Clustering and Community Detection in Directed Networks: A Survey

Networks (or graphs) appear as dominant structures in diverse domains, including sociology, biology, neuroscience and computer science. In most of the aforementioned cases graphs are directed - in the sense that there is directionality on the edges, making the semantics of the edges non symmetric. An interesting feature that real networks present is the clustering or community structure property, under which the graph topology is organized into modules commonly called communities or clusters. The essence here is that nodes of the same community are highly similar while on the contrary, nodes across communities present low similarity. Revealing the underlying community structure of directed complex networks has become a crucial and interdisciplinary topic with a plethora of applications. Therefore, naturally there is a recent wealth of research production in the area of mining directed graphs - with clustering being the primary method and tool for community detection and evaluation. The goal of this paper is to offer an in-depth review of the methods presented so far for clustering directed networks along with the relevant necessary methodological background and also related applications. The survey commences by offering a concise review of the fundamental concepts and methodological base on which graph clustering algorithms capitalize on. Then we present the relevant work along two orthogonal classifications. The first one is mostly concerned with the methodological principles of the clustering algorithms, while the second one approaches the methods from the viewpoint regarding the properties of a good cluster in a directed network. Further, we present methods and metrics for evaluating graph clustering results, demonstrate interesting application domains and provide promising future research directions.Comment: 86 pages, 17 figures. Physics Reports Journal (To Appear

Module Identification for Biological Networks

Advances in high-throughput techniques have enabled researchers to produce large-scale data on molecular interactions. Systematic analysis of these large-scale interactome datasets based on their graph representations has the potential to yield a better understanding of the functional organization of the corresponding biological systems. One way to chart out the underlying cellular functional organization is to identify functional modules in these biological networks. However, there are several challenges of module identification for biological networks. First, different from social and computer networks, molecules work together with different interaction patterns; groups of molecules working together may have different sizes. Second, the degrees of nodes in biological networks obey the power-law distribution, which indicates that there exist many nodes with very low degrees and few nodes with high degrees. Third, molecular interaction data contain a large number of false positives and false negatives. In this dissertation, we propose computational algorithms to overcome those challenges. To identify functional modules based on interaction patterns, we develop efficient algorithms based on the concept of block modeling. We propose a subgradient Frank-Wolfe algorithm with path generation method to identify functional modules and recognize the functional organization of biological networks. Additionally, inspired by random walk on networks, we propose a novel two-hop random walk strategy to detect fine-size functional modules based on interaction patterns. To overcome the degree heterogeneity problem, we propose an algorithm to identify functional modules with the topological structure that is well separated from the rest of the network as well as densely connected. In order to minimize the impact of the existence of noisy interactions in biological networks, we propose methods to detect conserved functional modules for multiple biological networks by integrating the topological and orthology information across different biological networks. For every algorithm we developed, we compare each of them with the state-of-the-art algorithms on several biological networks. The comparison results on the known gold standard biological function annotations show that our methods can enhance the accuracy of predicting protein complexes and protein functions

Probabilistic Random Walk Models for Comparative Network Analysis

Graph-based systems and data analysis methods have become critical tools in many fields as they can provide an intuitive way of representing and analyzing interactions between variables. Due to the advances in measurement techniques, a massive amount of labeled data that can be represented as nodes on a graph (or network) have been archived in databases. Additionally, novel data without label information have been gradually generated and archived. Labeling and identifying characteristics of novel data is an important first step in utilizing the valuable data in an effective and meaningful way. Comparative network analysis is an effective computational means to identify and predict the properties of the unlabeled data by comparing the similarities and differences between well-studied and less-studied networks. Comparative network analysis aims to identify the matching nodes and conserved subnetworks across multiple networks to enable a prediction of the properties of the nodes in the less-studied networks based on the properties of the matching nodes in the well-studied networks (i.e., transferring knowledge between networks). One of the fundamental and important questions in comparative network analysis is how to accurately estimate node-to-node correspondence as it can be a critical clue in analyzing the similarities and differences between networks. Node correspondence is a comprehensive similarity that integrates various types of similarity measurements in a balanced manner. However, there are several challenges in accurately estimating the node correspondence for large-scale networks. First, the scale of the networks is a critical issue. As networks generally include a large number of nodes, we have to examine an extremely large space and it can pose a computational challenge due to the combinatorial nature of the problem. Furthermore, although there are matching nodes and conserved subnetworks in different networks, structural variations such as node insertions and deletions make it difficult to integrate a topological similarity. In this dissertation, novel probabilistic random walk models are proposed to accurately estimate node-to-node correspondence between networks. First, we propose a context-sensitive random walk (CSRW) model. In the CSRW model, the random walker analyzes the context of the current position of the random walker and it can switch the random movement to either a simultaneous walk on both networks or an individual walk on one of the networks. The context-sensitive nature of the random walker enables the method to effectively integrate different types of similarities by dealing with structural variations. Second, we propose the CUFID (Comparative network analysis Using the steady-state network Flow to IDentify orthologous proteins) model. In the CUFID model, we construct an integrated network by inserting pseudo edges between potential matching nodes in different networks. Then, we design the random walk protocol to transit more frequently between potential matching nodes as their node similarity increases and they have more matching neighboring nodes. We apply the proposed random walk models to comparative network analysis problems: global network alignment and network querying. Through extensive performance evaluations, we demonstrate that the proposed random walk models can accurately estimate node correspondence and these can lead to improved and reliable network comparison results

