Graphs, which encode pairwise relations between entities, serve as a fundamental data structure across real-world domains. Many critical applications can be formulated as graph-based tasks, and graph machine learning (GML), from the shallow embedding models to graph neural networks and further advanced to the most powerful graph transformers, has been well-established to automate knowledge discovery and decision-making on graphs. In parallel, the recent emergence of large foundational models has driven machine learning into a new era of Generative Artificial Intelligence (Gen-AI), and this revolution presents both unprecedented opportunities and profound challenges for the well-established GML paradigms. However, few investigations have analyzed and envisioned how GML should evolve to harness these opportunities, address these challenges, and embrace this new Gen-AI era. To fill in this gap, we organize the first international Workshop on Machine Learning on Graphs in the Era of Generative Artificial Intelligence (MLoG-GenAI), held in connection with the 31st ACM Conference on Knowledge Discovery and Data Mining, which provides a venue to gather academic researchers and industry practitioners to discuss and picture the development of GML in the new Gen-AI era.

Graphs, which encode pairwise relations between entities, are a kind of universal data structure for a lot of real-world data, including social networks, transportation networks, and chemical molecules. Many important applications on these data can be treated as computational tasks on graphs. Recently, machine learning techniques are widely developed and utilized to effectively tame graphs for discovering actionable patterns and harnessing them for advancing various graph-related computational tasks. Huge success has been achieved and numerous real-world applications have benefited from it. However, since in today's world, we are generating and gathering data in a much faster and more diverse way, real-world graphs are becoming increasingly large-scale and complex. More dedicated efforts are needed to propose more advanced machine learning techniques and properly deploy them for real-world applications in a scalable way. Thus, we organize The 5th International Workshop on Machine Learning on Graphs (MLoG) (https://mlog-workshop.github.io/wsdm24.html), held in conjunction with the 17th ACM Conference on Web Search and Data Mining (WSDM), which provides a venue to gather academia researchers and industry researchers/practitioners to present the recent progress on machine learning on graphs.

Graph Neural Networks (GNNs) have become increasingly important due to their representational power and state-of-the-art predictive performance on many fundamental learning tasks. Despite this success, GNNs suffer from fairness issues that arise as a result of the underlying graph data and the fundamental aggregation mechanism that lies at the heart of the large class of GNN models. In this article, we examine and categorize fairness techniques for improving the fairness of GNNs. We categorize these techniques by whether they focus on improving fairness in the pre-processing, in-processing (during training), or post-processing phases. We discuss how such techniques can be used together whenever appropriate and highlight the advantages and intuition as well. We also introduce an intuitive taxonomy for fairness evaluation metrics, including graph-level fairness, neighborhood-level fairness, embedding-level fairness, and prediction-level fairness metrics. In addition, graph datasets that are useful for benchmarking the fairness of GNN models are summarized succinctly. Finally, we highlight key open problems and challenges that remain to be addressed.

Neural symbolic knowledge graph (KG) reasoning offers a promising approach that combines the expressive power of symbolic reasoning with the learning capabilities inherent in neural networks. This survey provides a comprehensive overview of advancements, techniques, and challenges in the field of neural symbolic KG reasoning. The survey introduces the fundamental concepts of KGs and symbolic logic, followed by an exploration of three significant KG reasoning tasks: KG completion, complex query answering, and logical rule learning. For each task, we thoroughly discuss three distinct categories of methods: pure symbolic methods, pure neural approaches, and the integration of neural networks and symbolic reasoning methods known as neural-symbolic. We carefully analyze and compare the strengths and limitations of each category of methods to provide a comprehensive understanding. By synthesizing recent research contributions and identifying open research directions, this survey aims to equip researchers and practitioners with a comprehensive understanding of the state-of-the-art in neural symbolic KG reasoning, fostering future advancements in this interdisciplinary domain.

