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Graph Mining has gained importance due to its wide range of applications. As graph mining is a form of data mining where data is depicted in the form of graphs. The data when represented in the form of graphs helps to model the real scenario and relationship well. Discovery of interesting pattern from real relationship is of utmost beneficial. Frequent Subgraph Mining (FSM) is a significant area of graph mining. We accompany our approach in the field of FSM by adding a graph sampling function. This sampling function takes the single graph and a sampling percentage as input and produces a sampled graph which is similar in properties with original graph. This sampled graph is then taken as input while implementing the GraMi framework. Our sampling approach successfully mines the subgraphs with lower frequency threshold thus significantly improving the efficiency of the original GraMi framework.

Sampling is a widely used graph reduction technique to accelerate graph computations and simplify graph visualizations. By comprehensively analyzing the literature on graph sampling, we assume that existing algorithms cannot effectively preserve minority structures that are rare and small in a graph but are very important in graph analysis. In this work, we initially conduct a pilot user study to investigate representative minority structures that are most appealing to human viewers. We then perform an experimental study to evaluate the performance of existing graph sampling algorithms regarding minority structure preservation. Results confirm our assumption and suggest key points for designing a new graph sampling approach named mino-centric graph sampling (MCGS). In this approach, a triangle-based algorithm and a cut-point-based algorithm are proposed to efficiently identify minority structures. A set of importance assessment criteria are designed to guide the preservation of important minority structures. Three optimization objectives are introduced into a greedy strategy to balance the preservation between minority and majority structures and suppress the generation of new minority structures. A series of experiments and case studies are conducted to evaluate the effectiveness of the proposed MCGS.

Real-world network data can be incomplete (e.g., the social connections are partially observed) due to reasons such as graph sampling and privacy concerns. Consequently, communities detected based on such incomplete network information could be not as reliable as the ones identified based on the fully observed network. While existing studies first predict missing links and then detect communities, in this paper, a joint optimization framework, Communities detected on Predicted Edges, is proposed. Our goal to improve the quality of community detection through learning the probability of unseen links and the probability of community affiliation of nodes simultaneously. Link prediction and community detection are mutually reinforced to generate better results of both tasks. Experiments conducted on a number of well-known network data show that the proposed COPE stably outperforms several state-of-the-art community detection algorithms.

An increasing number of networks are becoming large-scale and continuously growing in nature, such that clustering on them in their entirety could be intractable. A feasible way to overcome this problem is to sample a representative subgraph and exploit its clustering structure (namely, sample clustering process). However, there are two issues that we should address in current studies. One underlying question is how to evaluate the clustering quality of the entire sample clustering process. Another non-trivial issue is that multiple ground-truths exist in networks, thus evaluating the clustering results in such scenario is also a challenging task. In this paper, first we utilize the set-matching methodology to quantitatively evaluate how differently the clusters of the sampled counterpart correspond to the ground-truth(s) in the original graph, and propose several new quality metrics to capture the differences of clustering structure in various aspects. Second, we put forward an evaluation framework for the general problems of evaluating the clustering quality on graph samples. Extensive experiments on various synthetic and real-world graphs demonstrate that our new quality metrics are more accurate and insightful for the sample clustering evaluation than conventional metrics (e.g., NMI). Thus the evaluation framework is effective and practical to assess the clustering quality of the sample clustering process on massive graphs.

Κατά την τελευταία δεκαετία, τα Διαδικτυακά Κοινωνικά Δίκτυα (ΔΚΔ) εξελίχθηκαν σε ένα νέο μέσο επικοινωνίας, κοινωνικής σύνδεσης και διαμοιρασμού πληροφορίας. Η έρευνα μας έχει ως στόχο, να μελετήσει την δομή, ιδιότητες, διάχυση πληροφορίας, προκαταλήψεις και χαρακτηριστικά αυτών των δικτύων. Η διατριβή χωρίζεται σε τρία διακριτά τμήματα, όπου κάθε τμήμα καλύπτει ένα συγκεκριμένο τομέα έρευνας, με τις αντίστοιχες επιστημονικές μας συνεισφορές. Αυτές είναι επάνω στην δειγματοληψίας δεδομένων σε διαδικτυακά περιβάλλοντα περιορισμένης πρόσβασης, δια-ΔΚΔ διάχυση πληροφορίας, κοινωνικά θέματα γύρω από τα ΔΚΔ και μελλοντικές δυνατότητες. Η πρώτη ενότητα καλύπτει θέματα δειγματοληψίας ΔΚΔ σε πραγματικό χρόνο. Πριν από την παρουσίασης μιας νέας μεθόδου δειγματοληψίας, παρουσιάζουμε μια εκτεταμένη ανασκόπηση της σχετικής βιβλιογραφίας. Καθώς για τον έλεγχο της πρότασης μας, χρησιμοποιήσαμε πολλαπλά πρόσφατα δείγματα από το Twitter, και συγκρίναμε την προτεινόμενη μέθοδο με καθιερωμένες μεθόδους δειγματοληψίας. Το δεύτερο κομμάτι της έρευνας μας καλύπτει τον τομέα της διάχυσης και διαμοιρασμό πληροφορίας σε πολλαπλά κοινωνικά δίκτυα, έναν τομέα όπου κατά την περίοδο της έρευνας μας δεν υπήρχε κάποια σχετική δημοσίευση. Πέρα από την βιβλιογραφική επισκόπηση, παρακολουθήσαμε και μελετήσαμε μια ποικιλία θεμάτων σε 3 διαφορετικά κοινωνικά δίκτυα. Τα αποτελέσματα αυτής της μελέτης παρουσιάζονται σε αυτό το κεφάλαιο. Κλείνοντας, μέσα από την εκτεταμένη εμπλοκή με τα σύγχρονα ΔΚΔ, παρατηρήσαμε πολλαπλά θέματα και αδυναμίες, όπως η ιδιωτικότητα και η έλλειψη προστασίας προσωπικών δεδομένων, που επικρατούν στα περισσότερα εξ αυτών. Όλα αυτά τα ζητήματα μαζί με την ιδέα ενός νέου ανώνυμου κοινωνικού δικτύου οδηγούμενο από την πληροφορία και όχι τους χρήστες, παρουσιάζονται στο τρίτο τμήμα της διατριβής. Οι συνεισφορές μας παρέχουν βαθιά γνώση και νέες λύσεις στον τομέα των ΔΚΔ, ενώ η θεματολογία μας έχει εύρος από την εξόρυξη δεδομένων και την διάχυση πληροφορίας έως τις διαδικτυακές προκαταλήψεις και θέμα ισότητας.

