Graphs provide powerful abstractions, and are widely used in different areas. There has been an increasing demand in using the graph data model to represent data in many applications such as network management, web page analysis, knowledge graphs, social networks. These graphs are usually dynamic and represent the time evolving relationships between entities. Enforcing and maintaining data quality in graphs is a critical task for decision making, operational efficiency and accurate data analysis as recent studies have shown that data scientists spend 60-80% of their time cleaning and organizing data [2]. This effort motivates the need for effective data cleaning tools to reduce the user burden. The study of data quality management focuses along a set of dimensions, including data consistency, data deduplication, information completeness, data currency, and data accuracy. Achieving all these data characteristics is often not possible in practice due to personnel costs, and for performance reasons. In this thesis, we focus on tackling three problems in two data quality dimensions: data consistency and data deduplication. To address the problem of data consistency over temporal graphs, we present a new class of data dependencies called Temporal Graph Functional Dependency (TGFDs). TGFDs generalize functional dependencies to temporal graphs as a sequence of graph snapshots that are induced by time intervals, and enforce both topological constraints and attribute value dependencies that must be satisfied by these snapshots. We establish the complexity results for the satisfiability and implication problems of TGFDs. We propose a sound and complete axiomatization system for TGFDs. We also present efficient parallel algorithms to detect inconsistencies in temporal graphs as violations of TGFDs. To address the data deduplication problem, we first address the problem of key discovery for graphs. Keys for graphs use topology and value constraints to uniquely identify entities in a graph database and keys are the main tools for data deduplication in graphs. We present two properties that define a key, including minimality and support and an algorithm to mine keys over graphs via frequent subgraph expansion. However, existing key constraints identify entities by enforcing label equality on node types. These constraints can be too restrictive to characterize structures and node labels that are syntactically different but semantically equivalent. Lastly, we propose a new class of key constraints, Ontological Graph Keys (OGKs) that extend conventional graph keys by ontological subgraph matching between entity labels and an external ontology. We study the entity matching problem with OGKs. We develop efficient algorithms to perform entity matching based on a Chase procedure. The proposed dependencies and algorithms in this thesis improve consistency detection in temporal graphs, automate the discovery of keys in graphs, and enrich the semantic expressiveness of graph keys. / Dissertation / Doctor of Science (PhD)

Στη διπλωματική εργασία προς παρουσίαση, πραγματευόμαστε ένα νέο είδος γραφημάτων, τα χρονικά γραφήματα, και διάφορες παραλλαγές τους. Ένα χρονικό γράφημα είναι μια διατεταγμενη τριάδα G={V,E,L}, όπου V ένα μη κενό πεπερασμένο σύνολο που καλείται σύνολο κορυφών, E ένα σύνολο m στοιχείων, καθένα από τα οποία είναι δισύνολο στοιχείων του V (καλείται σύνολο ακμών), και L= {L_e, για κάθε e στοιχείο του E} = {L_e_1, L_e_2, ..., L_e_m}, όπου L_e_i, i = 1,..., m, σύνολο θετικών ακεραίων τιμών που αντιστοιχίζονται στην ακμή e_i του συνόλου E (καλείται ανάθεση χρονικών ετικετών ή απλώς ανάθεση). Οι τιμές που αντιστοιχίζονται σε κάθε ακμή του γραφήματος καλούνται χρονικές ετικέτες της ακμής και δηλώνουν τις χρονικές στιγμές, κατά τις οποίες έχουμε τη δυνατότητα να τη διασχίσουμε (από το ένα της άκρο προς το άλλο). Για να αντιληφθεί κανείς το ενδιαφέρον των χρονικών γραφημάτων, μπορεί να σκεφτεί τη δυνατότητα εφαρμογής τους στην καθημερινότητα. Για παράδειγμα, οι χρονικές ετικέτες που ανατίθενται σε μία ακμή ενός κατευθυνόμενου χρονικού γραφήματος μπορούν να παραλληλιστούν με τις ώρες, στις οποίες γίνονται αναχωρήσεις αεροπλάνων από μία πόλη προς μια άλλη. Έτσι, η μελέτη των χρονικών γραφημάτων θα μπορούσε να συμβάλει στην οργάνωση των πτήσεων ενός αεροδρομίου. Ένα χρονικό μονοπάτι (ή «ταξίδι») σε ένα χρονικό γράφημα είναι ένα μονοπάτι, στις ακμές του οποίου μπορούμε να βρούμε αυστηρά αύξουσα σειρά χρονικών ετικετών. Στην εργασία, μεταξύ άλλων, γίνεται μελέτη της συνδετικότητας στα χρονικά γραφήματα, καθώς και κατασκευή και μελέτη αλγορίθμων εύρεσης χρονικών μονοπατιών («ταξιδίων») που φθάνουν το δυνατόν συντομότερα στον προορισμό τους (τελική κορυφή μονοπατιού). Επιπλέον, μελετώνται στατιστικά τα Χρονικά Γραφήματα, με επικέντρωση στο αναμενόμενο πλήθος χρονικών μονοπατιών σε ένα γράφημα, καθώς και στη Χρονική