In this work, we formalize the problem of causal inference over graph-based relational time-series data where each node in the graph has one or more time-series associated to it. We propose causal inference models for this problem that leverage both the graph topology and time-series to accurately estimate local causal effects of nodes. Furthermore, the relational time-series causal inference models are able to estimate local effects for individual nodes by exploiting local node-centric temporal dependencies and topological/structural dependencies. We show that simpler causal models that do not consider the graph topology are recovered as special cases of the proposed relational time-series causal inference model. We describe how the DurbinWu-Hausman test of specification can be used to test for the consistency of the proposed estimator from data. Empirically, we demonstrate the effectiveness of the causal inference models on both synthetic data with known ground-truth and a largescale observational relational time-series data set collected from Wikipedia.

While graph neural networks (GNNs) provide a powerful way to learn structured representations, it remains challenging to learn long-range dependencies in graphs. Recurrent GNNs only partly address this problem. In this paper, we propose a general approach for augmenting recurrent GNNs with a cache memory to improve their expressivity, especially for modeling long-range dependencies. Specifically, we first introduce a method of augmenting recurrent GNNs with a cache of previous hidden states. Then we further propose a general Cache-GNN framework by adding additional modules, including attention mechanism and positional/structural encoders, to improve the expressivity. We show that the Cache-GNNs outperforms other models on synthetic datasets as well as tasks on real-world datasets that require long-range information.

The rapid development of network science and technologies depends on shareable datasets. Currently, there is no standard practice for reporting and sharing network datasets. Some network dataset providers only share links, while others provide some contexts or basic statistics. As a result, critical information may be unintentionally dropped, and network dataset consumers may misunderstand or overlook critical aspects. Inappropriately using a network dataset can lead to severe consequences (e.g., discrimination) especially when machine learning models on networks are deployed in high-stake domains. Challenges arise as networks are often used across different domains (e.g., network science, physics, etc) and have complex structures. To facilitate the communication between network dataset providers and consumers, we propose network report. A network report is a structured description that summarizes and contextualizes a network dataset. Network report extends the idea of dataset reports (e.g., Datasheets for Datasets) from prior work with network-specific descriptions of the non-i.i.d. nature, demographic information, network characteristics, etc. We hope network reports encourage transparency and accountability in network research and development across different fields.

Given entities and their interactions in the web data, which may have occurred at different time, how can we find communities of entities and track their evolution? In this paper, we approach this important task from graph clustering perspective. Recently, state-of-the-art clustering performance in various domains has been achieved by deep clustering methods. Especially, deep graph clustering (DGC) methods have successfully extended deep clustering to graph-structured data by learning node representations and cluster assignments in a joint optimization framework. Despite some differences in modeling choices (e.g., encoder architectures), existing DGC methods are mainly based on autoencoders and use the same clustering objective with relatively minor adaptations. Also, while many real-world graphs are dynamic, previous DGC methods considered only static graphs. In this work, we develop CGC, a novel end-to-end framework for graph clustering, which fundamentally differs from existing methods. CGC learns node embeddings and cluster assignments in a contrastive graph learning framework, where positive and negative samples are carefully selected in a multi-level scheme such that they reflect hierarchical community structures and network homophily. Also, we extend CGC for time-evolving data, where temporal graph clustering is performed in an incremental learning fashion, with the ability to detect change points. Extensive evaluation on real-world graphs demonstrates that the proposed CGC consistently outperforms existing methods.

Random walks are at the heart of many existing node embedding and network representation learning methods. However, such methods have many limitations that arise from the use of traditional random walks, e.g., the embeddings resulting from these methods capture proximity (communities) among the vertices as opposed to structural similarity (roles). Furthermore, the embeddings are unable to transfer to new nodes and graphs as they are tied to node identity. To overcome these limitations, we introduce theRole2Vecframework based on the proposed notion ofattributed random walksto learn structural role-based embeddings. Notably, the framework serves as a basis for generalizing any walk-based method. TheRole2Vecframework enables these methods to be more widely applicable by learning inductive functions that capture the structural roles in the graph. Furthermore, the original methods are recovered as a special case of the framework when each vertex is mapped to its own function that uniquely identifies it. Finally, theRole2Vecframework is shown to be effective with an average AUC improvement of 17.8 percent for link prediction while requiring on average 853x less space than existing methods on a variety of graphs from different domains.

