Regularizing graph centrality computations

In this chapter, the authors analyze the correlation between the computationally light degree centrality (DEG) and local clustering coefficient complement-based degree centrality (LCC'DC) metrics vs. the computationally heavy betweenness centrality (BWC), eigenvector centrality (EVC), and closeness centrality (CLC) metrics. Likewise, they also analyze the correlation between the computationally light complement of neighborhood overlap (NOVER') and the computationally heavy edge betweenness centrality (EBWC) metric. The authors analyze the correlations at three different levels: pair-wise (Kendall's correlation measure), network-wide (Spearman's correlation measure), and linear regression-based prediction (Pearson's correlation measure). With regards to the node centrality metrics, they observe LCC'DC-BWC to be the most strongly correlated at all the three levels of correlation. For the edge centrality metrics, the authors observe EBWC-NOVER' to be strongly correlated with respect to the Spearman's correlation measure, but not with respect to the other two measures.

Heuristic Algorithm for Approximation Betweenness Centrality Using Graph Coarsening

Congestion-aware core mapping for Network-on-Chip based systems using betweenness centrality

Recently, there has been increased interest in aminoacyl tRNA synthetases (aaRSs) as potential malarial drug targets. These enzymes play a key role in protein translation by the addition of amino acids to their cognate tRNA. The aaRSs are present in all Plasmodium life cycle stages, and thus present an attractive malarial drug target. Prolyl tRNA synthetase is a class II aaRS that functions in charging tRNA with proline. Various inhibitors against Plasmodium falciparum ProRS (PfProRS) active site have been designed. However, none have gone through clinical trials as they have been found to be highly toxic to human cells. Recently, a possible allosteric site was reported in PfProRS with two possible allosteric modulators: glyburide and TCMDC-124506. In this study, we sought to identify novel selective inhibitors targeting PfProRS active site and possible novel allosteric modulators of this enzyme. To achieve this, virtual screening of South African natural compounds against PfProRS and the human homologue was carried out using AutoDock Vina. The modulation of protein motions by ligand binding was studied by molecular dynamics (MD) using the GROningen MAchine for Chemical Simulations (GROMACS) tool. To further analyse the protein global motions and energetic changes upon ligand binding, principal component analysis (PCA), and free energy landscape (FEL) calculations were performed. Further, to understand the effect of ligand binding on the protein communication, dynamic residue network (DRN) analysis of the MD trajectories was carried out using the MD-TASK tool. A total of ten potential natural hit compounds were identified with strong binding energy scores. Binding of ligands to the protein caused observable global and residue level changes. Dynamic residue network calculations showed increase in betweenness centrality (BC) metric of residues at the allosteric site implying these residues are important in protein communication. A loop region at the catalytic domain between residues 300 and 350 and the anticodon binding domain showed significant contributions to both PC1 and PC2. Large motions were observed at a loop in the Z-domain between residues 697 and 710 which was also in agreement with RMSF calculations that showed increase in flexibility of residues in this region. Residues in this loop region are implicated in ATP binding and thus a change in dynamics may affect ATP binding affinity. Free energy landscape (FEL) calculations showed that the holo protein (protein-ADN complex) and PfProRS-SANC184 complexes were stable, as shown by the low energy with very few intermediates and hardly distinguishable low energy barriers. In addition, FEL results agreed with backbone RMSD distribution plots where stable complexes showed a normal RMSD distribution while unstable complexes had multimodal RMSD distribution. The betweenness centrality metric showed a loss of functional importance of key ATP binding site residues upon allosteric ligand binding. The deep basins in average L observed at the allosteric region imply that there is high accessibility of residues at this region. To further analyse BC and average L metrics data, we calculated the ΔBC and ΔL values by taking each value in the holo protein BC or L matrix less the corresponding value in the ligand-bound complex BC or L matrix. Interestingly, in allosteric complexes, residues located in a loop region implicated in ATP binding had negative ΔL values while in orthosteric complexes these residues had positive ΔL values. An increase in contact frequency between residues Ser263, Thr267, Tyr285, and Leu707 at the allosteric site and residues Thr397, Pro398, Thr402, and Gln395 at the ATP binding TXE loop was observed. In summary, this study identified five potential orthosteric inhibitors and five allosteric modulators against PfProRS. Allosteric modulators changed ATP binding site dynamics, as shown by RMSF, PCA, and DRN calculations. Changes in dynamics of the ATP binding site and increased contact frequency between residues at the proposed allosteric site and the ATP binding site may explain how allosteric modulators distort the ATP binding site and thus might inhibit PfProRS. The scaffolds of the identified hits in the study can be used as a starting point for antimalarial inhibitor development with low human cytotoxicity.