Διάμετρο ενός γραφήματος, όπως αυτή ορίζεται στην εργασία. / In the thesis, we are dealing with a new type of graphs,called Temporal Graphs, and several variants. A temporal graph is an ordered triplet G={V,E,L}, where V stands for a nonempty finite set (called set of vertices), E stands for a set of m elements, each of which are 2-element subsets of V (called set of edges), and L= {L_e, for all e in E} = {L_e_1, L_e_2, ..., L_e_m}, where L_e_i, i = 1, ..., m, is a set of positive integers mapped to edge e_i in E (called assignment of time labels or simply assignment). The values assigned to each edge of the graph are called time labels of the edge and indicate the times at which we can cross it (from one end to the other). In order to understand the interest of temporal graphs, one may think their applicability to everyday life. For example, the time labels assigned to an edge of a directed temporal graph can be paralleled to the flight departure times from one city to another. Therefore, the study of temporal graphs could contribute to the organization of flights at an airport. A temporal path (or «journey») in a temporal graph is a path, on the edges of which we can find strictly ascending time labels. In the thesis, among others, we study the connectivity of temporal graphs and we construct and study several algorithms that find temporal paths which arrive the soonest possible at their destination (final vertice of the path). Furthermore, we examine temporal graphs statistically, focusing on the expected number of temporal paths in a graph as well as in the Temporal Diameter of a graph, also defined in the thesis.

In der vorliegenden Arbeit untersuchte ich die komplexen Strukturen von Netzwerken, deren zeitliche Entwicklung, die Interpretationen von verschieden Netzwerk-Massen und die Klassen der Prozesse darauf. Als Erstes leitete ich Masse für die Charakterisierung der zeitlichen Entwicklung der Netzwerke her, um räumlich Veränderungsmuster zu erkennen. Als Nächstes führe ich eine neue Methode zur Konstruktion komplexer Netzwerke von Flussfeldern ein, bei welcher man das Set-up auch rein unter Berufung Berufung auf das Geschwindigkeitsfeld ändern kann. Diese Verfahren wurden für die Korrelationen skalarer Grössen, z. B. Temperatur, entwickelt, welche eine Advektions-Diffusions-Dynamik in der Gegenwart von Zwingen und Dissipation. Die Flussnetzwerk-Methode zur Zeitreihenanalyse konstruiert die Korrelationsmatrizen und komplexen Netzwerke. Dies ermöglicht die Charakterisierung von Transport in Flüssigkeiten, die Identifikation verschiedene Misch-Regimes in dem Fluss und die Anwendung auf die Advektions-DiffusionsDynamik, Klimadaten und anderen Systemen, in denen Teilchentransport eine entscheidende Rolle spielen. Als Letztes, entwickelte ich ein neuartiges Heterogener Opinion Status Modell (HOpS) und Analysetechnik basiert auf Random Walks und Netzwerktopologie Theorien, um dynamischen Prozesse in Netzwerken zu studieren, wie die Verbreitung von Meinungen in sozialen Netzwerken oder Krankheiten in der Gesellschaft. Ein neues Modell heterogener Verbreitung auf einem Netzwerk wird als Beispielssystem für HOpS verwendent, um die vergleichsweise Einfachheit zu nutzen. Die Analyse eines diskreten Phasenraums des HOPS-Modells hat überraschende Eigenschaften, welches sensibel auf die Netzwerktopologie reagieren. Sie können verallgemeinert werden, um verschiedene Klassen von komplexen Netzwerken zu quantifizieren, Transportphänomene zu charakterisieren und verschiedene Zeitreihen zu analysieren. / In the thesis I studied the complex architectures of networks, the network evolution in time, the interpretation of the networks measures and a particular class of processes taking place on complex networks. Firstly, I derived the measures to characterize temporal networks evolution in order to detect spatial variability patterns in evolving systems. Secondly, I introduced a novel flow-network method to construct networks from flows, that also allows to modify the set-up from purely relying on the velocity field. The flow-network method is developed for correlations of a scalar quantity (temperature, for example), which satisfies advection-diffusion dynamics in the presence of forcing and dissipation. This allows to characterize transport in the fluids, to identify various mixing regimes in the flow and to apply this method to advection-diffusion dynamics, data from climate and other systems, where particles transport plays a crucial role. Thirdly, I developed a novel Heterogeneous Opinion-Status model (HOpS) and analytical technique to study dynamical processes on networks. All in all, methods, derived in the thesis, allow to quantify evolution of various classes of complex systems, to get insight into physical meaning of correlation networks and analytically to analyze processes, taking place on networks.