Visualization recommendation work has focused solely on scoring visualizations based on the underlying dataset, and not the actualuserand their past visualization feedback. These systems recommend the same visualizations for every user, despite that the underlying user interests, intent, and visualization preferences are likely to be fundamentally different, yet vitally important. In this work, we formally introduce the problem ofpersonalized visualization recommendationand present a generic learning framework for solving it. In particular, we focus on recommending visualizations personalized for each individual user based on their past visualization interactions (e.g., viewed, clicked, manually created) along with the data from those visualizations. More importantly, the framework can learn from visualizations relevant to other users, even if the visualizations are generated from completely different datasets. Experiments demonstrate the effectiveness of the approach as it leads to higher quality visualization recommendations tailored to the specific user intent and preferences. To support research on this new problem, we release our user-centric visualization corpus consisting of 17.4k users exploring 94k datasets with 2.3 million attributes and 32k user-generated visualizations.

Learning representations of software codes is a critical problem for a wide range of system applications, e.g., compiler optimization, software classification, malicious software detection, and performance optimization. Recently, learning graph-based representations of software programs has been used to model the inherent structural dependencies in programming languages (e.g., C++, Python). In this paper, we propose a novel graph neural network framework that utilizes multifractal analysis for LLVM intermediate representations (IR). We then show empirically that the proposed framework is capable of capturing long-range structural dependencies that appear in software codes. We conduct experiments and comparisons on two downstream system applications: (1) predicting heterogeneous compute device mappings (graph classification), and (2) compiler reachability analysis (node classification). We observe that introducing a structural inductive bias through multifractal topological features enables GNNs to capture long-range dependencies among nodes, thus, it improves the accuracy of GNN models for applications that require learning code representations.

This paper introduces higher-order link prediction methods based on the notion of closing higher-order network motifs. The methods are fast and efficient for real-time ranking and link prediction-based applications such as online visitor stitching, web search, and online recommendation. In such applications, real-time performance is critical. The proposed methods do not require any explicit training data, nor do they derive an embedding from the graph data, or perform any explicit learning. Most existing unsupervised methods with the above desired properties are all based on closing triangles (common neighbors, Jaccard similarity, and the ilk). In this work, we develop unsupervised techniques based on the notion of closing higher-order motifs that generalize beyond closing simple triangles. Through extensive experiments, we find that these higher-order motif closures often outperform triangle-based methods, which are commonly used in practice. This result implies that one should consider other motif closures beyond simple triangles. We also find that the best motif closure depends highly on the underlying network and its structural properties. Furthermore, all methods described in this work are fast for link prediction-based applications requiring real-time performance. The experimental results indicate the importance of closing higher-order motifs for unsupervised link prediction. Finally, these new higher-order motif closures can serve as a basis for studying and developing better unsupervised real-time link prediction and ranking methods.

Abstract In many domains where data are represented as graphs, learning a similarity metric among graphs is considered a key problem, which can further facilitate various learning tasks, such as classification, clustering, and similarity search. Recently, there has been an increasing interest in deep graph similarity learning, where the key idea is to learn a deep learning model that maps input graphs to a target space such that the distance in the target space approximates the structural distance in the input space. Here, we provide a comprehensive review of the existing literature of deep graph similarity learning. We propose a systematic taxonomy for the methods and applications. Finally, we discuss the challenges and future directions for this problem.