Probabilistic Random Walk Models for Comparative Network Analysis

Graph-based systems and data analysis methods have become critical tools in many fields as they can provide an intuitive way of representing and analyzing interactions between variables. Due to the advances in measurement techniques, a massive amount of labeled data that can be represented as nodes on a graph (or network) have been archived in databases. Additionally, novel data without label information have been gradually generated and archived. Labeling and identifying characteristics of novel data is an important first step in utilizing the valuable data in an effective and meaningful way. Comparative network analysis is an effective computational means to identify and predict the properties of the unlabeled data by comparing the similarities and differences between well-studied and less-studied networks. Comparative network analysis aims to identify the matching nodes and conserved subnetworks across multiple networks to enable a prediction of the properties of the nodes in the less-studied networks based on the properties of the matching nodes in the well-studied networks (i.e., transferring knowledge between networks). One of the fundamental and important questions in comparative network analysis is how to accurately estimate node-to-node correspondence as it can be a critical clue in analyzing the similarities and differences between networks. Node correspondence is a comprehensive similarity that integrates various types of similarity measurements in a balanced manner. However, there are several challenges in accurately estimating the node correspondence for large-scale networks. First, the scale of the networks is a critical issue. As networks generally include a large number of nodes, we have to examine an extremely large space and it can pose a computational challenge due to the combinatorial nature of the problem. Furthermore, although there are matching nodes and conserved subnetworks in different networks, structural variations such as node insertions and deletions make it difficult to integrate a topological similarity. In this dissertation, novel probabilistic random walk models are proposed to accurately estimate node-to-node correspondence between networks. First, we propose a context-sensitive random walk (CSRW) model. In the CSRW model, the random walker analyzes the context of the current position of the random walker and it can switch the random movement to either a simultaneous walk on both networks or an individual walk on one of the networks. The context-sensitive nature of the random walker enables the method to effectively integrate different types of similarities by dealing with structural variations. Second, we propose the CUFID (Comparative network analysis Using the steady-state network Flow to IDentify orthologous proteins) model. In the CUFID model, we construct an integrated network by inserting pseudo edges between potential matching nodes in different networks. Then, we design the random walk protocol to transit more frequently between potential matching nodes as their node similarity increases and they have more matching neighboring nodes. We apply the proposed random walk models to comparative network analysis problems: global network alignment and network querying. Through extensive performance evaluations, we demonstrate that the proposed random walk models can accurately estimate node correspondence and these can lead to improved and reliable network comparison results

COMMUNITY DETECTION IN GRAPHS

Thesis (Ph.D.) - Indiana University, Luddy School of Informatics, Computing, and Engineering/University Graduate School, 2020Community detection has always been one of the fundamental research topics in graph mining. As a type of unsupervised or semi-supervised approach, community detection aims to explore node high-order closeness by leveraging graph topological structure. By grouping similar nodes or edges into the same community while separating dissimilar ones apart into different communities, graph structure can be revealed in a coarser resolution. It can be beneficial for numerous applications such as user shopping recommendation and advertisement in e-commerce, protein-protein interaction prediction in the bioinformatics, and literature recommendation or scholar collaboration in citation analysis. However, identifying communities is an ill-defined problem. Due to the No Free Lunch theorem [1], there is neither gold standard to represent perfect community partition nor universal methods that are able to detect satisfied communities for all tasks under various types of graphs. To have a global view of this research topic, I summarize state-of-art community detection methods by categorizing them based on graph types, research tasks and methodology frameworks. As academic exploration on community detection grows rapidly in recent years, I hereby particularly focus on the state-of-art works published in the latest decade, which may leave out some classic models published decades ago. Meanwhile, three subtle community detection tasks are proposed and assessed in this dissertation as well. First, apart from general models which consider only graph structures, personalized community detection considers user need as auxiliary information to guide community detection. In the end, there will be fine-grained communities for nodes better matching user needs while coarser-resolution communities for the rest of less relevant nodes. Second, graphs always suffer from the sparse connectivity issue. Leveraging conventional models directly on such graphs may hugely distort the quality of generate communities. To tackle such a problem, cross-graph techniques are involved to propagate external graph information as a support for target graph community detection. Third, graph community structure supports a natural language processing (NLP) task to depict node intrinsic characteristics by generating node summarizations via a text generative model. The contribution of this dissertation is threefold. First, a decent amount of researches are reviewed and summarized under a well-defined taxonomy. Existing works about methods, evaluation and applications are all addressed in the literature review. Second, three novel community detection tasks are demonstrated and associated models are proposed and evaluated by comparing with state-of-art baselines under various datasets. Third, the limitations of current works are pointed out and future research tracks with potentials are discussed as well

