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How can we analyze large graphs such as the Web, and social networks with hundreds of billions of vertices and edges? Although many graph mining systems have been proposed to perform various graph mining algorithms on such large graphs, they have difficulties in processing Web-scale graphs due to massive communication and I/O costs caused by communication between workers, and reading subgraphs repeatedly. In this paper, we propose FlexGraph, a scalable distributed graph mining method reducing the costs by exploiting properties of real-world graphs. FlexGraph significantly decreases the communication cost, which is the main bottleneck of distributed systems, by exploiting different edge placement policies based on types of vertices. Furthermore, we propose a flexible storage format to reduce I/O costs when reading input graph repeatedly. Experiments show that FlexGraph succeeds in processing up to 64× larger graphs than existing distributed memory-based graph mining methods, and consistently outperforms previous disk-based graph mining methods.

How do we find patterns and anomalies, on graphs with billions of nodes and edges, which do not fit in memory? How to use parallelism for such terabyte-scale graphs? In this work, we focus on inference, which often corresponds, intuitively, to "guilt by association" scenarios. For example, if a person is a drug-abuser, probably its friends are so, too; if a node in a social network is of male gender, his dates are probably females. We show how to do inference on such huge graphs through our proposed HADOOP Line graph Fixed Point (HA-LFP), an efficient parallel algorithm for sparse billion-scale graphs, using the HADOOP platform. Our contributions include (a) the design of HA-LFP, observing that it corresponds to a fixed point on a line graph induced from the original graph; (b) scalability analysis, showing that our algorithm scales up well with the number of edges, as well as with the number of machines; and (c) experimental results on two private, as well as two of the largest publicly available graphs - the Web Graphs from Yahoo! (6.6 billion edges and 0.24 Tera bytes), and the Twitter graph (3.7 billion edges and 0.13 Tera bytes). We evaluated our algorithm using M45, one of the top 50 fastest supercomputers in the world, and we report patterns and anomalies discovered by our algorithm, which would be invisible otherwise.

Zuckerli is a scalable compression system meant for large real-world graphs. Graphs are notoriously challenging structures to store efficiently due to their linked nature, which makes it hard to separate them into smaller, compact components. Therefore, effective compression is crucial when dealing with large graphs, which can have billions of nodes and edges. Furthermore, a good compression system should give the user fast and reasonably flexible access to parts of the compressed data without requiring full decompression, which may be unfeasible on their system. Compared to WebGraph, the de-facto standard in compressing real-world graphs, Zuckerli improves multiple aspects by using advanced compression techniques and novel heuristic graph algorithms. Zuckerli can produce both a compressed representation for storage and one which allows fast direct access to the adjacency lists of the compressed graph without decompressing the entire graph. We validate its effectiveness on real-world graphs with up to a billion nodes and 90 billion edges, conducting an extensive experimental evaluation of both compression density and decompression performance. We show that Zuckerli-compressed graphs are 10% to 29% smaller, and more than 20% in most cases, with a resource usage for decompression comparable to that of WebGraph.

Graphs appear in numerous applications including cyber security, the Internet, social networks, protein networks, recommendation systems, citation networks, and many more. Graphs with millions or even billions of nodes and edges are common-place. How to store such large graphs efficiently? What are the core operations/queries on those graph? How to answer the graph queries quickly? We propose Gbase, an efficient analysis platform for large graphs. The key novelties lie in (1) our storage and compression scheme for a parallel, distributed settings and (2) the carefully chosen graph operations and their efficient implementations. We designed and implemented an instance of Gbase using Mapreduce/Hadoop. Gbase provides a parallel indexing mechanism for graph operations that both saves storage space, as well as accelerates query responses. We run numerous experiments on real and synthetic graphs, spanning billions of nodes and edges, and we show that our proposed Gbase is indeed fast, scalable, and nimble, with significant savings in space and time.

Social network analysis has become a major research area that has impact in diverse applications ranging from search engines to product recommendation systems. A major problem in implementing social network analysis algorithms is the sheer size of many social networks, for example, the Facebook graph has more than 900 million vertices and even small networks may have tens of millions of vertices. One solution to dealing with these large graphs is dimensionality reduction using spectral or SVD analysis of the adjacency matrix of the network, but these global techniques do not necessarily take into account local structures or clusters of the network that are critical in network analysis. A more promising approach is clustered low-rank approximation: instead of computing a global low-rank approximation, the adjacency matrix is first clustered, and then a low-rank approximation of each cluster (i.e., diagonal block) is computed. The resulting algorithm is challenging to parallelize not only because of the large size of the data sets in social network analysis, but also because it requires computing with very diverse data structures ranging from extremely sparse matrices to dense matrices. In this paper, we describe the first parallel implementation of a clustered low-rank approximation algorithm for large social network graphs, and use it to perform link prediction in parallel. Experimental results show that this implementation scales well on large distributed-memory machines; for example, on a Twitter graph with roughly 11 million vertices and 63 million edges, our implementation scales by a factor of 86 on 128 processes and takes less than 2300 seconds, while on a much larger Twitter graph with 41 million vertices and 1.2 billion edges, our implementation scales by a factor of 203 on 256 processes with a running time about 4800 seconds.KeywordsSocial network analysislink predictionparallel computinggraph computationsclustered low-rank approximation