Temporal networks representing a stream of timestamped edges are seemingly ubiquitous in the real world. However, the massive size and continuous nature of these networks make them fundamentally challenging to analyze and leverage for descriptive and predictive modeling tasks. In this work, we propose a general framework for temporal network sampling with unbiased estimation. We develop online, single-pass sampling algorithms, and unbiased estimators for temporal network sampling. The proposed algorithms enable fast, accurate, and memory-efficient statistical estimation of temporal network patterns and properties. In addition, we propose a temporally decaying sampling algorithm with unbiased estimators for studying networks that evolve in continuous time, where the strength of links is a function of time, and the motif patterns are temporally weighted. In contrast to the prior notion of a △ t -temporal motif, the proposed formulation and algorithms for counting temporally weighted motifs are useful for forecasting tasks in networks such as predicting future links, or a future time-series variable of nodes and links. Finally, extensive experiments on a variety of temporal networks from different domains demonstrate the effectiveness of the proposed algorithms. A detailed ablation study is provided to understand the impact of the various components of the proposed framework.

In this article, we introduce a generalization of graphlets to heterogeneous networks called typed graphlets . Informally, typed graphlets are small typed induced subgraphs. Typed graphlets generalize graphlets to rich heterogeneous networks as they explicitly capture the higher-order typed connectivity patterns in such networks. To address this problem, we describe a general framework for counting the occurrences of such typed graphlets. The proposed algorithms leverage a number of combinatorial relationships for different typed graphlets. For each edge, we count a few typed graphlets, and with these counts along with the combinatorial relationships, we obtain the exact counts of the other typed graphlets in o (1) constant time. Notably, the worst-case time complexity of the proposed approach matches the time complexity of the best known untyped algorithm. In addition, the approach lends itself to an efficient lock-free and asynchronous parallel implementation. While there are no existing methods for typed graphlets, there has been some work that focused on computing a different and much simpler notion called colored graphlet. The experiments confirm that our proposed approach is orders of magnitude faster and more space-efficient than methods for computing the simpler notion of colored graphlet. Unlike these methods that take hours on small networks, the proposed approach takes only seconds on large networks with millions of edges. Notably, since typed graphlet is more general than colored graphlet (and untyped graphlets), the counts of various typed graphlets can be combined to obtain the counts of the much simpler notion of colored graphlets. The proposed methods give rise to new opportunities and applications for typed graphlets.

One of the primary tasks in neuroimaging is to simplify spatio-temporal scans of the brain (i.e., fMRI scans) by partitioning the voxels into a set of functional brain regions. An emerging line of research utilizes multiple fMRI scans, from a group of subjects, to calculate a single group consensus functional partition. This consensus-based approach is promising as it allows the model to improve the signal-to-noise ratio in the data. However, existing approaches are primarily non-parametric which poses problems when new samples are introduced. Furthermore, most existing approaches calculate a single partition for multiple subjects which fails to account for the functional and anatomical variability between different subjects. In this work, we study the problem of group-cohesive functional brain region discovery where the goal is to use information from a group of subjects to learn “group-cohesive” but individualized brain partitions for multiple fMRI scans. This problem is challenging since neuroimaging datasets are usually quite small and noisy. We introduce a novel deep parametric model based upon graph convolution, called the Brain Region Extraction Network (BREN). By treating the fMRI data as a graph, we are able to integrate information from neighboring voxels during brain region discovery which helps reduce noise for each subject. Our model is trained with a Siamese architecture to encourage partitions that are group-cohesive. Experiments on both synthetic and real-world data show the effectiveness of our proposed approach.

The success of many graph-based machine learning tasks highly depends on an appropriate representation learned from the graph data. Most work has focused on learning node embeddings that preserve proximity as opposed to structural role-based embeddings that preserve the structural similarity among nodes. These methods fail to capture higher-order structural dependencies and connectivity patterns that are crucial for structural role-based applications such as visitor stitching from web logs. In this work, we formulate higher-order network representation learning and describe a general framework called HONE for learning such structural node embeddings from networks via the subgraph patterns (network motifs, graphlet orbits/positions) in a nodes neighborhood. A general diffusion mechanism is introduced in HONE along with a space-efficient approach that avoids explicit construction of the k-step motif-based matrices using a k-step linear operator. Furthermore, HONE is shown to be fast and efficient with a worst-case time complexity that is nearly-linear in the number of edges. The experiments demonstrate the effectiveness of HONE for a number of important tasks including link prediction and visitor stitching from large web log data.

