Motifs in graphs (or networks) are subgraphs induced by a small set of vertices such as triangles and cliques. The frequency of motifs is used to compare and align networks across various domains, such as biology, epidemiology, and social sciences. Recent advances have made it feasible to solve the computational challenge of counting motifs in networks with over a billion edges. However, these algorithms apply only for static networks where the structure remains unchanged. In reality, networks dynamically evolve, and understanding how motifs change with the dynamic nature of these networks remains an unsolved challenge despite its potential to provide essential insights into the system. We present ParaDyMS (Parallel Dynamic Motif Counting at Scale), the first parallel algorithm for updating motif counts in fully dynamic networks using batched updates. Our algorithm updates the frequencies of motifs only in the modified parts of the network instead of recomputing them from scratch. We provide proof of the algorithm's correctness and complexity and empirically compare its execution time with another state-of-the-art static algorithm on shared memory and GPUs using realworld networks. Our results show that our algorithm is highly scalable and can significantly reduce the time to compute motifs by more than 90% in the best case and, on average, by 69%.

Over the last few decades, simple graphs have been extensively used for studying complex systems of interacting entities from diverse disciplines, such as social networks, transportation, epidemiology, etc. However, when studying data with multiple types of entities, relationships, and features, simple (or even attributed) graphs are not always sufficient. For example, to study accident patterns to take mitigating actions, one needs to explore accident patterns based on factors like weather (rain, sunny, sleet, etc.), light, and road surface conditions in different geographical regions. As another example, to find individuals who are influential across multiple social media, a single graph approach is not well-suited. Indeed, to model such multiple relationships, multiple related graphs are useful. This can be done using multilayer networks (MLNs). Any complex data analysis can immensely benefit from interactive graphic tools rather than working with raw data in command prompt mode. This is especially true as data and models become increasingly complex. To interpret and understand the results of analysis, drill-down, and visualization become critical. The MLN-Dashboard (called MLN-geeWhiz) presented in this demo paper aims to facilitate all aspects of MLN layer generation, analysis, and visualization through an intuitive, interactive web-based dashboard. In this paper, we discuss the dashboard, its architecture, the functionality currently supported, and some use cases.

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.

Writing large amounts of data concurrently to stable storage is a typical I/O pattern of many HPC workflows. This pattern introduces high I/O overheads and results in increased storage space utilization especially for workflows that need to capture the evolution of data structures with high frequency as checkpoints. In this context, many applications, such as graph pattern matching, perform sparse updates to large data structures between checkpoints. For these applications, incremental checkpointing techniques that save only the differences from one checkpoint to another can dramatically reduce the checkpoint sizes, I/O bottlenecks, and storage space utilization. However, such techniques are not without challenges: it is non-trivial to transparently determine what data has changed since a previous checkpoint and assemble the differences in a compact fashion that does not result in excessive metadata. State-of-art data reduction techniques (e.g., compression and de-duplication) have significant limitations when applied to modern HPC applications that leverage GPUs: slow at detecting the differences, generate a large amount of metadata to keep track of the differences, and ignore crucial spatiotemporal checkpoint data redundancy. This paper addresses these challenges by proposing a Merkle tree-based incremental checkpointing method to exploit GPUs’ high memory bandwidth and massive parallelism. Experimental results at scale show a significant reduction of the I/O overhead and space utilization of checkpointing compared with state-of-the-art incremental checkpointing and compression techniques.

Incremental graphs that change over time capture the changing relationships of different entities. Given that many real-world networks are extremely large, it is often necessary to partition the network over many distributed systems and solve a complex graph problem over the partitioned network. This paper presents a distributed algorithm for identifying strongly connected components (SCC) on incremental graphs. We propose a two-phase asynchronous algorithm that involves storing the intermediate results between each iteration of dynamic updates in a novel meta-graph storage format for efficient recomputation of the SCC for successive iterations. To the best of our knowledge, this is the first attempt at identifying SCC for incremental graphs across distributed compute nodes. Our experimental analysis on real and synthesized graphs shows up to 2.8x performance improvement over the state-of-the-art by reducing the overall memory utilized and improving the communication bandwidth.

