Showing papers on "Network theory published in 2019"

Network Medicine in the Age of Biomedical Big Data.

Abstract: Network medicine is an emerging area of research dealing with molecular and genetic interactions, network biomarkers of disease, and therapeutic target discovery. Large-scale biomedical data generation offers a unique opportunity to assess the effect and impact of cellular heterogeneity and environmental perturbations on the observed phenotype. Marrying the two, network medicine with biomedical data provides a framework to build meaningful models and extract impactful results at a network level. In this review, we survey existing network types and biomedical data sources. More importantly, we delve into ways in which the network medicine approach, aided by phenotype-specific biomedical data, can be gainfully applied. We provide three paradigms, mainly dealing with three major biological network archetypes: protein-protein interaction, expression-based, and gene regulatory networks. For each of these paradigms, we discuss a broad overview of philosophies under which various network methods work. We also provide a few examples in each paradigm as a test case of its successful application. Finally, we delineate several opportunities and challenges in the field of network medicine. We hope this review provides a lexicon for researchers from biological sciences and network theory to come on the same page to work on research areas that require interdisciplinary expertise. Taken together, the understanding gained from combining biomedical data with networks can be useful for characterizing disease etiologies and identifying therapeutic targets, which, in turn, will lead to better preventive medicine with translational impact on personalized healthcare.

Application of Complex Networks Theory in Urban Traffic Network Researches

Abstract: Complex network theory is a multidisciplinary research direction of complexity science which has experienced a rapid surge of interest over the last two decades. Its applications in land-based urban traffic network studies have been fruitful, but have suffered from the lack of a systematic cognitive and integration framework. This paper reviews complex network theory related knowledge and discusses its applications in urban traffic network studies in several directions. This includes network representation methods, topological and geographical related studies, network communities mining, network robustness and vulnerability, big-data-based research, network optimization, co-evolution research and multilayer network theory related studies. Finally, new research directions are pointed out. With these efforts, this physics-based concept will be more easily and widely accepted by urban traffic network planners, designers, and other related scholars.

Inference for multiple heterogeneous networks with a common invariant subspace

Abstract: The development of models for multiple heterogeneous network data is of critical importance both in statistical network theory and across multiple application domains. Although single-graph inference is well-studied, multiple graph inference is largely unexplored, in part because of the challenges inherent in appropriately modeling graph differences and yet retaining sufficient model simplicity to render estimation feasible. This paper addresses exactly this gap, by introducing a new model, the common subspace independent-edge (COSIE) multiple random graph model, which describes a heterogeneous collection of networks with a shared latent structure on the vertices but potentially different connectivity patterns for each graph. The COSIE model encompasses many popular network representations, including the stochastic blockmodel. The model is both flexible enough to meaningfully account for important graph differences and tractable enough to allow for accurate inference in multiple networks. In particular, a joint spectral embedding of adjacency matrices - the multiple adjacency spectral embedding (MASE) - leads, in a COSIE model, to simultaneous consistent estimation of underlying parameters for each graph. Under mild additional assumptions, MASE estimates satisfy asymptotic normality and yield improvements for graph eigenvalue estimation and hypothesis testing. In both simulated and real data, the COSIE model and the MASE embedding can be deployed for a number of subsequent network inference tasks, including dimensionality reduction, classification, hypothesis testing and community detection. Specifically, when MASE is applied to a dataset of connectomes constructed through diffusion magnetic resonance imaging, the result is an accurate classification of brain scans by patient and a meaningful determination of heterogeneity across scans of different subjects.