Structural roles define sets of structurally similar nodes that are more similar to nodes inside the set than outside, whereas communities define sets of nodes with more connections inside the set than outside. Roles based on structural similarity and communities based on proximity are fundamentally different but important complementary notions. Recently, the notion of structural roles has become increasingly important and has gained a lot of attention due to the proliferation of work on learning representations (node/edge embeddings) from graphs that preserve the notion of roles. Unfortunately, recent work has sometimes confused the notion of structural roles and communities (based on proximity) leading to misleading or incorrect claims about the capabilities of network embedding methods. As such, this article seeks to clarify the misconceptions and key differences between structural roles and communities, and formalize the general mechanisms (e.g., random walks and feature diffusion) that give rise to community- or role-based structural embeddings. We theoretically prove that embedding methods based on these mechanisms result in either community- or role-based structural embeddings. These mechanisms are typically easy to identify and can help researchers quickly determine whether a method preserves community- or role-based embeddings. Furthermore, they also serve as a basis for developing new and improved methods for community- or role-based structural embeddings. Finally, we analyze and discuss applications and data characteristics where community- or role-based embeddings are most appropriate.

This paper presents a general inductive graph representation learning framework called$\text{DeepGL}$for learning deep nodeandedge features that generalize across-networks. In particular,$\text{DeepGL}$begins by deriving a set of base features from the graph (e.g., graphlet features) and automatically learns a multi-layered hierarchical graph representation where each successive layer leverages the output from the previous layer to learn features of a higher-order. Contrary to previous work,$\text{DeepGL}$learnsrelational functions(each representing a feature) that naturally generalize across-networks and are therefore useful for graph-based transfer learning tasks. Moreover,$\text{DeepGL}$naturally supports attributed graphs, learns interpretable inductive graph representations, and is space-efficient (by learning sparse feature vectors). In addition,$\text{DeepGL}$is expressive, flexible with many interchangeable components, efficient with a time complexity of$\mathcal {O}(|E|)$, and scalable for large networks via an efficient parallel implementation. Compared with recent methods,$\text{DeepGL}$is (1)effectivefor across-network transfer learning tasksandlarge (attributed) graphs, (2)space-efficientrequiring up to 6x less memory, (3)fastwith up to 106x speedup in runtime performance, and (4)accuratewith an average improvement in AUC of 20 percent or more on many learning tasks and across a wide variety of networks.

We propose an end-to-end graph similarity learning framework called Higher-order Siamese GCN for multi-subject fMRI data analysis. The proposed framework learns the brain network representations via a supervised metric-based approach with siamese neural networks using two graph convolutional networks as the twin networks. Our proposed framework performs higher-order convolutions by incorporating higher-order proximity in graph convolutional networks to characterize and learn the community structure in brain connectivity networks. To the best of our knowledge, this is the first community-preserving graph similarity learning framework for multi-subject brain network analysis. Experimental results on four real fMRI datasets demonstrate the potential use cases of the proposed framework for multi-subject brain analysis in health and neuropsychiatric disorders. Our proposed approach achieves an average AUC gain of $75$% compared to PCA, an average AUC gain of $65.5$% compared to Spectral Embedding, and an average AUC gain of $24.3$% compared to S-GCN across the four datasets, indicating promising applications in clinical investigation and brain disease diagnosis.