Graph sampling methods have been used to reduce the size and complexity of big complex networks for graph mining and visualization. However, existing graph sampling methods often fail to preserve the connectivity and important structures of the original graph. This paper introduces a new divide and conquer approach to spectral graph sampling based on graph connectivity, called the BC Tree (i.e., decomposition of a connected graph into biconnected components) and spectral sparsification. Specifically, we present two methods, spectral vertex sampling$$BC\_SV$$BC_SVand spectral edge sampling$$BC\_SS$$BC_SSby computing effective resistance values of vertices and edges for each connected component. Furthermore, we present$$DBC\_SS$$DBC_SSand$$DBC\_GD$$DBC_GD, graph connectivity-based distributed algorithms for spectral sparsification and graph drawing respectively, aiming to further improve the runtime efficiency of spectral sparsification and graph drawing by integrating connectivity-based graph decomposition and distributed computing. Experimental results demonstrate that$$BC\_SV$$BC_SVand$$BC\_SS$$BC_SSare significantly faster than previous spectral graph sampling methods while preserving the same sampling quality.$$DBC\_SS$$DBC_SSand$$DBC\_GD$$DBC_GDobtain further significant runtime improvement over sequential approaches, and$$DBC\_GD$$DBC_GDfurther achieves significant improvements in quality metrics over sequential graph drawing layouts.

Significance Numerous COVID-19 studies used mobile phone data but with limited power in accounting for infection numbers. We have evaluated deidentified Global Positioning System (GPS) data from over 1 million devices in Germany and inferred contacts from coproximity of devices. Through calculating the contact graphs, we derived a contact index (CX) that exhibits a high correlation with the incidence-based reproduction number R so that changes in CX precede those in R by more than 2 wk. CX thus is an early indicator for outbreaks and can be used to guide social-distancing policies. Further questions, including those for the efficacy of vaccination, can be addressed with our method. We discuss limitations, e.g., transmission on international travel, and the relation to superspreading., Over the last months, cases of SARS-CoV-2 surged repeatedly in many countries but could often be controlled with nonpharmaceutical interventions including social distancing. We analyzed deidentified Global Positioning System (GPS) tracking data from 1.15 to 1.4 million cell phones in Germany per day between March and November 2020 to identify encounters between individuals and statistically evaluate contact behavior. Using graph sampling theory, we estimated the contact index (CX), a metric for number and heterogeneity of contacts. We found that CX, and not the total number of contacts, is an accurate predictor for the effective reproduction number R derived from case numbers. A high correlation between CX and R recorded more than 2 wk later allows assessment of social behavior well before changes in case numbers become detectable. By construction, the CX quantifies the role of superspreading and permits assigning risks to specific contact behavior. We provide a critical CX value beyond which R is expected to rise above 1 and propose to use that value to leverage the social-distancing interventions for the coming months.

Multi-layer network visualization techniques have been developed so that users can firstly overview the largescale network and then explore the interesting parts of the data. Meanwhile, local features of the networks are often more interesting rather than their overall structures. It often happens with particular kinds of applications such as social networks. We developed a visualization technique for such types of large-scale networks. The technique iteratively applies a graph sampling algorithm to extract small-scale sub-networks from a large-scale network and then visualize the features of the sub-networks as hierarchically arranged icons. User-specified sub-networks are then visualized by applying our own graph visualization technique. Using networks generated from Twitter data, we actually visualize small-scale networks using the proposed method.