We present the first GPU-based parallel algorithm to efficiently update vertex coloring on large dynamic networks. For single GPU, we introduce the concept of loosely maintained vertex color update that reduces computation and memory requirements. For multiple GPUs, in distributed environments, we propose priority-based ordering of vertices to reduce the communication time. We prove the correctness of our algorithms and experimentally demonstrate that for graphs of over 16 million vertices and over 134 million edges on a single GPU, our dynamic algorithm is as much as 20x faster than state-of-the-art algorithm on static graphs. For larger graphs with over 130 million vertices and over 260 million edges, our distributed implementation with 8 GPUs produces updated color assignments within 160 milliseconds. In all cases, the proposed parallel algorithms produce comparable or fewer colors than state-of-the-art algorithms.

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.

Article proposing the use of anonymization techniques coupled with graph algorithms over homomorphically encrypted (HE) graphs as a basis of analysis for this accumulated data. This approach ensures individuals’ privacy and anonymity while preserving the usefulness of the plaintext data. This article was originally presented at the 18th International Conference on Security and Cryptography - SECRYPT.

As the scientific community prepares to deploy an increasingly complex and diverse set of applications on exascale platforms, the need to assess reproducibility of simulations and identify the root causes of reproducibility failures increases correspondingly. One of the greatest challenges facing reproducibility issues at exascale is the inherent non-determinism at the level of inter-process communication. The use of non-deterministic communication constructs is necessary to boost performance, but communication non-determinism can also hamper software correctness and result reproducibility. To address this challenge, we propose a software framework for identifying the percentage and sources of communication non-determinism. We model parallel executions as directed graphs and leverage graph kernels to characterize run-to-run variations in inter-process communication. We demonstrate the effectiveness of graph kernel similarity as a proxy for non-determinism, by showing that these kernels can quantify the type and degree of non-determinism present in communication patterns. To demonstrate our framework's ability to link and quantify runtime non-determinism to root sources, demonstrate with present for an adaptive mesh refinement application, where our framework automatically quantifies the impact of function calls on non-determinism, and a Monte Carlo application, where our framework automatically quantifies the impact of parameter configurations on non-determinism.

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.

Many scale-free networks exhibit a "rich club" structure, where high degree vertices form tightly interconnected subgraphs. In this paper, we explore the emergence of "rich clubs" in the context of shortest path based centrality metrics. We term these subgraphs of connected high closeness or high betweeness vertices as rich centrality clubs (RCC). Our experiments on real world and synthetic networks high- light the inter-relations between RCCs, expander graphs, and the core-periphery structure of the network. We show empirically and theoretically that RCCs exist, if the core-periphery structure of the network is such that each shell is an expander graph, and their density decreases from inner to outer shells. We further demonstrate that in addition to being an interesting topological feature, the presence of RCCs is useful in several appli- cations. The vertices in the subgraph forming the RCC are effective seed nodes for spreading information. Moreover, networks with RCCs are robust under perturbations to their structure. Given these useful properties of RCCs, we present a network modification model that can efficiently create a RCC within net- works where they are not present, while retaining other structural properties of the original network. The main contributions of our paper are: (i) we demonstrate that the formation of RCC is related to the core-periphery structure and particularly the expander like properties of each shell, (ii) we show that the RCC property can be used to find effective seed nodes for spreading information and for improving the resilience of the network under perturbation and, finally, (iii) we present a modification algorithm that can insert RCC within networks, while not affecting their other structural properties. Taken together, these contributions present one of the first comprehensive studies of the properties and applications of rich clubs for path based centralities.

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.

