Link prediction is a fundamental problem in graph data. In its most realistic setting, the problem consists of predicting missing or future links between random pairs of nodes from the set of disconnected pairs. Graph Neural Networks (GNNs) have become the predominant framework for link prediction. GNN-based methods treat link prediction as a binary classification problem and handle the extreme class imbalance---real graphs are very sparse---by sampling (uniformly at random) a balanced number of disconnected pairs not only for training but also for evaluation. However, we show that the reported performance of GNNs for link prediction in the balanced setting does not translate to the more realistic imbalanced setting and that simpler topology-based approaches are often better at handling sparsity. These findings motivate Gelato, a similarity-based link-prediction method that applies (1) graph learning based on node attributes to enhance a topological heuristic, (2) a ranking loss for addressing class imbalance, and (3) a negative sampling scheme that efficiently selects hard training pairs via graph partitioning. Experiments show that Gelato outperforms existing GNN-based alternatives.

Flow graphs capture the directed flow of a quantity of interest (e.g., water, power, vehicles) being transported through an underlying network. Modeling and generating realistic flow graphs is key in many applications in infrastructure design, transportation, and biomedical and social sciences. However, they pose a great challenge to existing generative models due to a complex dynamics that is often governed by domain-specific physical laws or patterns. We introduce FlowGEN, an implicit generative model for flow graphs, that learns how to jointly generate graph topologies and flows with diverse dynamics directly from data using a novel (flow) graph neural network. Experiments show that our approach is able to effectively reproduce relevant local and global properties of flow graphs, including flow conservation, cyclic trends, and congestion around hotspots.

From the 2016 U.S. presidential election to the 2021 Capitol riots to the spread of misinformation related to COVID-19, many have blamed social media for today's deeply divided society. Recent advances in machine learning for signed networks hold the promise to guide small interventions with the goal of reducing polarization in social media. However, existing models are especially ineffective in predicting conflicts (or negative links) among users. This is due to a strong correlation between link signs and the network structure, where negative links between polarized communities are too sparse to be predicted even by state-of-the-art approaches. To address this problem, we first design a partition-agnostic polarization measure for signed graphs based on the signed random-walk and show that many real-world graphs are highly polarized. Then, we propose POLE (POLarized Embedding for signed networks), a signed embedding method for polarized graphs that captures both topological and signed similarities jointly via signed autocovariance. Through extensive experiments, we show that POLE significantly outperforms state-of-the-art methods in signed link prediction, particularly for negative links with gains of up to one order of magnitude.

Online social networks have become major battlegrounds for political campaigns, viral marketing, and the dissemination of news. As a consequence, “bad actors” are increasingly exploiting these platforms, which is a key challenge for their administrators, businesses and society in general. The spread of fake news is a classical example of the abuse of social networks by these bad actors. While some have advocated for stricter policies to control the spread of misinformation in social networks, this often happens in detriment of their democratic and organic structure. In this paper, we aim to limit the influence of a target group in a social network via the removal of a few users/links. We formulate the influence limitation problem in a data-driven fashion, by taking into account past propagation traces. More specifically, our algorithms find critical edges to be removed in order to decrease the influence of a target group based on past data. The idea is to control the diffusion processes while minimizing the amount of disturbance in the network structure. Moreover, we consider two types of constraints over edge removals, a budget constraint and also a, more general, set of matroid constraints. These problems lead to interesting challenges in terms of algorithm design. For instance, we are able to show that influence limitation is APX-hard and propose deterministic and probabilistic approximation algorithms for the budgeted and the matroid version of the problem, respectively. Experiments show that the proposed approaches outperform several baselines.

Graph embedding based on random-walks supports effective solutions for many graph-related downstream tasks. However, the abundance of embedding literature has made it increasingly difficult to compare existing methods and to identify opportunities to advance the state-of-the-art. Meanwhile, existing work has left several fundamental questions---such as how embeddings capture different structural scales and how they should be applied for effective link prediction---unanswered. This paper addresses these challenges with an analytical framework for random-walk based graph embedding that consists of three components: a random-walk process, a similarity function, and an embedding algorithm. Our framework not only categorizes many existing approaches but naturally motivates new ones. With it, we illustrate novel ways to incorporate embeddings at multiple scales to improve downstream task performance. We also show that embeddings based on autocovariance similarity, when paired with dot product ranking for link prediction, outperform state-of-the-art methods based on Pointwise Mutual Information similarity by up to 100%.