Many networks including spatial networks, social networks, and web networks, are not deterministic but probabilistic due to the uncertainty of link existence. From networks with such uncertainty, to extract densely connected nodes, we propose connectedness centrality and its extended version, group connectedness centrality, where the connectedness of each node is defined as the expected size of its connected component over all possible graphs produced by an uncertain graph. In a large-scale network, however, since the number of combinations of possible graphs is enormous, it is difficult to strictly calculate the expected value. Therefore, we also propose an efficient estimation method based on Monte Carlo sampling. When applying our method to road networks, the extracted nodes can be regarded as candidate sites of evacuation facilities that many residents can reach even in the situation where roads are stochastically blocked by natural disasters. In our experimental evaluations using actual road networks, we show the following promising characteristics: our proposed method 1) works stably with respect to the number of simulations; 2) extracts nodes set reachable from more nodes even in a situation that many links are deleted; and 3) computes much more efficient, compared to existing centrality measures and community extraction methods.

A crucial task in the process of constructing Internet testbeds is to substantially reduce the number of nodes in the interdomain Internet topology, while maintaining its essential properties. In this paper, we first decompose the Internet topology into seven bipartite graphs, a matching graph and a core graph using two normalized Laplacian spectral features, namely, the weighted spectral distribution and the multiplicity of the eigenvalue 1. Then, we accomplish a marked reduction in size of the topology by sampling and merging these graphs. The proposed approach was tested on realistic Internet graphs that were explored from 2000 to 2016 and a large-scale simulated graph. The experimental results confirm that our approach can effectively reduce the number of nodes in these graphs by more than 96%, while maintaining their essential properties.

Graph sampling methods have been used to reduce the size and complexity of big complex networks for graph mining and visualization. However, existing graph sampling methods often fail to preserve the connectivity and important structures of the original graph.

A graph contains plentiful structures. Some minority structures are important, such as high degree nodes and bridges. Detecting these minority structures is beneficial to accelerate computational graph analysis and improve the comprehension of graph visualization. Regarding four typical minority structures, this paper proposes two algorithms to detect these structures fast and efficiently. A set of experiments demonstrate the effectiveness of the proposed algorithms.

The Discrete Pulse Transform (DPT) makes use of LULU smoothing to decompose a signal into block pulses. The most recent and effective implementation of the DPT is an algorithm called the Roadmaker's Pavage, which uses a graph-based algorithm that produces a hierarchical tree of pulses as its final output, shown to have important applications in artificial intelligence and pattern recognition. Even though the Roadmaker's Pavage is an efficient implementation, the theoretical structure of the DPT results in a slow, deterministic algorithm. This paper examines the use of the spectral domain of graphs and designing graph filter banks to downsample the algorithm. We investigate the extent to which this speeds up the algorithm and allows parallel processing. Converting graph signals to the spectral domain can also be a costly overhead, so methods of estimation for filter banks are examined, as well as the design of a good filter bank that may be reused without needing recalculation. The sampled version requires different hyperparameters in order to reconstruct the same textures of the image as the original algorithm, selected previously either through trial and error (subjective) or grid search (costly) which prevented studying the results on many images effectively. Here an objective and efficient way of deriving similar results between the original Roadmaker's Pavage and our proposed Filtered Roadmaker's Pavage is provided. The method makes use of the Ht-index which separates the distribution of information in the graph at scale intervals by recursively calculating averages on decreasing subsections of the scale data stored. This has enabled empirical research using benchmark datasets providing improved results. The results of these empirical tests showed that using the Filtered Roadmaker's Pavage algorithm consistently runs faster, using less computational resources, while having a positive SSIM (structural similarity) with low variance. This provides an informative and faster approximation to the nonlinear DPT, a property which is not standardly achieveable.CATEGORIES: • Mathematics of Computing ~ Probability and Statistics • Probability and Statistics ~ Probabilistics Algorithms

Graph processing has become a topic of interest in many domains. However, we still observe a lack of representative datasets for in-depth performance and scalability analysis. Neither data collections, nor graph generators provide enough diversity and control for thorough analysis. To address this problem, we proposea heuristic method for scaling existing graphs. Our approach, based onsampling andinterconnection, can provide a scaled "version" of a given graph. Moreover, we provide analytical models to predict the topological properties of the scaled graphs (such as the diameter, degree distribution, density, or the clustering coefficient), and further enable the user to tweak these properties. Property control is achieved through a portfolio of graph interconnection methods (e.g., star, ring, chain, fully connected) applied for combining the graph samples. We further implement our method as an open-source tool which can be used to quickly provide families of datasets for in-depth benchmarking of graph processing algorithms. Our empirical evaluation demonstrates our tool provides scaled graphs of a wide range of sizes, whose properties match well with model predictions and/or user requirements. Finally, we also illustrate, through a case-study, how scaled graphs can be used for in-depth performance analysis of graph processing algorithms.