Computation in Complex Networks

Complex networks are one of the most challenging research focuses of disciplines, including physics, mathematics, biology, medicine, engineering, and computer science, among others. The interest in complex networks is increasingly growing, due to their ability to model several daily life systems, such as technology networks, the Internet, and communication, chemical, neural, social, political and financial networks. The Special Issue “Computation in Complex Networks" of Entropy offers a multidisciplinary view on how some complex systems behave, providing a collection of original and high-quality papers within the research fields of: • Community detection • Complex network modelling • Complex network analysis • Node classification • Information spreading and control • Network robustness • Social networks • Network medicin

Diffusion and Supercritical Spreading Processes on Complex Networks

Die große Menge an Datensätzen, die in den letzten Jahren verfügbar wurden, hat es ermöglicht, sowohl menschlich-getriebene als auch biologische komplexe Systeme in einem beispiellosen Ausmaß empirisch zu untersuchen. Parallel dazu ist die Vorhersage und Kontrolle epidemischer Ausbrüche für Fragen der öffentlichen Gesundheit sehr wichtig geworden. In dieser Arbeit untersuchen wir einige wichtige Aspekte von Diffusionsphänomenen und Ausbreitungsprozeßen auf Netzwerken. Wir untersuchen drei verschiedene Probleme im Zusammenhang mit Ausbreitungsprozeßen im überkritischen Regime. Zunächst untersuchen wir die Reaktionsdiffusion auf Ensembles zufälliger Netzwerke, die durch die beobachteten Levy-Flugeigenschaften der menschlichen Mobilität charakterisiert sind. Das zweite Problem ist die Schätzung der Ankunftszeiten globaler Pandemien. Zu diesem Zweck leiten wir geeignete verborgene Geometrien netzgetriebener Streuprozeße, unter Nutzung der Random-Walk-Theorie, her und identifizieren diese. Durch die Definition von effective distances wird das Problem komplexer raumzeitlicher Muster auf einfache, homogene Wellenausbreitungsmuster reduziert. Drittens führen wir durch die Einbettung von Knoten in den verborgenen Raum, der durch effective distances im Netzwerk definiert ist, eine neuartige Netzwerkzentralität ein, die ViralRank genannt wird und quantifiziert, wie nahe ein Knoten, im Durchschnitt, den anderen Knoten im Netzwerk ist. Diese drei Studien bilden einen einheitlichen Rahmen zur Charakterisierung von Diffusions- und Ausbreitungsprozeßen, die sich auf komplexen Netzwerken allgemein abzeichnen, und bieten neue Ansätze für herausfordernde theoretische Probleme, die für die Bewertung künftiger Modelle verwendet werden können.The large amount of datasets that became available in recent years has made it possible to empirically study humanly-driven, as well as biological complex systems to an unprecedented extent. In parallel, the prediction and control of epidemic outbreaks have become very important for public health issues. In this thesis, we investigate some important aspects of diffusion phenomena and spreading processes unfolding on networks. We study three different problems related to spreading processes in the supercritical regime. First, we study reaction-diffusion on ensembles of random networks characterized by the observed Levy-flight properties of human mobility. The second problem is the estimation of the arrival times of global pandemics. To this end, we derive and identify suitable hidden geometries of network-driven spreading processes, leveraging on random-walk theory. Through the definition of network effective distances, the problem of complex spatiotemporal patterns is reduced to simple, homogeneous wave propagation patterns. Third, by embedding nodes in the hidden space defined by network effective distances, we introduce a novel network centrality, called ViralRank, which quantifies how close a node is, on average, to the other nodes. These three studies constitute a unified framework to characterize diffusion and spreading processes unfolding on complex networks in very general settings, and provide new approaches to challenging theoretical problems that can be used to benchmark future models