The key player problem in complex oscillator networks and electric power grids: Resistance centralities identify local vulnerabilities

Abstract: Identifying key players in coupled individual systems is a fundamental problem in network theory. We investigate synchronizable network-coupled dynamical systems such as high-voltage electric power grids and coupled oscillators on complex networks. We define key players as nodes that, once perturbed, generate the largest excursion away from synchrony. A spectral decomposition of the coupling matrix gives an elegant solution to this identification problem. We show that, when the coupling matrix is Laplacian, key players are peripheral in the sense of a centrality measure defined from effective resistance distances. For linearly coupled systems, the ranking is efficiently obtained through a single Laplacian matrix inversion, regardless of the operational synchronous state. The resulting ranking index is termed LRank. When nonlinearities are present, a weighted Laplacian matrix inversion gives another ranking index, WLRank. LRank provides a faithful ranking even for well-developed nonlinearities, corresponding to oscillator angle differences up to approximately Δθ ≲ 40°.

Networks in Climate

Abstract: Over the last two decades the complex network paradigm has proven to be a fruitful tool for the investigation of complex systems in many areas of science; for example, the Internet, neural networks and social networks. This book provides an overview of applications of network theory to climate variability, such as the El Nino/Southern Oscillation and the Indian Monsoon, presenting recent important results obtained with these techniques and showing their potential for further development and research. The book is aimed at researchers and graduate students in climate science. A basic background in physics and mathematics is required. Several of the methodologies presented here will also be valuable to a broader audience of those interested in network science, for example, from biomedicine, ecology and economics.

Understanding the structural characteristics of a firm’s whole buyer–supplier network and its impact on international business performance

Abstract: Building on the network theory and the concept of organizational ambidexterity, we investigate the impact of structural characteristics of a firm’s whole buyer–supplier network: network density, betweenness centralization, and average clustering coefficient on its international business (IB) performance. We also explore the moderating roles of average path length and PageRank centrality. Using a manually-collected dataset and a robust empirical methodology, we find that, while network density is negatively related, betweenness centralization and average clustering coefficient have an inverted U-shape and a U-shaped relationship with IB performance, respectively. We also find significant moderation effects, and, in the process, we show the economic importance of firms’ whole buyer–supplier network to their IB performance. We contribute to the international business and whole buyer–supplier network literature.

A Centrality Measure for Urban Networks Based on the Eigenvector Centrality Concept.

Abstract: A massive amount of information as geo-referenced data is now emerging from the digitization of contemporary cities. Urban streets networks are characterized by a fairly uniform degree distribution...

Finding a Place for Networks in Archaeology

Abstract: Formal network analyses have a long history in archaeology but have recently seen a rapid florescence. Network models drawing on approaches from graph theory, social network analysis, and complexity science have been used to address a broad array of questions about the relationships among network structure, positions, and the attributes and outcomes for individuals and larger groups at a range of social scales. Current archaeological network research is both methodologically and theoretically diverse, but there are still many daunting challenges ahead for the formal exploration of social networks using archaeological data. If we can face these challenges, archaeologists are well positioned to contribute to long-standing debates in the broader sphere of network research on the nature of network theory, the relationships between networks and culture, and dynamics of social networks over the long term.

Measuring the complexity of complex network by Tsallis entropy

Abstract: Measuring the complexity degree of complex network has been an important issue of network theory. A number of complexity measures like structure entropy have been proposed to address this problem. However, these existing structure entropies are based on Shannon entropy which only focuses on global structure or local structure. To break the limitation of existing method, a novel structure entropy which is based on Tsallis entropy is introduced in this paper. This proposed measure combines the fractal dimension and local dimension which are both the significant property of network structure, and it would degenerate to the Shannon entropy based on the local dimension when fractal dimension equals to 1. This method is based on the dimension of network which is a different approach to measure the complexity degree compared with other methods. In order to show the performance of this proposed method, a series of complex networks which are grown from the simple nearest-neighbor coupled network and five real-world networks have been applied in this paper. With comparing with several existing methods, the results show that this proposed method performs well.