This paper proposes a new manifold-based dimension reduction algorithm framework. It can deal with the dimension reduction problem of data with noise and give the dimension reduction results with the deviation values caused by noise interference. Commonly used manifold learning methods are sensitive to noise in the data. Mean computation, a denoising method, is an important step in data preprocessing but leads to a loss of local structural information. In addition, it is difficult to measure the accuracy of the dimension reduction of noisy data. Thus, manifold learning methods often transform the data into an approximately smooth manifold structure; however, practical data from the physical world may not meet the requirements. The proposed framework follows the idea of the localization of manifolds and uses graph sampling to determine some local anchor points from the given data. Subsequently, the specific range of localities is determined using graph spectral analysis, and the density within each local range is estimated to obtain the distribution parameters. Then, manifold-based dimension reduction with distribution parameters is established, and the deviation values in each local range are measured and further extended to all data. Thus, our proposed framework gives a measurement method for deviation caused by noise.

In the graph signal processing literature, most methods were developed based on the assumption of Gaussian noise since it can lead to computationally efficient and mathematically tractable solutions. Unfortunately, the Gaussian distribution cannot capture the sharp spikes and tail heaviness of the signal noise in various natural phenomena. The α-stable distribution is a generalization of the Gaussian distribution and is a more appropriate model for such impulsive heavy-tailed noise. In this paper, we consider the problem of adaptive estimation and sparse sampling for signals defined over graphs in the presence of impulsive α-stable noise. To tackle the problems associated with α-stable noise, the graph signal estimation problem is formulated as a minimum dispersion (MD)-based optimization. A novel adaptive least mean pth power (LMP) algorithm is proposed for robust estimation of band-limited graph signals from partial observations in α-stable noise environments. The mean square performance of the proposed LMP algorithm is theoretically analyzed. To handle the case of band-limited graph signals with unknown and time-varying bandwidth and spectral contents, the sparse nature of the Graph Fourier transform of the signal is exploited to develop an adaptive graph sampling technique. Specifically, the proposed sparse sampling technique identifies the spectral signal support via sparse online estimation building on the iterative shrinkage-thresholding algorithm. Numerical simulation studies are presented to corroborate the performance advantages of the proposed adaptive estimation and sparse sampling algorithms. Refereed/Peer-reviewed

Sampling graphs is an important task in data mining. In this paper, we describe Little Ball of Fur a Python library that includes more than twenty graph sampling algorithms. Our goal is to make node, edge, and exploration-based network sampling techniques accessible to a large number of professionals, researchers, and students in a single streamlined framework. We created this framework with a focus on a coherent application public interface which has a convenient design, generic input data requirements, and reasonable baseline settings of algorithms. Here we overview these design foundations of the framework in detail with illustrative code snippets. We show the practical usability of the library by estimating various global statistics of social networks and web graphs. Experiments demonstrate that Little Ball of Fur can speed up node and whole graph embedding techniques considerably with mildly deteriorating the predictive value of distilled features., Comment: Code is available here: https://github.com/benedekrozemberczki/littleballoffur

While graphs capture pairwise relations between entities, hypergraphs deal with higher-order ones, thereby ensuring losslessness. However, in hyperlink (i.e., higher-order link) prediction, where hyperlinks and non-hyperlinks are treated as “positive” and “negative” classes respectively, hypergraphs suffer from the problem of extreme class imbalance. Given this context, “negative sampling”—under-sampling the negative class of non-hyperlinks—becomes mandatory for performing hyperlink prediction. No prior work on hyperlink prediction deals with this problem. In this work, which is the first of its kind, we deal with this problem in the context of hyperlink prediction. More specifically, we leverage graph sampling techniques for sampling non-hyperlinks in hyperlink prediction. Our analysis clearly establishes the effect of random sampling, which is the norm in both link- as well as hyperlink-prediction. Further, we formalize the notion of “hardness” of non-hyperlinks via a measure of density, and analyze its distribution over various negative sampling techniques. We experiment with some real-world hypergraph datasets and provide both qualitative and quantitative results on the effects of negative sampling. We also establish its importance in evaluating hyperlink prediction algorithms.

Random walk-based sampling methods are gaining popularity and importance in characterizing large networks. While powerful, they suffer from the slow mixing problem when the graph is loosely connected, which results in poor estimation accuracy. Random walk with jumps (RWwJ) can address the slow mixing problem but it is inapplicable if the graph does not support uniform vertex sampling (UNI). In this work, we develop methods that can efficiently sample a graph without the necessity of UNI but still enjoy the similar benefits as RWwJ. We observe that many graphs under study, called target graphs, do not exist in isolation. In many situations, a target graph is related to an auxiliary graph and a bipartite graph, and they together form a better connected {\em two-layered network structure}. This new viewpoint brings extra benefits to graph sampling: if directly sampling a target graph is difficult, we can sample it indirectly with the assistance of the other two graphs. We propose a series of new graph sampling techniques by exploiting such a two-layered network structure to estimate target graph characteristics. Experiments conducted on both synthetic and real-world networks demonstrate the effectiveness and usefulness of these new techniques., Comment: 14 pages, 17 figures, extended version