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.

Les réseaux sont des modèles qui nous permettent de comprendre les relations entre éléments du monde réel. Une grande quantité de réseaux sont dynamiques, c'est-à-dire que leur connexité change au cours du temps. Comprendre les changements de connexité signifie comprendre les interactions entre les éléments de systèmes complexes: comment se forment les relations sociales et commerciales, comment sont transmis les signaux entre les régions du cerveau, comment s'organisent les réseaux trophiques après des catastrophes environnementales. Au-delà de ce que nous permettent la technologie et les algorithmes d'analyses, l'homme dispose d'une capacité unique pour comprendre et interpréter des informations : la vision et la cognition. Cette thèse développe et examine des moyens pour explorer les réseaux dynamiques d'une manière interactive et visuelle. Je propose des techniques pour déplier la complexité des réseaux, avec le but de les rendre compréhensibles, de les voir à partir de perspectives différentes, d'examiner leurs composantes. Déplier des réseaux est une métaphore, comme la création des cartes bidimensionelles d'objets tridimensionnels comme la Terre: chaque méthode de projection a comme résultat une carte différente qui permet de voir des relations différentes entre la taille des continents et des océans, des distances, etc. Je propose les techniques de dépliage suivantes, implémentées et évaluées dans des systèmes interactifs : (i) une navigation temporelle qui permet de naviguer plus efficacement entre des différents instants, ainsi qu'un feedback visuel qui permet de mieux comprendre les changements dans les réseaux entre deux instants arbitraires. (ii) Des designs permettant la comparaison directe de deux réseaux avec des liens pondérés. (iii) Un modèle de visualisation pour des réseaux denses avec des liens pondérés, ainsi que (iv) la génération de réseaux synthétiques utilisés pour l'évaluation des visualisations. Afin de mieux créer et évaluer des visualisations, nous (v) proposons une taxonomie de tâche pour décrire des tâches accomplies par des analystes des réseaux. Pour compléter, (vi) nous généralisons l'idée de dépliage pour décrire d'autres genres de données temporelles, représentable dans des cubes espace-temps. Cela concerne la visualisation de vidéos, des données multi-variées, ainsi que la géographique. Une telle généralisation a pour but de fournir une base commune pour échanger des techniques de visualisation et de mieux comprendre l'espace de design pour les réseaux dynamiques. Dans cette optique, nous proposons une taxonomie d'opérations génériques qui nous permet de transformer un cube espace-temps en visualisation bidimensionelle, ainsi qu'une description des formes évoquées par les données dans le cube espace-temps. / 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.