Learning Analytics to Support Teachers’ Assessment of Problem Solving: A Novel Application for Machine Learning and Graph Algorithms

Abstract: In contrast to well-structured problems which have pre-defined, correct answers, complex real-world problems are often ill-structured problems (ISPs). The open-ended nature of ISPs creates considerable barriers to assess and guide students in forming better solutions, which results in low adoption levels of inquiry-based learning. Students can structure and represent their knowledge for an ISP in the form of knowledge maps or causal maps, which articulate relevant concepts and their causal relations (i.e., antecedents and consequents). Assessing such maps can involve a referent-free evaluation (e.g., to encourage the creation of maps with high density of concepts) or a comparison to an expert map used as reference. This chapter starts with a review of theories and tools to compare a student’s map to the expert map. Previous approaches often compared individual connections (e.g., scoring the number of connections that a student has/misses in contrast with the expert) or general map metrics (e.g., one map is denser than the other). In contrast, the problem of comparing two maps has been studied in network theory and graph theory for several decades, yielding categories of algorithms that are currently underutilized in educational research. This chapter reviews three categories of algorithms (i.e., graph kernel, graph editing distance, graph embedding) in light of their application to assessment and student success. We discuss an implementation of these algorithms through a new set of digital tools, designed to support a community of practice in problem-based instruction.

The plant body as a network of semi-autonomous agents: a review.

Abstract: Plants can solve amazingly difficult tasks while adjusting their growth and development to the environment. They can explore and exploit several resources simultaneously, even when the distributions of these vary in space and time. The systematic study of plant behaviour goes back to Darwin's book The power of movement in plants. Current research has highlighted that modularity is a key to understanding plant behaviour, as the production, functional specialization and death of modules enable the plant to adjust its movement to the environment. The adjustment is assisted by a flow of information and resources among the modules. Experiments have yielded many results about these processes in various plant species. Theoretical research, however, has lagged behind the empirical studies, possibly owing to the lack of a proper modelling framework that could encompass the high number of components and interactions. In this paper, I propose such a framework on the basis of network theory, viewing the plant as a group of connected, semi-autonomous agents. I review some characteristic plant responses to the environment through changing the states of agents and/or links. I also point out some unexplored areas, in which a dialogue between plant science and network theory could be mutually inspiring. This article is part of the theme issue 'Liquid brains, solid brains: How distributed cognitive architectures process information'.

BioNetStat: A Tool for Biological Networks Differential Analysis

Abstract: The study of interactions among biological components can be carried out by using methods grounded on network theory. Most of these methods focus on the comparison of two biological networks (e.g., control vs. disease). However, biological systems often present more than two biological states (e.g., tumor grades). To compare two or more networks simultaneously, we developed BioNetStat, a Bioconductor package with a user-friendly graphical interface. BioNetStat compares correlation networks based on the probability distribution of a feature of the graph (e.g., centrality measures). The analysis of the structural alterations on the network reveals significant modifications in the system. For example, the analysis of centrality measures provides information about how the relevance of the nodes changes among the biological states. We evaluated the performance of BioNetStat in both, toy models and two case studies. The latter related to gene expression of tumor cells and plant metabolism. Results based on simulated scenarios suggest that the statistical power of BioNetStat is less sensitive to the increase of the number of networks than Gene Set Coexpression Analysis (GSCA). Also, besides being able to identify nodes with modified centralities, BioNetStat identified altered networks associated with signaling pathways that were not identified by other methods.

A Map of Approaches to Temporal Networks

Abstract: The study of temporal networks is motivated by the simple and important observation that just as network structure can affect dynamics, so can structure in time, and just as network topology can teach us about the system in question, so can its temporal characteristics. In many cases, leaving out either one of these components would lead to an incomplete understanding of the system or poor predictions. Including time into network modeling, we argue, inevitably leads researchers away from the trodden paths of network science. Temporal network theory requires something different—new methods, new concepts, new questions—compared to static networks. In this introductory chapter, we give an overview of the ideas that the field of temporal networks has brought forward in the last decade. We also place the contributions to the current volume on this map of temporal-network approaches.