Dynamic network visualization is crucial to understand network evolving behavior. Massive sequence view (MSV) is a classic technique for visualizing dynamic networks and provides users with a fine-grained presentation of time-varying communication trend from both node pair and global network levels. However, MSV is vulnerable to visual clutter caused by overlapping edges, failing to show clear patterns or trends. This paper presents an edge sampling method, using the edge overlapping degree (EOD) concept, to reduce visual clutter in MSV while preserving the time-varying features of network communication. Referring to accept–reject sampling, we use kernel density estimation to characterize the time-varying features between node pairs and generate EOD probability density functions to accomplish sampling in a bottom-up manner. To enhance the sampling effect, we also consider the edge length factor and streaming processing. The case studies on two dynamic network data sets demonstrate that our method can significantly improve the overall readability of MSV and clearly reveal the temporal features of both node pairs and global network. A quantitative evaluation comparing with two other sampling methods using three real-world data sets indicates that our method can well balance visual clutter reduction and temporal feature preservation.

Graph sampling, simplying the networks while preserving primary graph characteristics, provides a convenient means for exploring large network. During the last few years a variety of graph sampling algorithms have been proposed, and the evaluation and comparison of the algorithms has witnessed a growing interest. Although different tests have been conducted, an important aspect of graph sampling, namely, uncertainty in graph sampling, has been ignored so far. Additionally, existing studies mainly rely on simple statistical analysis and a few relatively small datasets. They may not be applicable to other more complicated graphs with much larger numbers of nodes and edges. Furthermore, while graph clustering is becoming increasingly important, it is still unknown how different sampling algorithms and their associated uncertainty can impact the subsequent graph analysis, such as graph clustering. In this work, we propose an efficient visual analytics framework for measuring the uncertainty from different graph sampling methods and quantifying the influence of the uncertainty in general graph analysis procedures. A spreadsheet-style visualization with rich user interactions is presented to facilitate visual comparison and analysis of multiple graph sampling algorithms. Our framework helps users gain a better understanding of the graph sampling methods in producing uncertainty information. The framework also makes it possible for users to quickly evaluate graph sampling algorithms and select the most appropriate one for their applications.

Graph sampling is frequently used to address scalability issues when analyzing large graphs. Many algorithms have been proposed to sample graphs, and the performance of these algorithms has been quantified through metrics based on graph structural properties preserved by the sampling: degree distribution, clustering coefficient, and others. However, a perspective that is missing is the impact of these sampling strategies on the resultant visualizations. In this paper, we present the results of three user studies that investigate how sampling strategies influence node-link visualizations of graphs. In particular, five sampling strategies widely used in the graph mining literature are tested to determine how well they preserve visual features in node-link diagrams. Our results show that depending on the sampling strategy used different visual features are preserved. These results provide a complimentary view to metric evaluations conducted in the graph mining literature and provide an impetus to conduct future visualization studies.

Prior research has established that collaboration networks exhibit heavy-tailed degree distributions, assortative degree mixing, and large clustering coefficients. Using court record data, we assess these properties in a collaboration network among heroin traffickers. Consistent with prior research, we find an exponential degree distribution and strong local clustering. However, the traffickers mix dissortatively by degree rather than assortatively. Using a graph sampling method, we show that a consequence of dissortative mixing is that targeted vertex removals have a greater impact on the connectivity and cohesion of the trafficking network. We also note the importance of degree mixing for characterizing and identifying topological weaknesses.

Efficiently finding small samples with high diversity from large graphs has many practical applications such as community detection and online survey. This paper proposes a novel scalable node sampling algorithm for large graphs that can achieve better spread or diversity across communities intrinsic to the graph without requiring any costly pre-processing steps. The proposed method leverages a simple iterative sampling technique controlled by two parameters: infection rate, that controls the dynamics of the procedure and removal threshold that affects the end-of-procedure sampling size. We demonstrate that our method achieves very high community diversity with an extremely low sampling budget on both synthetic and real-world graphs, with either balanced or imbalanced communities. Additionally, we leverage the proposed technique for a very low sampling budget (only 2%) driven treatment assignment in Network A/B Testing scenario, and demonstrate competitive performance concerning baseline on both synthetic and real-world graphs.

This paper introduces a new vertex sampling method for big complex graphs, based on the spectral sparsification, a technique to reduce the number of edges in a graph while retaining its structural properties. More specifically, our method reduces the number of vertices in a graph while retaining its structural properties, based on the high effective resistance values. Extensive experimental results using graph sampling quality metrics, visual comparison and shape-based metrics confirm that our new method significantly outperforms the random vertex sampling and the degree centrality based sampling.