Graph-structured data arise naturally in many different application domains. By representing data as graphs, we can capture entities (i.e., nodes) as well as their relationships (i.e., edges) with each other. Many useful insights can be derived from graph-structured data as demonstrated by an ever-growing body of work focused on graph mining. However, in the real-world, graphs can be both large—with many complex patterns—and noisy, which can pose a problem for effective graph mining. An effective way to deal with this issue is to incorporate “attention” into graph mining solutions. An attention mechanism allows a method to focus on task-relevant parts of the graph, helping it to make better decisions. In this work, we conduct a comprehensive and focused survey of the literature on the emerging field of graph attention models. We introduce three intuitive taxonomies to group existing work. These are based on problem setting (type of input and output), the type of attention mechanism used, and the task (e.g., graph classification, link prediction). We motivate our taxonomies through detailed examples and use each to survey competing approaches from a unique standpoint. Finally, we highlight several challenges in the area and discuss promising directions for future work.

Networks evolve continuously over time with the addition, deletion, and changing of links and nodes. Although many networks contain this type of temporal information, the majority of research in network representation learning has focused on static snapshots of the graph and has largely ignored the temporal dynamics of the network. In this work, we describe a general framework for incorporating temporal information into network embedding methods. The framework gives rise to methods for learning time-respecting embeddings from continuous-time dynamic networks. Overall, the experiments demonstrate the effectiveness of the proposed framework and dynamic network embedding approach as it achieves an average gain of 11.9% across all methods and graphs. The results indicate that modeling temporal dependencies in graphs is important for learning appropriate and meaningful network representations.

Relational machine learning has become increasingly important due to the recent proliferation and ubiquity of network data. However, existing methods are not designed for interactive learning and have many unrealistic assumptions that greatly limit their utility in practice. For instance, most existing work has focused on graphs with high relational autocorrelation (homophily) and perform poorly otherwise. To overcome these limitations, this paper presents a similarity-based relational learning framework called Relational Similarity Machines (RSM) for networks with arbitrary relational autocorrelation. The RSM framework is designed to be fast, accurate, and flexible for learning on a wide variety of networks. The experiments demonstrate the effectiveness of the RSM framework.

This article presents a platform for interactive graph mining and relational machine learning called GraphVis. The platform combines interactive visual representations with state-of-the-art graph mining and relational machine learning techniques to aid in revealing important insights quickly as well as learning an appropriate and highly predictive model for a particular task (e.g., classification, link prediction, discovering the roles of nodes, and finding influential nodes). Visual representations and interaction techniques and tools are developed for simple, fast, and intuitive real-time interactive exploration, mining, and modeling of graph data. In particular, we propose techniques for interactive relational learning (e.g., node/link classification), interactive link prediction and weighting, role discovery and community detection, higher-order network analysis (via graphlets, network motifs), among others. GraphVis also allows for the refinement and tuning of graph mining and relational learning methods for specific application domains and constraints via an end-to-end interactive visual analytic pipeline that learns, infers, and provides rapid interactive visualization with immediate feedback at each change/prediction in real-time. Other key aspects include interactive filtering, querying, ranking, manipulating, exporting, as well as tools for dynamic network analysis and visualization, interactive graph generators (including new block model approaches), and a variety of multi-level network analysis techniques.

In recent years, graphlet counting has emerged as an important task in topological graph analysis. However, the existing works on graphlet counting obtain the graphlet counts for the entire network as a whole. These works capture the key graphical patterns that prevail in a given network but they fail to meet the demand of the majority of real-life graph related prediction tasks such as link prediction, edge/node classification, etc., which require to build features for an edge (or a vertex) of a network. To meet the demand for such applications, efficient algorithms are needed for counting local graphlets within the context of an edge (or a vertex). In this work, we propose an efficient method, titled E-CLOG, for counting all 3,4 and 5 size local graphlets with the context of a given edge for its all different edge orbits. We also provide a shared-memory, multi-core implementation of E-CLOG, which makes it even more scalable for very large real-world networks. In particular, We obtain strong scaling on a variety of graphs (14x-20x on 36 cores). We provide extensive experimental results to demonstrate the efficiency and effectiveness of the proposed method. For instance, we show that E-CLOG is faster than existing work by multiple order of magnitudes; for the Wordnet graph E-CLOG counts all 3,4 and 5-size local graphlets in 1.5 hours using a single thread and in only a few minutes using the parallel implementation, whereas the baseline method does not finish in more than 4 days. We also show that local graphlet counts around an edge are much better features for link prediction than well-known topological features; our experiments show that the former enjoys between 10% to 45% of improvement in the AUC value for predicting future links in three real-life social and collaboration networks.

