Graph Neural Networks (GNNs) are a popular machine learning framework for solving various graph processing applications. This framework exploits both the graph topology and the feature vectors of the nodes. One of the important applications of GNN is in the semi-supervised node classification task. The accuracy of the node classification using GNN depends on (i) the number and (ii) the choice of the training nodes. In this article, we demonstrate that increasing the training nodes by selecting nodes from the same class that are spread out across non-contiguous subgraphs, can significantly improve the accuracy. We accomplish this by presenting a novel input intervention technique that can be used in conjunction with different GNN classification methods to increase the non-contiguous training nodes and, thereby, improve the accuracy. We also present an output intervention technique to identify misclassified nodes and relabel them with their potentially correct labels. We demonstrate on real-world networks that our proposed methods, both individually and collectively, significantly improve the accuracy in comparison to the baseline GNN algorithms. Both our methods are agnostic. Apart from the initial set of training nodes generated by the baseline GNN methods, our techniques do not need any other extra knowledge about the classes of the nodes. Thus, our methods are modular and can be used as pre-and post-processing steps with many of the currently available GNN methods to improve their accuracy.

This paper presents a network-based template for analyzing large-scale dynamic data. Specifically, we propose a novel shared-memory parallel algorithm for updating tree-based structures or properties, such as connected components (CC) and minimum spanning trees (MST), on dynamic networks. The underlying idea is to update the information in a rooted tree data structure that stores the edges of the network that are most relevant to the analysis. Extensive experiments on real-world and synthetic networks demonstrate that, with the exception of the inherently sequential component for creating the rooted tree, our proposed updatiing algorithm is scalable and, in most cases, also requires significantly less memory, energy, and time than recomputing-from-scratch algorithm. To the best of our knowledge, this is the first parallel algorithm for updating MST on weighted dynamic networks. The rooted-tree based framework that we propose in this paper can be extended for updating other weighted and unweighted tree-based properties such as single source shortest path and betweenness and closeness centrality.

The Single Source Shortest Path (SSSP) problem is a classic graph theory problem that arises frequently in various practical scenarios; hence, many parallel algorithms have been developed to solve it. However, these algorithms operate on static graphs, whereas many real-world problems are best modeled as dynamic networks, where the structure of the network changes with time. This gap between the dynamic graph modeling and the assumed static graph model in the conventional SSSP algorithms motivates this work. We present a novel parallel algorithmic framework for updating the SSSP in large-scale dynamic networks and implement it on the shared-memory and GPU platforms. The basic idea is to identify the portion of the network affected by the changes and update the information in a rooted tree data structure that stores the edges of the network that are most relevant to the analysis. Extensive experimental evaluations on real-world and synthetic networks demonstrate that our proposed parallel updating algorithm is scalable and, in most cases, requires significantly less execution time than the state-of-the-art recomputing-from-scratch algorithms.

Constant communities, i.e., groups of vertices that are always clustered together, independent of the community detection algorithm used, are necessary for reducing the inherent stochasticity of community detection results. Current methods for identifying constant communities require multiple runs of community detection algorithm(s). This process is extremely time consuming and not scalable to large networks. We propose a novel approach for finding the constant communities, by transforming the problem to a binary classification of edges. We apply the Otsu method from image thresholding to classify edges based on whether they are always within a community or not. Our algorithm does not require any explicit detection of communities and can thus scale to very large networks of the order of millions of vertices. Our results on real-world graphs show that our method is significantly faster and the constant communities produced have higher accuracy (as per F1 and NMI scores) than state-of-the-art baseline methods.

Computing single-source shortest paths (SSSP) is one of the fundamental problems in graph theory. There are many applications of SSSP including finding routes in GPS systems and finding high centrality vertices for effective vaccination. In this paper, we focus on calculating SSSP on big dynamic graphs, which change with time. We propose a novel distributed computing approach, SSSPIncJoint, to update SSSP on big dynamic graphs using GraphX. Our approach considerably speeds up the recomputation of the SSSP tree by reducing the number of map-reduce operations required for implementing SSSP in the gather-apply- scatter programming model used by GraphX.

Computing the single-source shortest path (SSSP) is one of the fundamental graph algorithms, and is used in many applications. Here, we focus on computing SSSP on large dynamic graphs, i.e. graphs whose structure evolves with time. We posit that instead of recomputing the SSSP for each set of changes on the dynamic graphs, it is more efficient to update the results based only on the region of change. To this end, we present a novel two-step shared-memory algorithm for updating SSSP on weighted large-scale graphs. The key idea of our algorithm is to identify changes, such as vertex/edge addition and deletion, that affect the shortest path computations and update only the parts of the graphs affected by the change. We provide the proof of correctness of our proposed algorithm. Our experiments on real and synthetic networks demonstrate that our algorithm is as much as 4X faster compared to computing SSSP with Galois, a state-of-the-art parallel graph analysis software for shared memory architectures. We also demonstrate how increasing the asynchrony can lead to even faster updates. To the best of our knowledge, this is one of the first practical parallel algorithms for updating networks on shared-memory systems, that is also scalable to large networks.

The goal of community detection algorithms is to identify densely connected units within large networks. An implicit assumption is that all the constituent nodes belong equally to their associated community. However, some nodes are more important in the community than others. To date, efforts have been primarily made to identify communities as a whole, rather than understanding to what extent an individual node belongs to its community. Therefore, most metrics for evaluating communities, for example modularity, are global. These metrics produce a score for each community, not for each individual node. In this article, we argue that the belongingness of nodes in a community is not uniform. We quantify the degree of belongingness of a vertex within a community by a new vertex-based metric called permanence . The central idea of permanence is based on the observation that the strength of membership of a vertex to a community depends upon two factors (i) the extent of connections of the vertex within its community versus outside its community, and (ii) how tightly the vertex is connected internally. We present the formulation of permanence based on these two quantities. We demonstrate that compared to other existing metrics (such as modularity, conductance, and cut-ratio), the change in permanence is more commensurate to the level of perturbation in ground-truth communities. We discuss how permanence can help us understand and utilize the structure and evolution of communities by demonstrating that it can be used to -- (i) measure the persistence of a vertex in a community, (ii) design strategies to strengthen the community structure, (iii) explore the core-periphery structure within a community, and (iv) select suitable initiators for message spreading. We further show that permanence is an excellent metric for identifying communities. We demonstrate that the process of maximizing permanence (abbreviated as MaxPerm ) produces meaningful communities that concur with the ground-truth community structure of the networks more accurately than eight other popular community detection algorithms. Finally, we provide mathematical proofs to demonstrate the correctness of finding communities by maximizing permanence. In particular, we show that the communities obtained by this method are (i) less affected by the changes in vertex ordering, and (ii) more resilient to resolution limit, degeneracy of solutions, and asymptotic growth of values.

Despite the prevalence of community detection algorithms, relatively less work has been done on understanding whether a network is indeed modular and how resilient the community structure is under perturbations. To address this issue, we propose a new vertex-based metric called "permanence", that can quantitatively give an estimate of the community- like structure of the network.