Graph sampling allows a multidimensional signal generated on a graph to be represented by the signal at a smaller set of sampled nodes. On the other hand, self-reset analog-to-digital converters (ADCs) are used to sample high dynamic range signals resulting in modulo-operation based folded signals at the sampled nodes. In this paper, we study the problem of continuous-time graph signal recovery from the folded signals at discrete samples. We present a theoretical graph sampling rate that is sufficient for successful reconstruction of the graph signals from the folded signals. We deduce an optimal sample rate to recover a bandlimited continuous-time graph signal, such that integer programming can be applied for small graphs. To resolve the scalability issue of integer programming, we propose a sparse optimization based recovery method for graph signals satisfying certain conditions. Such an approach requires a novel graph sampling scheme that selects nodes with small signal variation. The proposed algorithm emphasizes that in our spatio-temporal sampling scenario, the inherent relationship among the graph nodes should be exploited in addition to the temporal correlation in the graph signal at different nodes to recover the signal.

Graph sampling is often used to reduce a large graph, with challenges to ensure the sample is representative of the original graph. Spectral sparsification is a related concept that creates a sparsified version of graphs that preserves the spectrum of the original graph.We present TSS, a sampling method combining spectral sparsification with topology-based decomposition of graphs. TSS aims to improve the runtime efficiency of spectral sparsification-based sampling through a Divide-and-Conquer approach using topology-based decomposition and combine it with the superior sampling quality spectral sparsification-based sampling offers over stochastic sampling. We also present DTSS, the distributed version of TSS, aimed for further runtime gains over sequential TSS.Experiments verify that TSS produces samples of the same quality as spectral sparsification-based sampling while attaining significant runtime improvements of up to 60% on real world datasets. DTSS on 5 servers runs up to another 80% faster compared to TSS.

Massive Sequence View(MSV) is an important timeline-based technique for dynamic network visualization. However, it often suffers from severe visual clutter when limited screen space holds excessive network edges. Inspired by the use of graph sampling in static graph analysis, we propose to utilize graph sampling to reduce visual clutter in MSV. An edge sampling method based on accept-reject random sampling is designed for visualizing dynamic network via MSV. The method is able to improve the overall readability of MSV while preserving time varying network behaviors. It is also a preliminary attempt to apply graph-sampling technique into dynamic network analysis.

In this paper, we calculate the optimal sampling sets for bandlimited signals on cographs. We take into account the tree structure of the cograph to derive closed form results for the uniqueness sets of signals with a given bandwidth. These results do not require expensive spectral decompositions and represent a promising tool for the analysis of signals on graphs that can be approximated by cographs.

Current sampling techniques on graphs (i.e., network-structured data) mainly study static graphs and suppose that the whole graph is available at all times. However, a surge of graphs are becoming too large-scale and/or fully-dynamic (i.e., nodes and edges are added or deleted arbitrarily) to be handled with small memory footprint . Moreover, the intrinsic property (i.e., clustering structure) has been ignored and is not preserved well when the sampling performs. To solve these issues, we propose a Cluster-preserving Partially Induced Edge Sampling (CPIES ) algorithm that dynamically keep up-to-date samples in an online fashion and preserve the inherent clustering structure in streaming graphs. The experiments on various synthetic and real-world graphs demonstrated that the proposed CPIES algorithm is capable of preserving the inherent clustering structure while sampling from the fully-dynamic streaming graphs, and performs better than other competing algorithms in cluster-related properties .

Graph-sketching algorithms summarize an input graph G in a manner that suffices to later answer (perhaps approximately) one or more optimization problems on G, like distances, cuts, and matchings. Two famous examples are the Gomory-Hu tree, which represents all the minimum st-cuts in a graph G using a tree on the same vertex set V(G); and the cut-sparsifier of Benczúr and Karger, which is a sparse graph (often a reweighted subgraph) that approximates every cut in G within factor 1 +/- epsilon. Another genre of these problems limits the queries to designated terminal vertices, denoted T subseteq V(G), and the sketch size depends on |T| instead of |V(G)|. The talk will survey this topic, particularly cut and flow problems such as the three examples above. Currently, most known sketches are based on a graphical representation, often called edge and vertex sparsification, which leaves room for potential improvements like smaller storage by using another representation, and faster running time to answer a query. These algorithms employ a host of techniques, ranging from combinatorial methods, like graph partitioning and edge or vertex sampling, to standard tools in data-stream algorithms and in sparse recovery. There are also several lower bounds known, either combinatorial (for the graphical representation) or based on communication complexity and information theory. Many of the recent efforts focus on characterizing the tradeoff between accuracy and sketch size, yet many intriguing and very accessible problems are still open, and I will describe them in the talk.