This paper introduces a new single-pass reservoir weighted-sampling stream aggregation algorithm, Priority-Based Aggregation (PBA). While order sampling is a powerful and efficient method for weighted sampling from a stream of uniquely keyed items, there is no current algorithm that realizes the benefits of order sampling in the context of stream aggregation over non-unique keys. A naive approach to order sample regardless of key then aggregate the results is hopelessly inefficient. In distinction, our proposed algorithm uses a single persistent random variable across the lifetime of each key in the cache, and maintains unbiased estimates of the key aggregates that can be queried at any point in the stream. The basic approach can be supplemented with a Sample and Hold pre-sampling stage with a sampling rate adaptation controlled by PBA. This approach represents a considerable reduction in computational complexity compared with the state of the art in adapting Sample and Hold to operate with a fixed cache size. Concerning statistical properties, we prove that PBA provides unbiased estimates of the true aggregates. We analyze the computational complexity of PBA and its variants, and provide a detailed evaluation of its accuracy on synthetic and trace data. Weighted relative error is reduced by 40% to 65% at sampling rates of 5% to 17%, relative to Adaptive Sample and Hold; there is also substantial improvement for rank queries.

We propose Graph Priority Sampling ( gps ), a new paradigm for order-based reservoir sampling from massive graph streams. gps provides a general way to weight edge sampling according to auxiliary and/or size variables so as to accomplish various estimation goals of graph properties. In the context of subgraph counting, we show how edge sampling weights can be chosen so as to minimize the estimation variance of counts of specified sets of subgraphs. In distinction with many prior graph sampling schemes, gps separates the functions of edge sampling and subgraph estimation. We propose two estimation frameworks: (1) Post-Stream estimation, to allow gps to construct a reference sample of edges to support retrospective graph queries, and (2) In-Stream estimation, to allow gps to obtain lower variance estimates by incrementally updating the subgraph count estimates during stream processing. Unbiasedness of subgraph estimators is established through a new Martingale formulation of graph stream order sampling, in which subgraph estimators, written as a product of constituent edge estimators, are unbiased, even when computed at different points in the stream. The separation of estimation and sampling enables significant resource savings relative to previous work. We illustrate our framework with applications to triangle and wedge counting. We perform a large-scale experimental study on real-world graphs from various domains and types. gps achieves high accuracy with < 1% error for triangle and wedge counting, while storing a small fraction of the graph with average update times of a few microseconds per edge. Notably, for billion-scale graphs, gps accurately estimates triangle and wedge counts with < 1% error, while storing a small fraction of < 0.01% of the total edges in the graph.

Graphlets represent small induced subgraphs and are becoming increasingly important for a variety of applications. Despite the importance of the local subgraph (graphlet) counting problem, existing work focuses mainly on counting graphlets globally over the entire graph. These global counts have been used for tasks such as graph classification as well as for understanding and summarizing the fundamental structural patterns in graphs. In contrast, this work proposes an accurate, efficient, and scalable parallel framework for the more challenging problem of counting graphlets locally for a given edge or set of edges. The local graphlet counts provide a topologically rigorous characterization of the local structure surrounding an edge. The aim of this work is to obtain the count of every graphlet of size k for each edge. The framework gives rise to efficient, parallel, and accurate unbiased estimation methods with provable error bounds, as well as exact algorithms for counting graphlets locally. Experiments demonstrate the effectiveness of the proposed exact and estimation methods on various datasets. In particular, the exact methods show strong scaling results (11-16x on 16 cores). Moreover, our estimation framework is accurate with error less than 5% on average.