Graph mining applications analyze the structural properties of large graphs. These applications are computationally expensive because finding structural patterns requires checking subgraph isomorphism, which is NP-complete. This paper exploits the sub-structural similarities across different patterns by employing Subgraph Morphing to accurately infer the results for a given set of patterns from the results of a completely different set of patterns that are less expensive to compute. To enable Subgraph Morphing in practice, we develop efficient query transformation techniques as well as automatic result conversion strategies for different application scenarios. We have implemented Subgraph Morphing in four state-of-the-art graph mining and subgraph matching systems: Peregrine, AutoMine/- GraphZero, GraphPi, and BigJoin; a thorough evaluation demonstrates that Subgraph Morphing improves the performance of these four systems by 34×, 10×, 18×, and 13×, respectively.

We have entered the age of big data. Massive datasets are now common in science, government and enterprises. Yet, making sense of these data remains a fundamental challenge. Where do we start our analysis? Where to go next? How to visualize our findings? We answers these questions by bridging Data Mining and Human- Computer Interaction (HCI) to create tools for making sense of graphs with billions of nodes and edges, focusing on: (1) Attention Routing: we introduce this idea, based on anomaly detection, that automatically draws people’s attention to interesting areas of the graph to start their analyses. We present three examples: Polonium unearths malware from 37 billion machine-file relationships; NetProbe fingers bad guys who commit auction fraud. (2) Mixed-Initiative Sensemaking: we present two examples that combine machine inference and visualization to help users locate next areas of interest: Apolo guides users to explore large graphs by learning from few examples of user interest; Graphite finds interesting subgraphs, based on only fuzzy descriptions drawn graphically. (3) Scaling Up: we show how to enable interactive analytics of large graphs by leveraging Hadoop, staging of operations, and approximate computation. This thesis contributes to data mining, HCI, and importantly their intersection, including: interactive systems and algorithms that scale; theories that unify graph mining approaches; and paradigms that overcome fundamental challenges in visual analytics. Our work is making impact to academia and society: Polonium protects 120 million people worldwide from malware; NetProbe made headlines on CNN, WSJ and USA Today; Pegasus won an opensource software award; Apolo helps DARPA detect insider threats and prevent exfiltration. We hope our Big Data Mantra “Machine for Attention Routing, Human for Interaction” will inspire more innovations at the crossroad of data mining and HCI.

Distributed-memory clusters are used for in-memory processing of very large graphs with billions of nodes and edges. This requires partitioning the graph among the machines in the cluster. When a graph is partitioned, a node in the graph may be replicated on several machines, and communication is required to keep these replicas synchronized. Good partitioning policies attempt to reduce this synchronization overhead while keeping the computational load balanced across machines. A number of recent studies have looked at ways to control replication of nodes, but these studies are not conclusive because they were performed on small clusters with eight to sixteen machines, did not consider work-efficient data-driven algorithms, or did not optimize communication for the partitioning strategies they studied. This paper presents an experimental study of partitioning strategies for work-efficient graph analytics applications on large KNL and Skylake clusters with up to 256 machines using the Gluon communication runtime which implements partitioning-specific communication optimizations. Evaluation results show that although simple partitioning strategies like Edge-Cuts perform well on a small number of machines, an alternative partitioning strategy called Cartesian Vertex-Cut (CVC) performs better at scale even though paradoxically it has a higher replication factor and performs more communication than Edge-Cut partitioning does. Results from communication micro-benchmarks resolve this paradox by showing that communication overhead depends not only on communication volume but also on the communication pattern among the partitions. These experiments suggest that high-performance graph analytics systems should support multiple partitioning strategies, like Gluon does, as no single graph partitioning strategy is best for all cluster sizes. For such systems, a decision tree for selecting a good partitioning strategy based on characteristics of the computation and the cluster is presented.

In this paper, we revisit the problem of influence maximization with fairness, which aims to select k influential nodes to maximise the spread of information in a network, while ensuring that selected sensitive user attributes (e.g., gender, location, origin, race, etc.) are fairly affected, i.e., are proportionally similar between the original network and the affected users. Recent studies on this problem focused only on extremely small networks, hence the challenge remains on how to achieve a scalable solution, applicable to networks with millions or billions of nodes. We propose an approach that is based on learning node representations (embeddings) for fair spread from diffusion cascades, instead of the social connectivity, and in this way we can deal with very large graphs. We propose two data-driven approaches: (a) fairness-based participant sampling (FPS), and (b) fairness as context (FAC). Spread related user features, such as the probability of diffusing information to others, are derived from the historical information cascades, using a deep neural network. The extracted features are then used in selecting influencers that maximize the influence spread, while being also fair with respect to the chosen sensitive attributes. In FPS, fairness and cascade length information are considered independently in the decision-making process, while FAC considers these information facets jointly and takes into account correlations between them. The proposed algorithms are generic and represent the first policy-driven solutions that can be applied to arbitrary sets of sensitive attributes at scale. We evaluate the performance of our solutions on a real-world public dataset (Sina Weibo) and on a hybrid real-synthetic dataset (Digg), which exhibit all the facets that we exploit, namely diffusion network, diffusion traces, and user profiles. These experiments show that our methods outperform the state-the-art solutions in terms of spread, fairness, and scalability.

