Network Metrics Research Articles

A Method-Level Defect Prediction Approach Based on Structural Features of Method-Calling Network

Software defect prediction models help testers find program modules that have a high probability of having defects. A method-calling network can express the dependencies between methods in a program. Existing approaches do not sufficiently utilize method-calling network to characterize the structural features between methods. To address this problem, in this study, it is proposed for the first time that the characteristics of methods in a program are obtained by analyzing the method-calling network, and a new approach is proposed for defect prediction at the method-level. Specifically in this study, the method-calling network of the program was first constructed and the network metrics of the method-calling network were obtained. Next, the new network embedding technique (node2vec) was used to automatically encode the method-calling network structure into a low-dimensional vector to obtain the network embedding metrics. Finally, they were combined with code metrics to construct defect prediction models. We evaluated our approaches on 13 open-source software systems. The experimental results show that the proposed method improved the values of area under the receiver operating characteristic curve by 2.5% to 6.7% and Matthews correlation coefficient by 13% to 178.4% compared to the baselines. Therefore the method-calling network contains rich structural features between methods, and the structural features extend the features used for method-level defect prediction and further improve the performance of defect prediction models.

Analyzing Text and Images in Digital Communication: The Case of Securitization in American White Supremacist Online Discourse

Sociological research on online discourse increasingly uses digital data consisting of messages combining multiple modes of media, with meaning arising from contents’ interaction across modes. Yet, techniques to study this interplay are underdeveloped relative to the toolkit for analyzing solely texts. The authors introduce an automated approach for relationally analyzing texts and images, focusing on how to examine the discursive meaning emerging from concepts’ connections across associated text and image modes. The authors validate this approach using a crowdsourced task and obtain results suggesting that applying social network metrics to semantic space can generate useful insights into how people understand discourse. To illustrate this approach, the authors examine the concept of “securitization” in online white supremacist discourse. The findings indicate that ideas of securitization link notions of personalistic leadership with imagery of space and place. This analysis demonstrates how the authors’ approach helps researchers understand multimodal material and meaning-making in digital discourse.

Global Production Networks in the Regional Analysis Framework: Case of the EU Peripheral Automotive Manufacturing

Recent transformations following the global financial crisis of 2009, COVID-19 pandemic, supply chains disruptions and newest shocks have radically reshaped global production landscape and challenged comparative benefits of global production networks (GPN) vs global value chains (GVC) paradigms in international production analysis. The study tests the hypothesis that GPN concept allows for a better identification of structural shifts in international production structures while revealing regional patterns of cooperation. In the first section, the main methodological constraints of GVC paradigm are specified. Additionally, the reasons for the application of network-based approach to international production are outlined. The second section dissects the EU automotive manufacturing to support the theoretical propositions. While comparing GVC and GPN quantitative toolkits, the possible trade-off has been reached which is to calculate network indicators (transitivity, centrality, etc.) on the inter-country input-output tables. As a result, the hypothesis was confirmed. Specifically, betweenness centrality metric suggests that Czechia and Slovakia have immediately favoured a positive effect of the entry into the EU, whereas neither of GVC indicators reveals such a shift. Simultaneously, 2008 crisis is depicted via GVC indicators, whilst network metrics suggest no structural changes in the production system. These results corroborate to our theoretical juxtaposition of GVC/GPN approaches. The methodological cohesion of two sets of indicators further advances the views on European regional coreperiphery integration and automotive production networks dynamics. At the same time, the findings may contribute to the reassessment of regional integration developments in Europe, as well as in Latin America and Eurasia.