Detecting important actors in social networks is still a hot research topic in the complex network area. Various metrics of centrality are proposed to deal with this problem. Each metric addresses the problem from one point of view. Therefore, this paper introduces a new method to estimate the influence of nodes using multi-criteria decision-making MCDM. The proposed approach is based on the technique for order preference by similarity to an ideal solution (TOPSIS). TOPSIS aggregates centrality measures. Degree, betweenness, closeness, and eigenvector centralities are combined in this work to detect the importance of each actor. Each metric of centrality has its limitations, thus the proposed approach takes advantage of these four centralities together through TOPSIS. To illustrate the effectiveness of the proposed methodology, the Facebook ego network as an example of a social network is used for experimentation. The SI model is used to compare the spreading ability of nodes between centralities and the proposed approach on the Facebook ego network. The experimental results show that the proposed methodology can rank the important nodes more efficiently than a single measure of centrality.KeywordsComplex networksTOPSISImportant actorsCentrality measuresSI model

In this paper we investigate the dissimilar multithreading programming paradigms on x86 CPU architectures, where the recently released Intel Xeon Phi Coprocessor and commonly used Intel Xeon processors were studied, as well as the NVIDIA K20 GPU, which represents the cutting-edge general purpose graphics processing unit. The relevant numerical algorithm selected to address the problem is power method, which is widely used to compute the dominant eigenvalue of a matrix. This work focuses on dense linear algebra. The frequently used multi-core or many-core processor parallelism techniques include OpenMP, Intel Cilk Plus, Intel Threading Building Blocks, i.e. TBB, along with the optimized computing libraries such as Intel Math Kernel Library(MKL) or the NVIDIA CUDA Basic Linear Algebra Subroutines(cuBLAS) library. Optimized implementations of these techniques were separately applied to the aforementioned architectures. For the reason that a unitary programming model may not satisfy the growing performance demand, we also explored some possible mix of these languages. The study shows that the hybrid pattern of multithreading and data parallelism via explicit vectorization maximizes the performance on x86 architectures, which allows us to obtain 80% of the sustainable peak performance in double precision on the Intel Many Integrated Core(MIC) Architecture. In the case of single precision, this number reaches even 96%. In addition, this approach enables a reasonable performance by requiring least developing time. The numbers of iterations till convergence are roughly the same in both architectures of CPU and GPU. The GPU performs better in small matrix sizes. However, the Intel Xeon Phi coprocessor excels for large sizes with a better scalability.

We present correlation analysis between the centrality values observed for nodes (a computationally lightweight metric) and the maximal clique size (a computationally hard metric) that each node is part of in complex real-world network graphs. We consider the four common centrality metrics: degree centrality (DegC), eigenvector centrality (EVC), closeness centrality (ClC) and betweenness centrality (BWC). We define the maximal clique size for a node as the size of the largest clique (in terms of the number of constituent nodes) the node is part of. The real-world network graphs studied range from regular random network graphs to scale-free network graphs. We observe that the correlation between the centrality value and the maximal clique size for a node increases with increase in the spectral radius ratio for node degree, which is a measure of the variation of the node degree in the network. We observe the degree-based centrality metrics (DegC and EVC) to be relatively better correlated with the maximal clique size compared to the shortest path-based centrality metrics (ClC and BWC).

Fast, scalable, low-cost, and low-power execution of parallel graph algorithms is important for a wide variety of commercial and public sector applications. Breadth First Search (BFS) imposes an extreme burden on memory bandwidth and network communications and has been proposed as a benchmark that may be used to evaluate current and future parallel computers. Hardware trends and manufacturing limits strongly imply that many-core devices, such as NVIDIA® GPUs and the Intel® Xeon Phi®, will become central components of such future systems. GPUs are well known to deliver the highest FLOPS/watt and enjoy a very significant memory bandwidth advantage over CPU architectures. Recent work has demonstrated that GPUs can deliver high performance for parallel graph algorithms and, further, that it is possible to encapsulate that capability in a manner that hides the low level details of the GPU architecture and the CUDA language but preserves the high throughput of the GPU. We extend previous research on GPUs and on scalable graph processing on supercomputers and demonstrate that a high-performance parallel graph machine can be created using commodity GPUs and networking hardware.

In network analysis, the betweenness centrality of a node informally captures\nthe fraction of shortest paths visiting that node. The computation of the\nbetweenness centrality measure is a fundamental task in the analysis of modern\nnetworks, enabling the identification of the most central nodes in such\nnetworks. Additionally to being massive, modern networks also contain\ninformation about the time at which their events occur. Such networks are often\ncalled temporal networks. The temporal information makes the study of the\nbetweenness centrality in temporal networks (i.e., temporal betweenness\ncentrality) much more challenging than in static networks (i.e., networks\nwithout temporal information). Moreover, the exact computation of the temporal\nbetweenness centrality is often impractical on even moderately-sized networks,\ngiven its extremely high computational cost. A natural approach to reduce such\ncomputational cost is to obtain high-quality estimates of the exact values of\nthe temporal betweenness centrality. In this work we present ONBRA, the first\nsampling-based approximation algorithm for estimating the temporal betweenness\ncentrality values of the nodes in a temporal network, providing rigorous\nprobabilistic guarantees on the quality of its output. ONBRA is able to compute\nthe estimates of the temporal betweenness centrality values under two different\noptimality criteria for the shortest paths of the temporal network. In\naddition, ONBRA outputs high-quality estimates with sharp theoretical\nguarantees leveraging on the \\emph{empirical Bernstein bound}, an advanced\nconcentration inequality. Finally, our experimental evaluation shows that ONBRA\nsignificantly reduces the computational resources required by the exact\ncomputation of the temporal betweenness centrality on several real world\nnetworks, while reporting high-quality estimates with rigorous guarantees.\n