Methodology of predicting novel key regulators in ovarian cancer network: a network theoretical approach

Abstract: Identification of key regulator/s in ovarian cancer (OC) network is important for potential drug target and prevention from this cancer. This study proposes a method to identify the key regulators of this network and their importance. The protein-protein interaction (PPI) network of ovarian cancer (OC) is constructed from curated 6 hundred genes from standard six important ovarian cancer databases (some of the genes are experimentally verified). We proposed a method to identify key regulators (KRs) from the complex ovarian cancer network based on the tracing of backbone hubs, which participate at all levels of organization, characterized by Newmann-Grivan community finding method. Knockout experiment, constant Potts model and survival analysis are done to characterize the importance of the key regulators in regulating the network. The PPI network of ovarian cancer is found to obey hierarchical scale free features organized by topology of heterogeneous modules coordinated by diverse leading hubs. The network and modular structures are devised by fractal rules with the absence of centrality-lethality rule, to enhance the efficiency of signal processing in the network and constituting loosely connected modules. Within the framework of network theory, we device a method to identify few key regulators (KRs) from a huge number of leading hubs, that are deeply rooted in the network, serve as backbones of it and key regulators from grassroots level to complete network structure. Using this method we could able to identify five key regulators, namely, AKT1, KRAS, EPCAM, CD44 and MCAM, out of which AKT1 plays central role in two ways, first it serves as main regulator of ovarian cancer network and second serves as key cross-talk agent of other key regulators, but exhibits disassortive property. The regulating capability of AKT1 is found to be highest and that of MCAM is lowest. The popularities of these key hubs change in an unpredictable way at different levels of organization and absence of these hubs cause massive amount of wiring energy/rewiring energy that propagate over all the network. The network compactness is found to increase as one goes from top level to bottom level of the network organization.

Combining network theory with corporate governance: converging models for connected stakeholders

Abstract: JEL Classification: G32, K22, M13, M21, O31 DOI: 10.22495/cocv17i1art12 Traditional corporate governance patterns are based on the interaction among composite stakeholders and the various forms of separation between ownership and control. Stakeholders cooperate around the Coasian firm represented by a nexus of increasingly complex contracts. These well-known occurrences have been deeply investigated by growing literature and nurtured by composite empirical evidence. Apparently, unrelated network theory is concerned with the study of graphs as a representation of (a)symmetric relations between discrete objects (nodes connected by links). Network theory is highly interdisciplinary, and its versatile nature is fully consistent with the complex interactions of (networked) stakeholders, even in terms of gametheoretic patterns. The connection between traditional corporate governance issues and network theory properties is, however, still under-investigated. Hence the importance of an innovative reinterpretation that brings to “network governance”. Innovation may, for instance, concern the principal-agent networked relationships and their conflicts of interest or the risk contagion and value drivers – three core governance issues. Networks and their applications (like blockchains, P2P platforms, game-theoretic interactions or digital supply chains) foster unmediated decentralization. In decentralized digital platforms stakeholders inclusively interact, promoting cooperation and sustainability. To the extent that network properties can be mathematically measured, governance issues may be quantified and traced with recursive patterns of expected occurrences.

Large-Scale Network Reduction Towards Scale-Free Structure

Abstract: This paper deals with a particular problem of graph reduction. The reduced graph is aimed to have a particular structure, namely to be scale-free. To this end, we define a metric to measure the scale-freeness by measuring the difference between the degree distribution and the scale-free degree distribution. The reduction is made under constraints to preserve consistency with the initial graph. In particular, the reduced graph preserves the eigenvector centrality of the initial graph. We study the optimization problem and, based on the gained insights, we derive an algorithm allowing to find an approximate solution. We also show that, if the initial network is a flow network, it is possible to design the algorithm such that the output remains a flow network. Experimental results are then presented to optimally choose the parameters of the algorithm suggesting that, by tuning a parameter, it is possible to speed up the algorithm with a comparable efficiency. Finally, the algorithm is applied to an example of large physical network: the Grenoble urban traffic network.