Network centrality plays an important role in many applications. Central nodes in social networks can be influential, driving opinions and spreading news or rumors. In hyperlinked environments, such as the Web, where users navigate via clicks, central content receives high traffic, becoming target for advertising campaigns. While there is an extensive amount of work on centrality measures and their efficient computation, controlling nodes' centrality via network updates is a more recent and challenging task. Performing minimal modifications to a network to achieve a desired property falls under the umbrella of network design problems. This paper is focused on improving group (coverage and betweenness) centrality, which is a function of the shortest paths passing through a set of nodes, by adding edges to the network. Several variations of the problem, which are NP-hard as well as APX-hard, are introduced. We present a greedy algorithm, and even faster sampling algorithms, for group centrality maximization with theoretical quality guarantees under realistic constraints. The experimental results show that our sampling algorithms outperform the best baseline solution in terms of centrality by up to 5 times while being 2–3 orders of magnitude faster than our greedy approach.

The sparsest cut problem consists of identifying a small set of edges that breaks the graph into balanced sets of vertices. The normalized cut problem balances the total degree, instead of the size, of the resulting sets. Applications of graph cuts include community detection and computer vision. However, cut problems were originally proposed for static graphs, an assumption that does not hold in many modern applications where graphs are highly dynamic. In this paper, we introduce sparsest and normalized cuts in temporal graphs, which generalize their standard definitions by enforcing the smoothness of cuts over time. We propose novel formulations and algorithms for computing temporal cuts using spectral graph theory, divide-and-conquer and low-rank matrix approximation. Furthermore, we extend temporal cuts to dynamic graph signals, where vertices have attributes. Experiments show that our solutions are accurate and scalable, enabling the discovery of dynamic communities and the analysis of dynamic graph processes.

Detecting a small number of outliers from a set of data observations is always challenging. This problem is more difficult in the setting of multiple network samples, where computing the anomalous degree of a network sample is generally not sufficient. In fact, explaining why a given network is exceptional, expressed in the form of subnetwork, is also equally important. We develop a novel algorithm to address these two key problems. We treat each network sample as a potential outlier and identify subnetworks that help discriminate it from nearby samples. The algorithm is developed in the framework of network regression combined with the constraints on both network topology and L1-norm shrinkage to perform subnetwork discovery. Our method thus goes beyond subspace/subgraph discovery. We also show that the developed method converges to a global optimum. Empirical evaluation on various real-world network datasets demonstrates the advantages of our algorithm over various baseline methods.

Modeling information that resides on vertices of large graphs is a key problem in several real-life applications, ranging from social networks to the Internet-of-things. Signal Processing on Graphs and, in particular, graph wavelets can exploit the intrinsic smoothness of these datasets in order to represent them in a compact and accurate manner. However, how to discover wavelet bases that capture the geometry of the data with respect to the signal as well as the graph structure remains an open problem. In this paper, we study the problem of computing graph wavelet bases via sparse cuts in order to produce low-dimensional encodings of data-driven bases. This problem is connected to known hard problems in graph theory (e.g. multiway cuts) and thus requires an efficient heuristic. We formulate the basis discovery task as a relaxation of a vector optimization problem, which leads to an elegant solution as a regularized eigenvalue computation. Moreover, we propose several strategies in order to scale our algorithm to large graphs. Experimental results show that the proposed algorithm can effectively encode both the graph structure and signal, producing compressed and accurate representations for vertex values in a wide range of datasets (e.g. sensor and gene networks) and significantly outperforming the best baseline.

Many real-world complex systems can be modeled as dynamic networks with real-valued vertex/edge attributes. Examples include users' opinions in social networks and average speeds in a road system. When managing these large dynamic networks, compressing attribute values becomes a key requirement, since it enables the answering of attribute-based queries regarding a node/edge or network region based on a compact representation of the data. To address this problem, we introduce a lossy network compression scheme called Slice Tree (ST), which partitions a network into smooth regions with respect to node/edge values and compresses each value as the average of its region. ST applies a compact representation for network partitions, called slices, that are defined as a center node and radius distance. We propose an importance sampling algorithm to efficiently prune the search space of candidate slices in the ST construction by biasing the sampling process towards the node values that most affect the compression error. The effectiveness of ST in terms of compression error, compression rate, and running time is demonstrated using synthetic and real datasets. ST scales to million-node instances and removes up to 87% of the error in attribute values with a 103compression ratio. We also illustrate how ST captures relevant phenomena in real networks, such as research collaboration patterns and traffic congestions.

In this work, we study the correlation between attribute sets and the occurrence of dense subgraphs in large attributed graphs, a task we call structural correlation pattern mining. A structural correlation pattern is a dense subgraph induced by a particular attribute set. Existing methods are not able to extract relevant knowledge regarding how vertex attributes interact with dense subgraphs. Structural correlation pattern mining combines aspects of frequent itemset and quasi-clique mining problems. We propose statistical significance measures that compare the structural correlation of attribute sets against their expected values using null models. Moreover, we evaluate the interestingness of structural correlation patterns in terms of size and density. An efficient algorithm that combines search and pruning strategies in the identification of the most relevant structural correlation patterns is presented. We apply our method for the analysis of three real-world attributed graphs: a collaboration, a music, and a citation network, verifying that it provides valuable knowledge in a feasible time.