subgraphs and assigns them to workers. They compute the properties of their respective subgraph using standard algorithms. Their results are used by the collator component to merge them to the properties of the original graph. We evaluate the performance of pDNA for the computation of five graph properties on two real-world dynamic graphs with up to 32 workers. Our approach achieves great speedups, especially for the analysis of complex graph measures. We introduce two novel approaches for the selection of efficient graph data structures. The compile-time approach estimates the workload of an analysis after an initial profiling phase and recommends efficient data structures based on benchmarking results. It achieves speedups of up to 5.4 x over baseline data structure configurations for the analysis of real-word dynamic graphs. The run-time approach monitors the workload during analysis and exchanges the graph representation if it finds a configuration that promises to be more efficient for the current workload. Compared to baseline configurations, it achieves speedups up to 7.3 x for the analysis of a synthetic workload. Our contributions provide novel approaches for the efficient analysis of dynamic graphs and tools to further investigate the trade-offs between different factors that influence the performance.:1 Introduction 2 Notation and Terminology 3 Related Work 4 DNA - Dynamic Network Analyzer 5 Algorithms 6 Parallel Dynamic Network Analysis 7 Selection of Efficient Graph Data Structures 8 Use Cases 9 Conclusion A DNA - Dynamic Network Analyzer B Algorithms C Selection of Efficient Graph Data Structures D Parallel Dynamic Network Analysis E Graph-based Intrusion Detection System F Molecular Dynamics

We have seen a rapid increase in the development of deep learning algorithms in recent decades. However, while these algorithms have unlocked new business areas and led to great development in many fields, they are usually limited to Euclidean data. Researchers are increasingly starting to find out that they can better represent the data used in many real-life applications as graphs. Examples include high-risk domains such as finding the side effects when combining medicines using a protein-protein network. In high-risk domains, there is a need for trust and transparency in the results returned by deep learning algorithms. In this work, we explore how we can quantify uncertainty in Graph Neural Network predictions using conventional methods for conformal prediction as well as novel methods exploiting graph connectivity information. We evaluate the methods on both static and dynamic graphs and find that neither of the novel methods offers any clear benefits over the conventional methods. However, we see indications that using the graph connectivity information can lead to more efficient conformal predictors and a lower prediction latency than the conventional methods on large data sets. We propose that future work extend the research on using the connectivity information, specifically the node embeddings, to boost the performance of conformal predictors on graphs. / De senaste årtiondena har vi sett en drastiskt ökad utveckling av djupinlärningsalgoritmer. Även fast dessa algoritmer har skapat nya potentiella affärsområden och har även lett till nya upptäckter i flera andra fält, är dessa algoritmer dessvärre oftast begränsade till Euklidisk data. Samtidigt ser vi att allt fler forskare har upptäckt att data i verklighetstrogna applikationer oftast är bättre representerade i form av grafer. Exempel inkluderar hög-risk domäner som läkemedelsutveckling, där man förutspår bieffekter från mediciner med hjälp av protein-protein nätverk. I hög-risk domäner finns det ett krav på tillit och att resultaten från djupinlärningsalgoritmer är transparenta. I den här tesen utforskar vi hur man kan kvantifiera osäkerheten i resultaten hos Neurala Nätverk för grafer (eng. Graph Neural Networks) med hjälp av konform prediktion (eng. Conformal Prediction). Vi testar både konventionella metoder för konform prediktion, samt originella metoder som utnyttjar strukturell information från grafen. Vi utvärderar metoderna både på statiska och dynamiska grafer, och vi kommer fram till att de originella metoderna varken är bättre eller sämre än de konventionella metoderna. Däremot finner vi indikationer på att användning av den strukturella informationen från grafen kan leda till effektivare prediktorer och till lägre svarstid än de konventionella metoderna när de används på stora grafer. Vi föreslår att framtida arbete i området utforskar vidare hur den strukturella informationen kan användas, och framförallt nod representationerna, kan användas för att öka prestandan i konforma prediktorer för grafer.

Indiana University-Purdue University Indianapolis (IUPUI) / Graph Neural Networks (GNNs) have become excessively popular and prominent deep learning techniques to analyze structural graph data for their ability to solve complex real-world problems. Because graphs provide an efficient approach to contriving abstract hypothetical concepts, modern research overcomes the limitations of classical graph theory, requiring prior knowledge of the graph structure before employing traditional algorithms. GNNs, an impressive framework for representation learning of graphs, have already produced many state-of-the-art techniques to solve node classification, link prediction, and graph classification tasks. GNNs can learn meaningful representations of graphs incorporating topological structure, node attributes, and neighborhood aggregation to solve supervised, semi-supervised, and unsupervised graph-based problems. In this study, the usefulness of GNNs has been analyzed primarily from two aspects - clustering and classification. We focus on these two techniques, as they are the most popular strategies in data mining to discern collected data and employ predictive analysis.