Teoria de Redes de Influências de "Stakeholders": uma abordagem revisitada

Abstract: The interactions among multiple stakeholders have gained importance in the last decades, given the speed information spreads and connections established between individuals and groups. However, there is still a research gap, which is the lack of consolidation of the empirical studies that analyzed the phenomenon of stakeholder networks and their contribution to the advancement of the theory. This work aims to investigate the evolution of the stakeholder networks approach in the last 20 years, that is, to revisit Rowley’s theory (1997) and to bring a panorama of its evolution to the present day. This essay is based on two research scopes: Network Theories - society in networks and interoganizational networks and Theory of Stakeholders, integrated into the composition of Rowley’s proposal (1997) - Network Theory of Stakeholders Influences. From a sociometric analysis and systematic review of 228 articles collected from the Web of Science database between 1997 and 2017, it was possible to analyze the evolution of this approach. The study indicates that recent research shifts the focus of the relations with the stakeholders, centered in the organization, to those of a decentralized network with several actors. In addition, there is a trend of studies of networks formed by groups of stakeholders and the social identities of individuals members of these groups. This study contributes to the field by presenting an overview of the Network Theory of Stakeholder Influences analyzing reference networks, theoretical and empirical contributions, trends and research agenda for the theme, which will help in the development of future works.

Supply chain technologies, interorganizational network and firm performance

Abstract: Supply chain management literature recognizes that interorganizational networks provide resources that convey critical benefits, such as capital, competitive advantage and efficient strategy implementation. The purpose of this paper is to leverage network theory and identify technological innovations as the antecedents for organizations to achieve stronger interorganizational networks. Specifically, this paper investigates how supply chain technologies of its logistics affiliate, Cainiao Network (CN), affect Alibaba Group’s three fundamental network mechanisms reachability, richness and receptivity and how interorganizational networks subsequently drive Alibaba Group’s performance.,A case study approach was chosen as a methodology to develop an in-depth understanding of the proposed innovations-network-performance framework.,Results indicate that innovative technologies positively lead to network reachability, richness and receptivity. Stronger interorganizational networks directly lead to higher performance. In addition, CN is identified as a unique innovative business model.,The key contribution of this research is that it investigates Alibaba Group’s performance from a network and innovation perspective. It identifies technological innovations as a key driver for stronger interorganizational networks. Furthermore, three network mechanisms are introduced and investigated as the antecedents of organizational performance. This research also provides a comprehensive description of Alibaba Group and CN.

Travel in city road networks follows similar transport trade-off principles to neural and plant arbors.

Abstract: Both engineered and biological transportation networks face trade-offs in their design. Network users desire to quickly get from one location in the network to another, whereas network planners need to minimize costs in building infrastructure. Here, we use the theory of Pareto optimality to study this design trade-off in the road networks of 101 cities, with wide-ranging population sizes, land areas and geographies. Using a simple one parameter trade-off function, we find that most cities lie near the Pareto front and are significantly closer to the front than expected by alternate design structures. To account for other optimization dimensions or constraints that may be important (e.g. traffic congestion, geography), we performed a higher-order Pareto optimality analysis and found that most cities analysed lie within a region of design space bounded by only four archetypal cities. The trade-offs studied here are also faced and well-optimized by two biological transport networks-neural arbors in the brain and branching architectures of plant shoots-suggesting similar design principles across some biological and engineered transport systems.

The Evolution and Growth Patterns of the Road Network in a Medium-Sized Developing City: A Historical Investigation of Changchun, China, from 1912 to 2017