Edge Learning for B5G Networks With Distributed Signal Processing: Semantic Communication, Edge Computing, and Wireless Sensing

To process and transfer large amounts of data in emerging wireless services, it has become increasingly appealing to exploit distributed data communication and learning. Specifically, edge learning (EL) enables local model training on geographically disperse edge nodes and minimizes the need for frequent data exchange. However, the current design of separating EL deployment and communication optimization does not yet reap the promised benefits of distributed signal processing, and sometimes suffers from excessive signalling overhead, long processing delay, and unstable learning convergence. In this paper, we provide an overview on practical distributed EL techniques and their interplay with advanced communication optimization designs. In particular, typical performance metrics for dual-functional learning and communication networks are discussed. Also, recent achievements of enabling techniques for the dual-functional design are surveyed with exemplifications from the mutual perspectives of "communications for learning" and "learning for communications." The application of EL techniques within a variety of future communication systems are also envisioned for beyond 5G (B5G) wireless networks. For the application in goal-oriented semantic communication, we present a first mathematical model of the goal-oriented source entropy as an optimization problem. In addition, from the viewpoint of information theory, we identify fundamental open problems of characterizing rate regions for communication networks supporting distributed learning-and-computing tasks. We also present technical challenges as well as emerging application opportunities in this field, with the aim of inspiring future research and promoting widespread developments of EL in B5G.

Artificial intelligence application and performance in forensic age estimation with mandibular third molars on panoramıc radiographs

Background/Aim: Age estimation is of great importance due to legal requirements. Although there are many methods used, most of them are based on age related dental changes. Artificial intelligence based programs, one of the most current and popular topics in recent years, are becoming more and more important in dental studies. This study aims to measure the performance of deep learning in forensic age estimation from mandibular third molars using panoramic radiographs. Material and Methods: In our study, panoramic radiographs of male and female patients between the ages of 16-26 years who applied to our department for various reasons were used. The pixel-based Convolutional Neural Networks (CNN) method, one of the types of artificial neural networks, was applied. The high performance ResNeXt-101 model and Adamax algorithm were selected. The learning rate was set to 0.001. The dataset was labeled with the DentiAssist platform and randomly divided into 80% training and 20% testing. 1296 data under 18 and 1036 data over 18 were used. Dropout method was applied in case of over memorization. In the last step of the hidden layer, a linear two-class prediction was obtained using a structured fully connected layer. Results: The performance metrics for the ResNeXt neural network were 4.36% accuracy, 83.95% precision, 84.56% recall, 84.56% F1-score and 84.14% F1-score (80% confidence interval) when adequate training was provided. Conclusions: Artificial intelligence, which eliminates the subjective margin of error compared to conventional methods and rapidly processes a large amount of data, has achieved promising results in forensic age determination.

Application of artificial intelligence in the detection and stratification of prostate cancer: Literature review

This review examines the current methodologies employed in utilizing artificial intelligence for the identification and classification of prostate cancer using magnetic resonance imaging data. It outlines the volume of data utilized and highlights the most commonly sought-after sequences employed for training neural networks. The review further presents the accuracy metrics of the neural networks analyzed, accompanied by a succinct explanation of each metric. Furthermore, the review pinpoints the limitations associated with contemporary neural networks devised for the detection and classification of prostate cancer using magnetic resonance imaging data, as well as the challenges encountered during their creation and implementation.In summary, this comprehensive analysis delves into the existing approaches in leveraging artificial intelligence for prostate cancer detection and stratification through magnetic resonance imaging data. It addresses the data scale and preferred magnetic resonance imaging sequences employed for neural network training. The review provides a breakdown of accuracy indicators for the neural networks evaluated, elucidating their respective capabilities. Moreover, the review identifies the drawbacks associated with current neural network models developed for prostate cancer detection and stratification via magnetic resonance imaging data, while also recognizing the complexities involved in their development and practical application.