This work presents an investigation of tailoring Network Representation Learning (NRL) for an application in the Financial Industry. NRL approaches are data-driven models that learn how to encode graph structures into low-dimensional vector spaces, which can be further exploited by downstream Machine Learning applications. They can potentially bring a lot of benefits in the Financial Industry since they extract in an automatic way features that can provide useful input regarding graph structures, called embeddings. Financial transactions can be represented as a network, and through NRL, it is possible to extract embeddings that reflect the intrinsic inter-connected nature of economic relationships. Such embeddings can be used for several purposes, among which Anomaly Detection to fight financial crime.This work provides a qualitative analysis over state-of-the-art NRL models, which identifies Graph Convolutional Network (ConvGNN) as the most suitable category of approaches for Financial Industry but with a certain need for further improvement. Financial Industry poses additional challenges when modelling a NRL solution. Despite the need of having a scalable solution to handle real-world graph with considerable dimensions, it is necessary to take into consideration several characteristics: transactions graphs are inherently dynamic since every day new transactions are executed and nodes can be heterogeneous. Besides, everything is further complicated by the need to have updated information in (near) real-time due to the sensitivity of the application domain. For these reasons, GraphSAGE has been considered as a base for the experiments, which is an inductive ConvGNN model. Two variants of GraphSAGE are presented: a dynamic variant whose weights evolve accordingly with the input sequence of graph snapshots, and a variant specifically meant to handle bipartite graphs. These variants have been evaluated by applying them to real-world data and leveraging the generated embeddings to perform Anomaly Detection. The experiments demonstrate that leveraging these variants leads toimagecomparable results with other state-of-the-art approaches, but having the advantage of being suitable to handle real-world financial data sets. / Detta arbete presenterar en undersökning av tillämpningar av Network Representation Learning (NRL) inom den finansiella industrin. Metoder inom NRL möjliggör datadriven kondensering av grafstrukturer till lågdimensionella och lätthanterliga vektorer.Dessa vektorer kan sedan användas i andra maskininlärningsuppgifter. Närmare bestämt, kan metoder inom NRL underlätta hantering av och informantionsutvinning ur beräkningsintensiva och storskaliga grafer inom den finansiella sektorn, till exempel avvikelsehantering bland finansiella transaktioner. Arbetet med data av denna typ försvåras av det faktum att transaktionsgrafer är dynamiska och i konstant förändring. Utöver detta kan noderna, dvs transaktionspunkterna, vara vitt skilda eller med andra ord härstamma från olika fördelningar.I detta arbete har Graph Convolutional Network (ConvGNN) ansetts till den mest lämpliga lösningen för nämnda tillämpningar riktade mot upptäckt av avvikelser i transaktioner. GraphSAGE har använts som utgångspunkt för experimenten i två olika varianter: en dynamisk version där vikterna uppdateras allteftersom nya transaktionssekvenser matas in, och en variant avsedd särskilt för bipartita (tvådelade) grafer. Dessa varianter har utvärderats genom användning av faktiska datamängder med avvikelsehantering som slutmål.

Les réseaux dynamiques sont constitués d’entités établissant des contacts les unes avec les autres dans le temps. Un défi majeur dans les réseaux dynamiques est de prédire les modèles de mobilité et de décider si l’évolution de la topologie satisfait aux exigences du succès d’un algorithme donné. Les types de dynamique résultant de ces réseaux sont variés en échelle et en nature. Par exemple,certains de ces réseaux restent connexes tout le temps; d’autres sont toujours déconnectés mais offrent toujours une sorte de connexité dans le temps et dans l’espace(connexité temporelle); d’autres sont connexes de manière récurrente, périodique,etc. Tous ces contextes peuvent être représentés sous forme de classes de graphes dynamiques correspondant à des conditions nécessaires et/ou suffisantes pour des problèmes ou algorithmes distribués donnés. Étant donné un graphe dynamique,une question naturelle est de savoir à quelles classes appartient ce graphe. Dans ce travail, nous apportons une contribution à l’automatisation de la classification de graphes dynamiques. Nous proposons des stratégies pour tester l’appartenance d’un graphe dynamique à une classe donnée et nous définissons un cadre générique pour le test de propriétés dans les graphes dynamiques. Nous explorons également le cas où aucune propriété sur le graphe n’est garantie, à travers l’étude du problème de maintien d’une forêt d’arbres couvrants dans un graphe dynamique. / Dynamic networks consist of entities making contact over time with one another. A major challenge in dynamic networks is to predict mobility patterns and decide whether the evolution of the topology satisfies requirements for the successof a given algorithm. The types of dynamics resulting from these networks are varied in scale and nature. For instance, some of these networks remain connected at all times; others are always disconnected but still offer some kind of connectivity over time and space (temporal connectivity); others are recurrently connected,periodic, etc. All of these contexts can be represented as dynamic graph classes corresponding to necessary or sufficient conditions for given distributed problems or algorithms. Given a dynamic graph, a natural question to ask is to which of the classes this graph belongs. In this work we provide a contribution to the automation of dynamic graphs classification. We provide strategies for testing membership of a dynamic graph to a given class and a generic framework to test properties in dynamic graphs. We also attempt to understand what can still be done in a context where no property on the graph is guaranteed through the distributed problem of maintaining a spanning forest in highly dynamic graphs.

<p><strong>Graph Neural Networks</strong> (GNNs) have become excessively popular and prominent deep learning techniques to analyze structural graph data for their ability to solve complex real-world problems. Because graphs provide an efficient approach to contriving abstract hypothetical concepts, modern research overcomes the limitations of classical graph theory, requiring prior knowledge of the graph structure before employing traditional algorithms. GNNs, an impressive framework for representation learning of graphs, have already produced many state-of-the-art techniques to solve node classification, link prediction, and graph classification tasks. GNNs can learn meaningful representations of graphs incorporating topological structure, node attributes, and neighborhood aggregation to solve supervised, semi-supervised, and unsupervised graph-based problems. In this study, the usefulness of GNNs has been analyzed primarily from two aspects - <strong>clustering and classification</strong>. We focus on these two techniques, as they are the most popular strategies in data mining to discern collected data and employ predictive analysis.</p>