Recent innovations focused around parallel processing, either through systems containingmultiple processors or processors containing multiple cores, holdgreat promise for enhancing the performance of the trigger at the LHCand extending its physics program. The flexibility of the CMS/ATLAStrigger system allows for easy integration of computationalaccelerators, such as NVIDIA's Tesla Graphics Processing Unit (GPU) orIntel's Xeon Phi, in the High Level Trigger. These accelerators have thepotential to provide faster or more energy efficient event selection,thus opening up possibilities for new complex triggers that were notpreviously feasible. At the same time, it is crucial to explore theperformance limits achievable on the latest generation multicore CPUswith the use of the best software optimization methods. In thisarticle, a new tracking algorithm based on the Hough transform will beevaluated for the first time on multi-core Intel i7-3770 and IntelXeon E5-2697v2 CPUs, an NVIDIA Tesla K20c GPU, and an Intel Xeon Phi7120 coprocessor. Preliminary time performance will be presented.

A large dataset network is considered for computation of maximal clique size (MC). Additionally, its link with popular centrality metrics to decrease uncertainty and complexity and for finding influential points of any network has also been investigated. Previous studies focus on centrality metrics like degree centrality (DC), closeness centrality (CC), betweenness centrality (BC) and Eigenvector centrality (EVC) and compare them with maximal clique size however, in this study Katz centrality measure is also considered and shows a pretty robust relation with maximal clique size (MC). Secondly, maximal clique size (MC) algorithm is also revised for network analysis to avoid complexity in computation. Association between MC and five centrality metrics has been evaluated through recognized methods that are Pearson’s correlation coefficient (PCC), Spearman’s correlation coefficient (SCC) and Kendall’s correlation coefficient (KCC). The strong strength of association between them is seen through all three correlation coefficients measure.

Nowadays a large amount of data is originated by complex systems, such as social networks, transportation systems, computer and service networks. These systems can be modeled by using graphs and studied by exploiting graph metrics, such as betweenness centrality (BC), a popular metric to analyze node centrality of graphs. In spite of its great potential, this metric requires long computation time, especially for large graphs. In this paper, we present a very fast algorithm to compute BC of undirected graphs by exploiting clustering. The algorithm leverages structural properties of graphs to find classes of equivalent nodes: by selecting one representative node for each class, we are able to compute BC by significantly reducing the number of single-source shortest path explorations adopted by Brandes’ algorithm. We formally prove the graph properties that we exploit to define the algorithm and present an implementation based on Scala for both sequential and parallel map-reduce executions. The experimental evaluation of both versions, conducted with synthetic and real graphs, reveals that our solution largely outperforms Brandes’ algorithm and significantly improves known heuristics.

A centrality model for directed graphs based on the Two-Way-Random Path and associated indices for characterizing the nodes

Betweenness centrality is an important centrality measure widely used in social network analysis, route planning etc. However, even for mid-size networks, it is practically intractable to compute exact betweenness scores. In this paper, we propose a generic randomized framework for unbiased approximation of betweenness centrality. The proposed framework can be adapted with different sampling techniques and give diverse methods. We discuss the conditions a promising sampling technique should satisfy to minimize the approximation error and present a sampling method partially satisfying the conditions. We perform extensive experiments and show the high efficiency and accuracy of the proposed method.

In 2020, the world is facing a Covid-19 virus pandemic. The fields of epidemiology and networks are needed in dealing with its spread. Individual (contact) tracing is an important control measure in the spread of infectious diseases. The network of contacts describes the potential pathways for the spread of the disease. Social Network Analysis (SNA) is the study of structural construction based on graph theory with Degree Centrality, Betweenness Centrality, and Closeness Centrality. In this paper, the SNA graph provides a description of the contact network in a resident cluster. Visualization of the formed SNA graph provides information on the pattern of contact relationships in the cluster. The measurement of centrality in the SNA method identifies who has a high value of connectedness and closeness in the cluster. The calculation of degree centrality shows that node-F391 is the node with the highest interaction, which is 3,203. This indicates that node interacts the most with residents in its environment within 14 days before and after being positive for COVID-19 based on the date of the swab test. The calculation of Betweenness Centrality shows that nodes-B041 and C371 are important actors with the highest value of 0.006. The two node becomes an important link. The use of graphs on SNA provides visualization of the contact network to distinguish potential relationships between close contacts, so that contact tracing can be carried out based on disease path mapping. Compared to the conventional way of reviewing individual contact records, graph visualization on the SNA is a good adjunct tool for healthcare workers in contact tracing investigations.