Cyber attacks are ubiquitous and increasingly prevalent in industry, society, and governmental departments. They affect the economy, politics, and individuals. Ever-increasingly skilled, organized, and funded threat actors combined with ever-increasing volumes and modalities of data require increasingly sophisticated and innovative cyber defense solutions. Current state-of-the-art security systems conduct threat detection on dynamic graph representations of computer systems and enterprise communication networks known as provenance graphs. Most of these security systems are statistics-based, based on rules defined by domain experts, or discard temporal information, and as such come with a set of drawbacks (e.g., incapability to pinpoint the attack, incapability to adapt to evolving systems, reduced expressibility due to lack of temporal information). At the same time, there is little research in the machine learning community on graphs such as provenance graphs, which are a form of largescale, heterogeneous, and continuous-time dynamic graphs, as most research on graph learning has been devoted to static homogeneous graphs to date. Therefore, this thesis aims to bridge these two fields and investigate the potential of learning-based methods operating on continuous-time dynamic provenance graphs for cyber threat detection. Without loss of generality, this work adopts the general Temporal Graph Networks framework for learning representations and detecting anomalies in such graphs. This method explicitly addresses the drawbacks of current security systems by considering the temporal setting and bringing the adaptability of learning-based methods. In doing so, it also introduces and releases two large-scale, continuoustime temporal, heterogeneous benchmark graph datasets with expert-labeled anomalies to foster future research on representation learning and anomaly detection on complex real-world networks. To the best of the author’s knowledge, these are one of the first datasets of their kind. Extensive experimental analyses of modules, datasets, and baselines validate the potency of continuous-time graph neural network-based learning, endorsing its practical applicability to the detection of cyber threats and possibly other semantically meaningful anomalies in similar real-world systems. / Cyberattacker är allestädes närvarande och blir allt vanligare inom industrin, samhället och statliga myndigheter. De påverkar ekonomin, politiken och enskilda individer. Allt skickligare, organiserade och finansierade hotaktörer i kombination med ständigt ökande volymer och modaliteter av data kräver alltmer sofistikerade och innovativa cyberförsvarslösningar. Dagens avancerade säkerhetssystem upptäcker hot på dynamiska grafrepresentationer (proveniensgrafer) av datorsystem och företagskommunikationsnät. De flesta av dessa säkerhetssystem är statistikbaserade, baseras på regler som definieras av domänexperter eller bortser från temporär information, och som sådana kommer de med en rad nackdelar (t.ex. oförmåga att lokalisera attacken, oförmåga att anpassa sig till system som utvecklas, begränsad uttrycksmöjlighet på grund av brist på temporär information). Samtidigt finns det lite forskning inom maskininlärning om grafer som proveniensgrafer, som är en form av storskaliga, heterogena och dynamiska grafer med kontinuerlig tid, eftersom den mesta forskningen om grafinlärning hittills har ägnats åt statiska homogena grafer. Därför syftar denna avhandling till att överbrygga dessa två områden och undersöka potentialen hos inlärningsbaserade metoder som arbetar med dynamiska proveniensgrafer med kontinuerlig tid för detektering av cyberhot. Utan att för den skull göra avkall på generaliserbarheten använder detta arbete det allmänna Temporal Graph Networks-ramverket för inlärning av representationer och upptäckt av anomalier i sådana grafer. Denna metod tar uttryckligen itu med nackdelarna med nuvarande säkerhetssystem genom att beakta den temporala induktiva inställningen och ge anpassningsförmågan hos inlärningsbaserade metoder. I samband med detta introduceras och släpps också två storskaliga, kontinuerliga temporala, heterogena referensgrafdatauppsättningar med expertmärkta anomalier för att främja framtida forskning om representationsinlärning och anomalidetektering i komplexa nätverk i den verkliga världen. Såvitt författaren vet är detta en av de första datamängderna i sitt slag. Omfattande experimentella analyser av moduler, dataset och baslinjer validerar styrkan i induktiv inlärning baserad på kontinuerliga grafneurala nätverk, vilket stöder dess praktiska tillämpbarhet för att upptäcka cyberhot och eventuellt andra semantiskt meningsfulla avvikelser i liknande verkliga system.

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.

