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1. FOUND GRAPH DATA AND PLANTED VERTEX COVERS

   Benson, Austin R; Kleinberg, Jon. (April 2018, arXiv.org)

   ABSTRACT. A typical way in which network data is recorded is to measure all the interactions among a specified set of core nodes; this produces a graph containing this core together with a potentially larger set of fringe nodes that have links to the core. Interactions between pairs of nodes in the fringe, however, are not recorded by this process, and hence not present in the resulting graph data. For example, a phone service provider may only have records of calls in which at least one of the participants is a customer; this can include calls between a customer and a non-customer, but not between pairs of non-customers. Knowledge of which nodes belong to the core is an important piece of metadata that is crucial for interpreting the network dataset. But in many cases, this metadata is not available, either because it has been lost due to difficulties in data provenance, or because the network consists of “found data” obtained in settings such as counter-surveillance. This leads to a natural algorithmic problem, namely the recovery of the core set. Since the core set forms a vertex cover of the graph, we essentially have a planted vertex cover problem, but with an arbitrary underlying graph. We develop a theoretical framework for analyzing this planted vertex cover problem, based on results in the theory of fixed- parameter tractability, together with algorithms for recovering the core. Our algorithms are fast, simple to implement, and out-perform several methods based on network core-periphery structure on various real-world datasets. 

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2. Link Prediction in Networks with Core-Fringe Data

   https://doi.org/10.1145/3308558.3313626  

   Benson, Austin; Kleinberg, Jon (January 2019, The World Wide Web Conference)

   Data collection often involves the partial measurement of a larger system. A common example arises in collecting network data: we often obtain network datasets by recording all of the interactions among a small set of core nodes, so that we end up with a measurement of the network consisting of these core nodes along with a potentially much larger set of fringe nodes that have links to the core. Given the ubiquity of this process for assembling network data, it is crucial to understand the role of such a “core-fringe” structure. Here we study how the inclusion of fringe nodes affects the standard task of network link prediction. One might initially think the inclusion of any additional data is useful, and hence that it should be beneficial to include all fringe nodes that are available. However, we find that this is not true; in fact, there is substantial variability in the value of the fringe nodes for prediction. Once an algorithm is selected, in some datasets, including any additional data from the fringe can actually hurt prediction performance; in other datasets, including some amount of fringe information is useful before prediction performance saturates or even declines; and in further cases, including the entire fringe leads to the best performance. While such variety might seem surprising, we show that these behaviors are exhibited by simple random graph models. 

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3. Clustering in graphs and hypergraphs with categorical edge labels

   https://doi.org/10.1145/3366423.3380152  

   Amburg, Ilya; Veldt, Nate; Benson, Austin R (April 2020, WWW '20: Proceedings of The Web Conference 2020)

   Modern graph or network datasets often contain rich structure that goes beyond simple pairwise connections between nodes. This calls for complex representations that can capture, for instance, edges of different types as well as so-called “higher-order interactions” that involve more than two nodes at a time. However, we have fewer rigorous methods that can provide insight from such representations. Here, we develop a computational framework for the problem of clustering hypergraphs with categorical edge labels — or different interaction types — where clusters corresponds to groups of nodes that frequently participate in the same type of interaction. Our methodology is based on a combinatorial objective function that is related to correlation clustering on graphs but enables the design of much more efficient algorithms that also seamlessly generalize to hypergraphs. When there are only two label types, our objective can be optimized in polynomial time, using an algorithm based on minimum cuts. Minimizing our objective becomes NP-hard with more than two label types, but we develop fast approximation algorithms based on linear programming relaxations that have theoretical cluster quality guarantees. We demonstrate the efficacy of our algorithms and the scope of the model through problems in edge-label community detection, clustering with temporal data, and exploratory data analysis. 

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4. Accelerating k-Core Decomposition by a GPU

   https://doi.org/10.1109/ICDE55515.2023.00142  

   Ahmad, Akhlaque; Yuan, Lyuheng; Yan, Da; Guo, Guimu; Chen, Jieyang; Zhang, Chengcui (April 2023, 2023 IEEE 39th International Conference on Data Engineering (ICDE))

   The k-core of a graph is the largest induced sub-graph with minimum degree k. The problem of k-core decomposition finds the k-cores of a graph for all valid values of k, and it has many applications such as network analysis, computational biology and graph visualization. Currently, there are two types of parallel algorithms for k-core decomposition: (1) degree-based vertex peeling, and (2) iterative h-index refinement. There is, however, few studies on accelerating k-core decomposition using GPU. In this paper, we propose a highly optimized peeling algorithm on a GPU, and compare it with possible implementations on top of think-like-a-vertex graph-parallel GPU systems as well as existing serial and parallel k-core decomposition algorithms on CPUs. Extensive experiments show that our GPU algorithm is the overall winner in both time and space. Our source code is released at https://github.com/akhlaqueak/KCoreGPU. 

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5. A Local Algorithm for Structure-Preserving Graph Cut

   https://doi.org/10.1145/3097983.3098015  

   Zhou, Dawei; Zhang, Si; Yildirim, Mehmet Yigit; Alcorn, Scott; Tong, Hanghang; Davulcu, Hasan; He, Jingrui (August 2017, KDD)

   Nowadays, large-scale graph data is being generated in a variety of real-world applications, from social networks to co-authorship networks, from protein-protein interaction networks to road traffic networks. Many existing works on graph mining focus on the vertices and edges, with the first-order Markov chain as the underlying model. They fail to explore the high-order network structures, which are of key importance in many high impact domains. For example, in bank customer personally identifiable information (PII) networks, the star structures often correspond to a set of synthetic identities; in financial transaction networks, the loop structures may indicate the existence of money laundering. In this paper, we focus on mining user-specified high-order network structures and aim to find a structure-rich subgraph which does not break many such structures by separating the subgraph from the rest. A key challenge associated with finding a structure-rich subgraph is the prohibitive computational cost. To address this problem, inspired by the family of local graph clustering algorithms for efficiently identifying a low-conductance cut without exploring the entire graph, we propose to generalize the key idea to model high-order network structures. In particular, we start with a generic definition of high-order conductance, and define the high-order diffusion core, which is based on a high-order random walk induced by user-specified high-order network structure. Then we propose a novel High-Order Structure-Preserving LOcal Cut (HOSPLOC) algorithm, which runs in polylogarithmic time with respect to the number of edges in the graph. It starts with a seed vertex and iteratively explores its neighborhood until a subgraph with a small high-order conductance is found. Furthermore, we analyze its performance in terms of both effectiveness and efficiency. The experimental results on both synthetic graphs and real graphs demonstrate the effectiveness and efficiency of our proposed HOSPLOC algorithm. 

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