From social science to biology, numerous applications often rely on graphlets for intuitive and meaningful characterization of networks at both the global macro-level as well as the local micro-level. While graphlets have witnessed a tremendous success and impact in a variety of domains, there has yet to be a fast and efficient approach for computing the frequencies of these subgraph patterns. However, existing methods are not scalable to large networks with millions of nodes and edges, which impedes the application of graphlets to new problems that require large-scale network analysis. To address these problems, we propose a fast, efficient, and parallel algorithm for counting graphlets of size k={3,4}-nodes that take only a fraction of the time to compute when compared with the current methods used. The proposed graphlet counting algorithms leverages a number of proven combinatorial arguments for different graphlets. For each edge, we count a few graphlets, and with these counts along with the combinatorial arguments, we obtain the exact counts of others in constant time. On a large collection of 300+ networks from a variety of domains, our graphlet counting strategies are on average 460x faster than current methods. This brings new opportunities to investigate the use of graphlets on much larger networks and newer applications as we show in the experiments. To the best of our knowledge, this paper provides the largest graphlet computations to date as well as the largest systematic investigation on over 300+ networks from a variety of domains.

Roles represent node-level connectivity patterns such as star-center, star-edge nodes, near-cliques or nodes that act as bridges to different regions of the graph. Intuitively, two nodes belong to the same role if they are structurally similar. Roles have been mainly of interest to sociologists, but more recently, roles have become increasingly useful in other domains. Traditionally, the notion of roles were defined based on graph equivalences such as structural, regular, and stochastic equivalences. We briefly revisit these early notions and instead propose a more general formulation of roles based on the similarity of a feature representation (in contrast to the graph representation). This leads us to propose a taxonomy of three general classes of techniques for discovering roles that includes (i) graph-based roles, (ii) feature-based roles, and (iii) hybrid roles. We also propose a flexible framework for discovering roles using the notion of similarity on a feature-based representation. The framework consists of two fundamental components: (a) role feature construction and (b) role assignment using the learned feature representation. We discuss the different possibilities for discovering feature-based roles and the tradeoffs of the many techniques for computing them. Finally, we discuss potential applications and future directions and challenges.

Sampling is a standard approach in big-graph analytics; the goal is to efficiently estimate the graph properties by consulting a sample of the whole population. A perfect sample is assumed to mirror every property of the whole population. Unfortunately, such a perfect sample is hard to collect in complex populations such as graphs (e.g. web graphs, social networks), where an underlying network connects the units of the population. Therefore, a good sample will be representative in the sense that graph properties of interest can be estimated with a known degree of accuracy.

Network sampling is integral to the analysis of social, information, and biological networks. Since many real-world networks are massive in size, continuously evolving, and/or distributed in nature, the network structure is often sampled in order to facilitate study. For these reasons, a more thorough and complete understanding of network sampling is critical to support the field of network science. In this paper, we outline a framework for the general problem of network sampling by highlighting the different objectives, population and units of interest, and classes of network sampling methods. In addition, we propose a spectrum of computational models for network sampling methods, ranging from the traditionally studied model based on the assumption of a static domain to a more challenging model that is appropriate for streaming domains. We design a family of sampling methods based on the concept of graph induction that generalize across the full spectrum of computational models (from static to streaming) while efficiently preserving many of the topological properties of the input graphs. Furthermore, we demonstrate how traditional static sampling algorithms can be modified for graph streams for each of the three main classes of sampling methods: node, edge, and topology-based sampling. Experimental results indicate that our proposed family of sampling methods more accurately preserve the underlying properties of the graph in both static and streaming domains. Finally, we study the impact of network sampling algorithms on the parameter estimation and performance evaluation of relational classification algorithms.