In this paper we evaluate the effect of noise on community scoring and centrality-based parameters with respect to two different aspects of network analysis: (i) sensitivity, that is how the parameter value changes as edges are removed and (ii) reliability in the context of message spreading, that is how the time taken to broadcast a message changes as edges are removed. Our experiments on synthetic and real-world networks and three different noise models demonstrate that for both the aspects over all networks and all noise models, permanence qualifies as the most effective metric. For the sensitivity experiments closeness centrality is a close second. For the message spreading experiments, closeness and betweenness centrality based initiator selection closely competes with permanence. This is because permanence has a dual characteristic where the cumulative permanence over all vertices is sensitive to noise but the ids of the top-rank vertices, which are used to find seeds during message spreading remain relatively stable under noise.

Networks created from real-world data contain some inaccuracies or noise, manifested as small changes in the network structure. An important question is whether these small changes can signficantly affect the analysis results.

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.

Detection of non-overlapping and overlapping communities are essentially the same problem. However, current algorithms focus either on finding overlapping or non-overlapping communities. We present a generalized framework that can identify both non-overlapping and overlapping communities, without any prior input about the network or its community distribution. To do so, we introduce a vertex-based metric,GenPerm, that quantifies by how much a vertex belongs to each of its constituent communities. Our community detection algorithm is based on maximizing the GenPerm over all the vertices in the network. We demonstrate, through experiments over synthetic and real-world networks, that GenPerm is more effective than other metrics in evaluating community structure. Further, we show that due to its vertex-centric property, GenPerm can be used to unfold several inferences beyond community detection, such as core-periphery analysis and message spreading. Our algorithm for maximizing GenPerm outperforms six state-of-the-art algorithms in accurately predicting the ground-truth labels. Finally, we discuss the problem of resolution limit in overlapping communities and demonstrate that maximizing GenPerm can mitigate this problem.

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.

Network modeling of biological systems is a powerful tool for analysis of high-throughput datasets by computational systems biologists. Integration of networks to form a heterogeneous model requires that each network be as noise-free as possible while still containing relevant biological information. In earlier work, we have shown that the graph theoretic properties of gene correlation networks can be used to highlight and maintain important structures such as high degree nodes, clusters, and critical links between sparse network branches while reducing noise. In this paper, we propose the design of advanced network filters using structurally related graph theoretic properties. While spanning trees and chordal subgraphs provide filters with special advantages, we hypothesize that a hybrid subgraph sampling method will allow for the design of a more effective filter preserving key properties in biological networks. That the proposed approach allows us to optimize a number of parameters associated with the filtering process which in turn improves upon the identification of essential genes in mouse aging networks.

Chordal graphs are triangulated graphs where any cycle larger than three is bisected by a chord. Many combinatorial optimization problems such as computing the size of the maximum clique and the chromatic number are NP-hard on general graphs but have polynomial time solutions on chordal graphs. In this paper, we present a novel multithreaded algorithm to extract a maximal chordal sub graph from a general graph. We develop an iterative approach where each thread can asynchronously update a subset of edges that are dynamically assigned to it per iteration and implement our algorithm on two different multithreaded architectures - Cray XMT, a massively multithreaded platform, and AMD Magny-Cours, a shared memory multicore platform. In addition to the proof of correctness, we present the performance of our algorithm using a test set of synthetical graphs with up to half-a-billion edges and real world networks from gene correlation studies and demonstrate that our algorithm achieves high scalability for all inputs on both types of architectures.

In this paper, we investigate how class relationships are disrupted after large scale changes. We use graphs to represent different software versions and study changes to graph properties. We explore different combinatorial metrics to measure the extent of disruption after perfective maintenance activities. Our early results, on JHotDraw, demonstrate that combinatorial metrics can provide a good indicator to the degree to which relationships are disrupted or preserved across different versions.

Unsupervised classification typically concerns identifying clusters of similar entities in an unlabeled dataset. Popular methods include clustering based on (i) distance-based metrics between the entities in the feature space (K-Means), and (ii) combinatorial properties in a weighted graph representation of the dataset (Multilevel K-Means).