Abstract: Understanding the evolution and growth patterns of urban road networks helps to design an efficient and sustainable transport network. The paper proposed a general study framework and analytical workflow based on network theory that could be applied to almost any city to analyze the temporal evolution of road networks. The main tasks follow three steps: vector road network drawing, topology graph generation, and measure classification. Considering data availability and the limitations of existing studies, we took Changchun, China, a middle-sized developing city that is seldom reported in existing studies, as the study area. The research results of Changchun (1912–2017) show the road networks sprawled and densified over time, and the evolution patterns depend on the historical periods and urban planning modes. The evolution of network scales exhibits significant correlation; the population in the city is well correlated with the total road length and car ownership. Each network index also presents specific rules. All road networks are small-world networks, and the arterial roads have been consistent over time; however, the core area changes within the adjacent range but is generally far from the old city. More importantly, we found the correlation between structure and function of the urban road networks in terms of the temporal evolution. However, the temporal evolution pattern shows the correlation varies over time or planning modes, which had not been reported

Leveraging Network Theory and Stress Tests to Assess Interdependencies in Critical Infrastructures

Abstract: Many modern critical infrastructures manifest reciprocal dependencies at various levels and on a time-evolving scale. Network theory has been exploited in the last decades to achieve a better understanding of topologies, correlations and propagation paths in case of perturbations. The discipline is providing interesting insights into aspects such as fragility and robustness of different network layouts against various types of threats, despite the difficulties arising in the modeling of the associated processes and entity relationships. Indeed, the evolution of infrastructures is not, in general, the straightforward outcome of a comprehensive a priori design. Rather, factors such as societal priorities, technical and budgetary constraints, critical events and the quest for better and cost-effective services induce a continuous change, while new kinds of interdependencies emerge. As a consequence, mapping emerging behavior can constitute a challenge and promote the development of innovative approaches to analysis and management. Among them, stress tests are entering the stage in order to assess networked infrastructures and reveal the associated operational boundaries and risk exposures. In this chapter, we first overview key developments of network science and its applications to primary infrastructure sectors. Secondly, we address the implementation of network-theoretical concepts in actions related to resilience enhancement, referring in particular to the case of stress tests in the banking sector. Finally, a discussion on the relevance of those concepts to critical infrastructure governance is provided.

Blockchain Economic Networks: Economic Network Theory—Systemic Risk and Blockchain Technology

Abstract: This chapter discusses how the widespread adoption of blockchain technology (distributed ledgers) might contribute to solving a larger class of economic problems related to systemic risk, specifically the degree of systemic risk in financial networks (ongoing credit relationships between parties). The chapter introduces economic network theory, drawing from Konig and Battiston (2009). Then, Part I develops payment network analysis (analyzing immediate cash transfers) in the classical payment network setting (Fedwire (Soramaki 2007)) synthesized with the cryptocurrency environment (Bitcoin (Maesa 2017), Monero (Miller 2017), and Ripple (Moreno-Sanchez et al. 2018)). The key finding is that the replication of network statistical behavior in cryptographic networks indicates the robust (not merely anecdotal) adoption of blockchain systems. Part II addresses balance sheet network analysis (ongoing obligations over time), first from the classical sense of central bank balance sheet network analysis developed by Castren (2009, 2013), Gai and Kapadia (2010), and Chan-Lau (2010), and then proposes how blockchain economic networks might help solve systemic risk problems. The chapter concludes with the potential economic and social benefits of blockchain economic networks, particularly as a new technological affordance is created, algorithmic trust, to support financial systems.

Security assessment and key management in a quantum network.

Abstract: Quantum key distribution allows secure key distribution between remote communication parties. In a quantum network, multiple users are connected by quantum links for key distribution and classical links for encrypted data transmission. When the quantum network structure becomes complicated with a large number of users, it is important to investigate network issues, including security, key management, latency, reliability, scalability, and cost. In this work, we utilize the classical network theory and graph theory to establish a framework for a quantum network, addressing two critical issues, security and key management. First, we design a communication scheme with the highest security level that trusts a minimum number of intermediate nodes. Second, when the quantum key is a limited resource, we design key management and data scheduling schemes to optimize the utility of data transmission. Our results can be directly applied to the current metropolitan and free-space quantum network implementations and can potentially be a standard approach for future quantum network designs.