For big data practitioners, data integration/entity resolution/record linkage is one of the key challenges we face from day to day. Entity resolution/record linkage with high precision and recall on a large graph with billions of nodes, and hundreds of times more edges poses significant scalability challenges. Similarity based graph partition is still the most scalable method available. This paper presents a probabilistic method to approximate the match likelihood of a pair of records by incorporating values of different attributes and their aggregates/statistics. The quality of the approximates depend on the accuracy of the estimates of the aggregated values. The paper adapts the GTM model described in [1] to obtain the estimates. We present experimental results based on real world commercial data sources to show that the estimates obtained via GTM model is better than the baseline. Our experimental results also showed that the approximate match likelihood can improve the recall of the similarity function.

Shortest distance queries are essential not only in graph analysis and graph mining tasks but also in database applications, when a large graph needs to be dealt with. Such shortest distance queries are frequently issued by end-users or requested as a subroutine in real applications. For intensive queries on large graphs, it is impractical to compute shortest distances on-line from scratch, and impractical to materialize all-pairs shortest distances. In the literature, 2-hop distance labeling is proposed to index the all-pairs shortest distances. It assigns distance labels to vertices in a large graph in a pre-computing step off-line and then answers shortest distance queries on-line by making use of such distance labels, which avoids exhaustively traversing the large graph when answering queries. However, the existing algorithms to generate 2-hop distance labels are not scalable to large graphs. Finding an optimal 2-hop distance labeling is NP-hard, and heuristic algorithms may generate large size distance labels while still needing to pre-compute all-pairs shortest paths. In this paper, we propose a multi-hop distance labeling approach, which generates a subset of the 2-hop distance labels as index off-line. We can compute the multi-hop distance labels efficiently by avoiding pre-computing all-pairs shortest paths. In addition, our multi-hop distance labeling is small in size to be stored. To answer a shortest distance query between two vertices, we first generate the query-specific small set of 2-hop distance labels for the two vertices based on our multi-hop distance labels stored and compute the shortest distance between the two vertices based on the 2-hop distance labels generated on-line. We conducted extensive performance studies on large real graphs and confirmed the efficiency of our multi-hop distance labeling scheme.

Subgraph matching, which belongs to NP-hard, faces significant challenges on a large scale graph with billions of nodes, and existing methods are usually confronted with greater challenges from both stability and efficiency. In this article, a subgraph matching method in a distributed system, tree model-based subgraph matching method (TBSGM) is proposed. The authors provide a transformed efficient query tree as a replacement for a query graph. In order to get the tree, they present a cost evaluation model which may help to generate the efficient query tree according to network communication-cost and calculation-cost evaluation. Also, a key set based indexing strategy for intermediate results is given to simplify the matching results during network communication. Extensive experiments with real-world datasets show that TBSGM significantly outperforms other methods in the aspects of scalability and efficiency.

GraphChi is the first reported disk-based graph engine that can handle billion-scale graphs on a single PC efficiently. GraphChi is able to execute several advanced data mining, graph mining and machine learning algorithms on very large graphs. With the novel technique of parallel sliding windows (PSW) to load subgraph from disk to memory for vertices and edges updating, it can achieve data processing performance close to and even better than those of mainstream distributed graph engines. GraphChi mentioned that its memory is not effectively utilized with large dataset, which leads to suboptimal computation performances. In this paper we are motivated by the concepts of "pin " from TurboGraph and "ghost" from GraphLab to propose a new memory utilization mode for GraphChi, which is called Part-in-memory mode, to improve the GraphChi algorithm performance. The main idea is to pin a fixed part of data inside the memory during the whole computing process. Part-in-memory mode is successfully implemented with only about 40 additional lines of code to the original GraphChi engine. Extensive experiments are performed with large real datasets (including Twitter graph with 1.4 billion edges). The preliminary results show that Part-in-memory mode memory management approach effectively reduces the GraphChi running time by up to 60% in PageRank algorithm. Interestingly it is found that a larger portion of data pinned in memory does not always lead to better performance in the case that the whole dataset cannot be fitted in memory. There exists an optimal portion of data which should be kept in the memory to achieve the best computational performance.

In this paper, we discuss how graph mining system is applied to sales transaction data so as to understand consumer behavior. First, existing research of consumer behavior analysis for sequential purchase pattern is reviewed. Then we propose to represent the complicated customer purchase behavior by a directed graph retaining temporal information in a purchase sequence and apply a graph mining technique to analyze the frequent occurring patterns. In this paper, we demonstrate through the case of healthy cooking oil analysis how graph mining technology helps us understand complex purchase behavior.

Efficient breadth first search on multi-GPU systems