Dans le domaine de la biologie développementale, un des principaux défis est de comprendre comment des tissus multicellulaires, à l'origine indifférenciés, peuvent engendrer des formes aussi complexes que celles d'une fleur. De part son implication dans l'organogenèse florale, l'auxine est une phytohormone majeure. Nous avons donc déterminé son réseau binaire potentiel, puis y avons appliqué des modèles de clustering de graphes s'appuyant sur les profils de connexion présentés par ces 52 facteurs de transcription (FT). Nous avons ainsi pu identifier trois groupes, proches des groupes biologiques putatifs: les facteurs de réponse à l'auxine activateurs (ARF+), répresseurs (ARF-) et les Aux/IAAs. Nous avons détecté l'auto-interaction des ARF+ et des Aux/IAA, ainsi que leur interaction, alors que les ARF- en présentent un nombre restreint. Ainsi, nous proposons un mode de compétition auxine indépendent entre ARF+ et ARF- pour la régulation transcriptionelle. Deuxièmement, nous avons modélisé l'influence des séquences de dimérisation des FT sur la structure de l'interactome en utilisant des modèles de mélange Gaussien pour graphes aléatoires. Les groupes obtenus sont proches des précédents, et les paramètres estimés nous on conduit à conclure que chaque sous-domaine peut jouer un rôle différent en fonction de leur proximité phylogénétique.Enfin, nous sommes passés à l'échelle multi-cellulaire ou, par un graphe spatio-temporel, nous avons modélisé les premiers stades du développement floral d'A. thaliana. Nous avons pu extraire des caractéristiques cellulaires (3D+t) de reconstruction d'imagerie confocale, et avons démontré la possibilité de caractériser l'identité cellulaire en utilisant des méthodes de classification hiérarchique et des arbres de Markov cachés. / A striking aspect of flowering plants is that, although they seem to display a great diversity of size and shape, they are made of the same basics constituents, that is the cells. The major challenge is then to understand how multicellular tissues, originally undifferentiated, can give rise to such complex shapes. We first investigated the uncharacterised signalling network of auxin since it is a major phytohormone involved in flower organogenesis.We started by determining the potential binary network, then applied model-based graph clustering methods relying on connectivity profiles. We demonstrated that it could be summarise in three groups, closely related to putative biological groups. The characterisation of the network function was made using ordinary differential equation modelling, which was later confirmed by experimental observations.In a second time, we modelled the influence of the protein dimerisation sequences on the auxin interactome structure using mixture of linear models for random graphs. This model lead us to conclude that these groups behave differently, depending on their dimerisation sequence similarities, and that each dimerisation domains might play different roles.Finally, we changed scale to represent the observed early stages of A. thaliana flower development as a spatio-temporal property graph. Using recent improvements in imaging techniques, we could extract 3D+t cellular features, and demonstrated the possibility of identifying and characterising cellular identity on this basis. In that respect, hierarchical clustering methods and hidden Markov tree have proven successful in grouping cell depending on their feature similarities.

With the arrival of 5G networks, telecommunication systems are becoming more intelligent, integrated, and broadly used. This thesis focuses on predicting the upcoming traffic to efficiently promote resource allocation, guarantee stability and reliability of the network. Since networks modeled as graphs potentially capture more information than tabular data, the construction of the graph and choice of the model are key to achieve a good prediction. In this thesis traffic prediction is based on a time-evolving graph, whose node and edges encode the structure and activity of the system. Edges are created by dynamic time-warping (DTW), geographical distance, and $k$-nearest neighbors. The node features contain different temporal information together with spatial information computed by methods from topological data analysis (TDA). To capture the temporal and spatial dependency of the graph several dynamic graph methods are compared. Throughout experiments, we could observe that the most successful model GConvGRU performs best for edges created by DTW and node features that include temporal information across multiple time steps. / Med ankomsten av 5G nätverk blir telekommunikationssystemen alltmer intelligenta, integrerade, och bredare använda. Denna uppsats fokuserar på att förutse den kommande nättrafiken, för att effektivt hantera resursallokering, garantera stabilitet och pålitlighet av nätverken. Eftersom nätverk som modelleras som grafer har potential att innehålla mer information än tabulär data, är skapandet av grafen och valet av metod viktigt för att uppnå en bra förutsägelse. I denna uppsats är trafikförutsägelsen baserad på grafer som ändras över tid, vars noder och länkar fångar strukturen och aktiviteten av systemet. Länkarna skapas genom dynamisk time warping (DTW), geografisk distans, och $k$-närmaste grannarna. Egenskaperna för noderna består av dynamisk och rumslig information som beräknats av metoder från topologisk dataanalys (TDA). För att inkludera såväl det dynamiska som det rumsliga beroendet av grafen, jämförs flera dynamiska grafmetoder. Genom experiment, kunde vi observera att den mest framgångsrika modellen GConvGRU presterade bäst för länkar skapade genom DTW och noder som innehåller dynamisk information över flera tidssteg.