In online debates, as in offline ones, individual utterances or arguments support or attack each other, leading to some subset of arguments (potentially from different sides of the debate) being considered more relevant than others. However, online conversations are much larger in scale than offline ones, with often hundreds of thousands of users weighing in, collaboratively forming large trees of comments by starting from an original post and replying to each other. In large discussions, readers are often forced to sample a subset of the arguments being put forth. Since such sampling is rarely done in a principled manner, users may not read all the relevant arguments to get a full picture of the debate from a sample. This article is interested in answering the question of how users should sample online conversations to selectively favour the currently justified or accepted positions in the debate. We apply techniques from argumentation theory and complex networks to build a model that predicts the probabilities of the normatively justified arguments given their location in idealised online discussions of comments and replies, which we represent as trees. Our model shows that the proportion of replies that are supportive, the distribution of the number of replies that comments receive, and the locations of comments that do not receive replies (i.e., the “leaves” of the reply tree) all determine the probability that a comment is a justified argument given its location. We show that when the distribution of the number of replies is homogeneous along the tree length, for acrimonious discussions (with more attacking comments than supportive ones), the distribution of justified arguments depends on the parity of the tree level, which is the distance from the root expressed as number of edges. In supportive discussions, which have more supportive comments than attacks, the probability of having justified comments increases as one moves away from the root. For discussion trees that have a non-homogeneous in-degree distribution, for supportive discussions we observe the same behaviour as before, while for acrimonious discussions we cannot observe the same parity-based distribution. This is verified with data obtained from the online debating platform Kialo. By predicting the locations of the justified arguments in reply trees, we can therefore suggest which arguments readers should sample, to grasp the currently accepted opinions in such discussions. Our models have important implications for the design of future online debating platforms.

Whilst grading neurovascular abnormalities is critical for prompt surgical repair, no statistical markers are currently available for predicting the risk of adverse events, such as stroke, and the overall resilience of a network to vascular complications. The lack of compact, fast, and scalable simulations with network perturbations impedes the analysis of the vascular resilience to life-threatening conditions, surgical interventions and long-term follow-up. We introduce a graph-based approach for efficient simulations, which statistically estimates biomarkers from a series of perturbations on the patient-specific vascular network. Analog-equivalent circuits are derived from clinical angiographies. Vascular graphs embed mechanical attributes modelling the impedance of a tubular structure with stenosis, tortuosity and complete occlusions. We evaluate pressure and flow distributions, simulating healthy topologies and abnormal variants with perturbations in key pathological scenarios. These describe the intrinsic network resilience to pathology, and delineate the underlying cerebrovascular autoregulation mechanisms. Lastly, a putative graph sampling strategy is devised on the same formulation, to support the topological inference of uncertain neurovascular graphs.

This paper proposes strategies for distributed Wiener-based reconstruction of graph signals from subsampled measurements. Given a stationary signal on a graph, we fit a distributed autoregressive moving average graph filter to a Wiener graph frequency response and propose two reconstruction strategies: i) reconstruction from a single temporal snapshot; ii) recursive signal reconstruction from a stream of noisy measurements. For both strategies, a mean square error analysis is performed to highlight the role played by the filter response and the sampled nodes, and to propose a graph sampling strategy. Our findings are validated with numerical results, which illustrate the potential of the proposed algorithms for distributed reconstruction of graph signals.

In this paper the focus is on sampling and reconstruction of signals supported on nodes of arbitrary graphs or arbitrary signals that may be represented using graphs, where we extend concepts from generalized sampling theory to the graph setting. To recover such signals from a given set of samples, we develop algorithms that incorporate prior knowledge on the original signal when available such as smoothness or subspace priors related to the underlying graph. For reconstructing arbitrary signals, we constrain the reconstruction to the graph, and provide a consistent reconstruction method, in which both the reconstructed signal and the input yield exactly the same measurements. Given a set of graph frequency domain samples, the sampling and interpolation operations may be efficiently implemented using linear shift-invariant graph filters.

© 2018, The Author(s). Counting the number of times a pattern occurs in a database is a fundamental data mining problem. It is a subroutine in a diverse set of tasks ranging from pattern mining to supervised learning and probabilistic model learning. While a pattern and a database can take many forms, this paper focuses on the case where both the pattern and the database are graphs (networks). Unfortunately, in general, the problem of counting graph occurrences is #P-complete. In contrast to earlier work, which focused on exact counting for simple (i.e., very short) patterns, we present a sampling approach for estimating the statistics of larger graph pattern occurrences. We perform an empirical evaluation on synthetic and real-world data that validates the proposed algorithm, illustrates its practical behavior and provides insight into the trade-off between its accuracy of estimation and computational efficiency. ispartof: Data Mining And Knowledge Discovery vol:32 issue:4 pages:913-948 status: published

We introduce a language-independent, graph-based probabilistic model of morphology, which uses transformation rules operating on whole words instead of the traditional morphological segmentation. The morphological analysis of a set of words is expressed through a graph having words as vertices and structural relationships between words as edges. We define a probability distribution over such graphs and develop a sampler based on the Metropolis-Hastings algorithm. The sampling is applied in order to determine the strength of morphological relationships between words, filter out accidental similarities and reduce the set of rules necessary to explain the data. The model is evaluated on the task of finding pairs of morphologically similar words, as well as generating new words. The results are compared to a state-of-the-art segmentation-based approach.