Network Position Advantage and Technological Innovation of China’s New Energy Vehicle Based on the Perspective of Network Theory

Abstract: This paper attempts to explore the role of innovation networks in the new energy vehicle industry from the perspective of evolution, by integrating of the overall network and the entities’ microscopic features and designing relative variables. Based on market orientation theory social network analysis, the relationship between network location and technological niche and the role of the network relationship strength was examined through empirical data of China’s 2009–2017 patents for new energy vehicles. The results show that: (1) There is an inverted U-shaped relationship between the central position and the technological niche “state” and “potential”; (2) There is an inverted U-shaped relationship between the brokerage position and the entities’ technological niche “state”, and the inverted U-shaped relationship with the technological niche “potential” is not significant; (3) The overall relationship strength of the network modulates the inverted U relationship between the central location and the technological niche. This paper opens up new ideas for the research of the role of innovation networks. The research conclusions have important implications for the management practice of new energy vehicle industries in China through collaborative networks to achieve technological innovation.

Football pass network based on the measurement of player position by using network theory and clustering

Abstract: The present study proposed the new method to create a pass network based on the measurement of the pass positions. The pass positions were determined from the player positions measured by the autom...

Graph-time signal processing : Filtering and sampling strategies

Abstract: The necessity to process signals living in non-Euclidean domains, such as signals defined on the top of a graph, has led to the extension of signal processing techniques to the graph setting. Among different approaches, graph signal processing distinguishes itself by providing a Fourier analysis of these signals. Analogously to the Fourier transform for time and image signals, the graph Fourier transform decomposes the graph signals decomposes in terms of the harmonics provided by the underlying topology. For instance, a graph signal characterized by a slow variation between adjacent nodes has a low frequency content. Along with the graph Fourier transform, graph filters are the key tool to alter the graph frequency content of a graph signal. This thesis focuses on graph filters that are performed distributively in the node domain–that is, each node needs to exchange information only within its neighbor to perform a given filtering operation. Similarly to the classical filters, we propose ways to design and implement distributed finite impulse response and infinite impulse response graph filters. One of the key contributions of this thesis is to bring the temporal dimension to graph signal processing and build upon a graph-time signal processing framework. This is done in different ways. First, we analyze the effects that the temporal variations on the graph signal and graph topology have on the filtering output. Second, we introduce the notion of joint graph-time filtering. Third, we presentpr a statistical analysis of the distributed graph filtering when the graph signal and the graph topology change randomly in time. Finally, we extend the sampling framework from the reconstruction of graph signals to the observation and tracking of time-varying graph processes. We characterize the behavior of the distributed autoregressivemoving average (ARMA) graph filters when the graph signal and the graph topology are time-varying. The latter analysis is exploited in two ways: i ) to quantify the limitations of graph filters in a dynamic environment, such as a moving sensors processing a time-varying signal in a sensor network; and i i ) to provide ways for filtering with low computation and communication complexity time-varying graph signals. We develop the notion of distributed graph-time filtering, which is an operation that jointly processes the graph frequencies of a time-varying graph signal on one hand and its temporal frequencies on the other hand. We propose distributed finite impulse response and infinite impulse response recursions to implement a two-dimensional graphtime filtering operation. Finally, we propose design strategies to find the filter coefficients that approximate a desired two-dimensional frequency response. We extend the analysis of graph filters to a stochastic environment, i.e., when the graph topology and the graph signal change randomly over time. By characterizing the first and second order moments of the filter output, we quantify the impact of the graph signal and the graph topology randomness into the distributed filtering operation. The latter allows us to develop the notion of graph filtering in the mean, which is also used to ease the computational burden of classical graph filters. Finally, we propose a sampling framework for time-varying graph signals. Particularly, when the graph signal changes over time following a state-space model, we extend the graph signal sampling theory to the tasks of observing and tracking the time-varying graph signal froma few relevant nodes. The latter theory considers the graph signal sampling as a particular case and shows that tools from sparse sensing and sensor selection can be used for sampling.