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1. Node, Motif and Subgraph: Leveraging Network Functional Blocks Through Structural Convolution

   https://doi.org/10.1109/ASONAM.2018.8508729  

   Yang, Carl ; Liu, Mengxiong ; Zheng, Vincent W. ; Han, Jiawei ( August 2018 , IEEE/ACM 2018 International Conference on Advances in Social Networks Analysis and Mining, ASONAM 2018)

   Networks or graphs provide a natural and generic way for modeling rich structured data. Recent research on graph analysis has been focused on representation learning, of which the goal is to encode the network structures into distributed embedding vectors, so as to enable various downstream applications through off-the-shelf machine learning. However, existing methods mostly focus on node-level embedding, which is insufficient for subgraph analysis. Moreover, their leverage of network structures through path sampling or neighborhood preserving is implicit and coarse. Network motifs allow graph analysis in a finer granularity, but existing methods based on motif matching are limited to enumeratedmore »simple motifs and do not leverage node labels and supervision. In this paper, we develop NEST, a novel hierarchical network embedding method combining motif filtering and convolutional neural networks. Motif-based filtering enables NEST to capture exact small structures within networks, and convolution over the filtered embedding allows it to fully explore complex substructures and their combinations. NEST can be trivially applied to any domain and provide insight into particular network functional blocks. Extensive experiments on protein function prediction, drug toxicity prediction and social network community identification have demonstrated its effectiveness and efficiency.« less
2. Scalable Mining of Maximal Quasi-Cliques: An Algorithm-System Codesign Approach

   https://doi.org/10.14778/3436905.3436916  

   Guo, Guimu ; Yan, Da ; Özsu, M. Tamer ; Jiang, Zhe ; Khalil, Jalal ( January 2020 , Proceedings of the VLDB Endowment)

   Given a user-specified minimum degree threshold γ, a γ-quasi-clique is a subgraph g = (Vg, Eg) where each vertex ν ∈ Vg connects to at least γ fraction of the other vertices (i.e., ⌈γ · (|Vg|- 1)⌉ vertices) in g. Quasi-clique is one of the most natural definitions for dense structures useful in finding communities in social networks and discovering significant biomolecule structures and pathways. However, mining maximal quasi-cliques is notoriously expensive. In this paper, we design parallel algorithms for mining maximal quasi-cliques on G-thinker, a distributed graph mining framework that decomposes mining into compute-intensive tasks to fully utilize CPUmore »cores. We found that directly using G-thinker results in the straggler problem due to (i) the drastic load imbalance among different tasks and (ii) the difficulty of predicting the task running time. We address these challenges by redesigning G-thinker's execution engine to prioritize long-running tasks for execution, and by utilizing a novel timeout strategy to effectively decompose long-running tasks to improve load balancing. While this system redesign applies to many other expensive dense subgraph mining problems, this paper verifies the idea by adapting the state-of-the-art quasi-clique algorithm, Quick, to our redesigned G-thinker. Extensive experiments verify that our new solution scales well with the number of CPU cores, achieving 201× runtime speedup when mining a graph with 3.77M vertices and 16.5M edges in a 16-node cluster.« less
3. Attributed Graph Clustering: an Attribute-aware Graph Embedding Approach

   Akbas, Esra ; Zhao, Peixiang ( January 2017 , 2017 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining)

   Graph clustering is a fundamental problem in social network analysis, the goal of which is to group vertices of a graph into a series of densely knitted clusters with each cluster well separated from all the others. Classical graph clustering methods take advantage of the graph topology to model and quantify vertex proximity. With the proliferation of rich graph contents, such as user profiles in social networks, and gene annotations in protein interaction networks, it is essential to consider both the structure and content information of graphs for high-quality graph clustering. In this paper, we propose a graph embedding approachmore »to clustering content-enriched graphs. The key idea is to embed each vertex of a graph into a continuous vector space where the localized structural and attributive information of vertices can be encoded in a unified, latent representation. Specifically, we quantify vertex-wise attribute proximity into edge weights, and employ truncated, attribute-aware random walks to learn the latent representations for vertices. We evaluate our attribute-aware graph embedding method in real-world attributed graphs, and the results demonstrate its effectiveness in comparison with state-of-the-art algorithms.« less
4. Approximate Mining of Frequent -Subgraph Patterns in Evolving Graphs

   https://doi.org/10.1145/3442590  

   Nasir, Muhammad Anis ; Aslay, Cigdem ; Morales, Gianmarco De ; Riondato, Matteo ( April 2021 , ACM Transactions on Knowledge Discovery from Data)

   “Perhaps he could dance first and think afterwards, if it isn’t too much to ask him.” S. Beckett, Waiting for Godot Given a labeled graph, the collection of -vertex induced connected subgraph patterns that appear in the graph more frequently than a user-specified minimum threshold provides a compact summary of the characteristics of the graph, and finds applications ranging from biology to network science. However, finding these patterns is challenging, even more so for dynamic graphs that evolve over time, due to the streaming nature of the input and the exponential time complexity of the problem. We study this task inmore »both incremental and fully-dynamic streaming settings, where arbitrary edges can be added or removed from the graph. We present TipTap , a suite of algorithms to compute high-quality approximations of the frequent -vertex subgraphs w.r.t. a given threshold, at any time (i.e., point of the stream), with high probability. In contrast to existing state-of-the-art solutions that require iterating over the entire set of subgraphs in the vicinity of the updated edge, TipTap operates by efficiently maintaining a uniform sample of connected -vertex subgraphs, thanks to an optimized neighborhood-exploration procedure. We provide a theoretical analysis of the proposed algorithms in terms of their unbiasedness and of the sample size needed to obtain a desired approximation quality. Our analysis relies on sample-complexity bounds that use Vapnik–Chervonenkis dimension, a key concept from statistical learning theory, which allows us to derive a sufficient sample size that is independent from the size of the graph. The results of our empirical evaluation demonstrates that TipTap returns high-quality results more efficiently and accurately than existing baselines.« less
5. FIRST: Fast Interactive Attributed Subgraph Matching

   https://doi.org/10.1145/3097983.3098040  

   Du, Boxin ; Zhang, Si ; Cao, Nan ; Tong, Hanghang ( August 2017 , KDD)

   Attributed subgraph matching is a powerful tool for explorative mining of large attributed networks. In many applications (e.g., network science of teams, intelligence analysis, finance informatics), the user might not know what exactly s/he is looking for, and thus require the user to constantly revise the initial query graph based on what s/he finds from the current matching results. A major bottleneck in such an interactive matching scenario is the efficiency, as simply rerunning the matching algorithm on the revised query graph is computationally prohibitive. In this paper, we propose a family of effective and efficient algorithms (FIRST) to supportmore »interactive attributed subgraph matching. There are two key ideas behind the proposed methods. The first is to recast the attributed subgraph matching problem as a cross-network node similarity problem, whose major computation lies in solving a Sylvester equation for the query graph and the underlying data graph. The second key idea is to explore the smoothness between the initial and revised queries, which allows us to solve the new/updated Sylvester equation incrementally, without re-solving it from scratch. Experimental results show that our method can achieve (1) up to 16x speed-up when applying on networks with 6M$+$ nodes; (2) preserving more than 90% accuracy compared with existing methods; and (3) scales linearly with respect to the size of the data graph.« less