International audience; Are Online Social Network (OSN) A users more likely to form friendships with those with similar attributes? Do users at an OSN B score content more favorably than OSN C users? Such questions frequently arise in the context of Social Network Analysis (SNA) but often crawling an OSN network via its Application Programming Interface (API) is the only way to gather data from a third party. To date, these partial API crawls are the majority of public datasets and the synonym of lack of statistical guarantees in incomplete-data comparisons, severely limiting SNA research progress. Using regenerative properties of the random walks, we propose estimation techniques based on short crawls that have proven statistical guarantees. Moreover, our short crawls can be implemented in massively distributed algorithms. We also provide an adaptive crawler that makes our method parameter-free, significantly improving our statistical guarantees. We then derive the Bayesian approximation of the posterior of the estimates, and in addition, obtain an estima-tor for the expected value of node and edge statistics in an equivalent configuration model or Chung-Lu random graph model of the given network (where nodes are connected randomly) and use it as a basis for testing null hypotheses. The theoretical results are supported with simulations on a variety of real-world networks.

We propose a method for network anonymization that consists on sampling a subset of vertices and merging its neighborhoods in the network. In such a way, by publishing the merged graph of the network together with the sampled vertices and their locally anonymized neighborhoods, we obtain a complete anonymized picture of the network. We prove that the anonymization of the merged graph incurs in lower information loss, hence, it has more utility than the direct anonymization of the graph. It also yields an improvement on the quality of the anonymization of the local neighbors of a given subset of vertices.

Purpose– In order to initialize a student model in intelligent tutoring systems, some form of initial knowledge test should be given to a student. Since the authors cannot include all domain knowledge in that initial test, a domain knowledge subset should be selected. The paper aims to discuss this issue.Design/methodology/approach– In order to generate a knowledge sample that represents truly a certain domain knowledge, the authors can use sampling algorithms. In this paper, the authors present five sampling algorithms (Random Walk, Metropolis-Hastings Random Walk, Forest Fire, Snowball and Represent algorithm) and investigate which structural properties of the domain knowledge sample are preserved after sampling process is conducted.Findings– The samples that the authors got using these algorithms are compared and the authors have compared their cumulative node degree distributions, clustering coefficients and the length of the shortest paths in a sampled graph in order to find the best one.Originality/value– This approach is original as the authors could not find any similar work that uses graph sampling methods for student modeling.

Link prediction is the problem of determining future or missing associations between social entities. Most of the methods have focused on social networks under a certain framework neglecting some of the inherent properties of data from real applications. These latter are usually noisy, missing or partially observed. Therefore, uncertainty is an important feature to be taken into account. In this paper, proposals for handling the problem of missing link prediction while being attentive to uncertainty are presented along with a technique for uncertain social networks generation. Uncertainty is not only handled in the graph model but also in the method itself using the assets of the belief function theory as a general framework for reasoning under uncertainty. The approach combines sampling techniques and information fusion and returns good results in real-life settings.

Graphs or networks very commonly are used to represent connected or linked data. With the penetration of www in every sphere of life networked relationships can be easily established through communication links over web and network and graph analysis come as obvious choices of data representation and analysis. There are processes which can be analysed as network not through web but through the knowledge links available in these domains. In both these cases network analysis is challenged by the enormous size of the network in terms of nodes and links. Sub graph sampling can effectively be employed on large network structures to reduce the size of data while preserving the original properties of the network. Through this paper authors present a case study on application of sub graph sampling approach to obtain reduced case citation network in legal domain.

The modular organization of RNA structure has been exploited in various computational and theoretical approaches to identify RNA tertiary (3D) motifs and assemble RNA structures. Riboswitches exemplify this modularity in terms of both structural and functional adaptability of RNA components. Here, we extend our computational approach based on tree graph sampling to the prediction of riboswitch topologies by defining additional edges to mimick pseudoknots. Starting from a secondary (2D) structure, we construct an initial graph deduced from predicted junction topologies by our data-mining algorithm RNAJAG trained on known RNAs; we sample these graphs in 3D space guided by knowledge-based statistical potentials derived from bending and torsion measures of internal loops as well as radii of gyration for known RNAs. We present graph sampling results for 10 representative riboswitches, 6 of them with pseudoknots, and compare our predictions to solved structures based on global and local RMSD measures. Our results indicate that the helical arrangements in riboswitches can be approximated using our combination of modified 3D tree graph representations for pseudoknots, junction prediction, graph moves, and scoring functions. Future challenges in the field of riboswitch prediction and design are also discussed.

© 2015 IEEE. Random walk based graph sampling has been recognized as a fundamental technique to collect uniform node samples from a large graph. In this paper, we first present a comprehensive analysis of the drawbacks of three widely-used random walk based graph sampling algorithms, called re-weighted random walk (RW) algorithm, Metropolis-Hastings random walk (MH) algorithm and maximum-degree random walk (MD) algorithm. Then, to address the limitations of these algorithms, we propose two general random walk based algorithms, named rejection-controlled Metropolis-Hastings (RCMH) algorithm and generalized maximum-degree random walk (GMD) algorithm. We show that RCMH balances the tradeoff between the limitations of RW and MH, and GMD balances the tradeoff between the drawbacks of RW and MD. To further improve the performance of our algorithms, we integrate the so-called delayed acceptance technique and the non-backtracking random walk technique into RCMH and GMD respectively. We conduct extensive experiments over four real-world datasets, and the results demonstrate the effectiveness of the proposed algorithms.