INVESTGATING POWER METRICS OF NEURAL NETWORKS AFTER PRUNING, QUANTIZATION, DPU IMPLEMENTATION: A COMPARATIVE ANALYSIS

The rapid proliferation of deep learning applications in various fields has highlighted the need for efficient neural network implementations, especially on resource-constrained edge devices. In response to this demand, pruning and quantization have emerged as essential techniques to reduce the computational and memory requirements of neural networks. Additionally, the deployment of dedicated hardware, such as Digital Processing Units (DPUs), has gained momentum for accelerating neural network inference. This paper presents a comprehensive comparative analysis of the power metrics of neural networks after pruning and quantization, with a particular focus on their implement-ation on DPUs. The objective of this research is to investigate the energy efficiency and power consumption of pruned and quantized neural networks when executed on DPU platforms. The trade-offs between model size reduction and inference accuracy, as well as the power efficiency of different DPU architectures are researched. The results reveal insights into the power efficiency of pruned and quantized neural networks on DPU platforms, offering a clear understanding of the benefits and trade-offs associated with these optimization techniques. This research provides a valuable resource for researchers, developers, and practitioners interested in optimizing neural network implementations for power efficiency. The findings contribute to the ongoing effort to make deep learning more accessible and sustainable on edge devices and other power-constrained environments, ultimately enabling a wider range of applications with reduced energy consumption.

Multi-query Vehicle Re-identification: Viewpoint-conditioned Network, Unified Dataset and New Metric.

Existing vehicle re-identification methods mainly rely on the single query, which has limited information for vehicle representation and thus significantly hinders the performance of vehicle Re-ID in complicated surveillance networks. In this paper, we propose a more realistic and easily accessible task, called multi-query vehicle Re-ID, which leverages multiple queries to overcome viewpoint limitation of single one. Based on this task, we make three major contributions. First, we design a novel viewpoint-conditioned network (VCNet), which adaptively combines the complementary information from different vehicle viewpoints, for multi-query vehicle Re-ID. Moreover, to deal with the problem of missing vehicle viewpoints, we propose a cross-view feature recovery module which recovers the features of the missing viewpoints by learnt the correlation between the features of available and missing viewpoints. Second, we create a unified benchmark dataset, taken by 6142 cameras from a real-life transportation surveillance system, with comprehensive viewpoints and large number of crossed scenes of each vehicle for multi-query vehicle Re-ID evaluation. Finally, we design a new evaluation metric, called mean cross-scene precision (mCSP), which measures the ability of cross-scene recognition by suppressing the positive samples with similar viewpoints from the same camera. Comprehensive experiments validate the superiority of the proposed method against other methods, as well as the effectiveness of the designed metric in the evaluation of multi-query vehicle Re-ID. The codes and dataset are available at: https://github.com/zhangchaobin001/VCNet.

Structural Cerebral Network Differences in Prodromal Alzheimer’s Disease and Prodromal Dementia with Lewy Bodies

Introduction: Alzheimer’s disease (AD) and dementia with Lewy bodies (DLB) have long prodromal phases without dementia. However, the patterns of cerebral network alteration in this early stage of the disease remain to be clarified. Method: Participants were 48 patients with mild cognitive impairment (MCI) due to AD (MCI-AD), 18 patients with MCI with DLB (MCI with Lewy bodies: MCI-LB), and 23 healthy controls who underwent a 1.5-Tesla magnetic resonance imaging scan. Cerebral networks were extracted from individual T1-weighted images based on the intracortical similarity, and we estimated the differences of network metrics among the three diagnostic groups. Results: Whole-brain analyses for degree, betweenness centrality, and clustering coefficient images were performed using SPM8 software. The patients with MCI-LB showed significant reduction of degree in right putamen, compared with healthy subjects. The MCI-AD patients showed significant lower degree in left insula and bilateral posterior cingulate cortices compared with healthy subjects. There were no significant differences in small-world properties and in regional gray matter volume among the three groups. Conclusions: We found the change of degree in the patients with MCI-AD and with MCI-LB, compared with healthy controls. These findings were consistent with the past single-photon emission computed tomography studies focusing on AD and DLB. The disease-related difference in the cerebral neural network might provide an adjunct biomarker for the early detection of AD and DLB.

A Mini Review of Node Centrality Metrics in Biological Networks

Survey/review study A Mini Review of Node Centrality Metrics in Biological Networks Mengyuan Wang 1,2, Haiying Wang 1, and Huiru Zheng 1,* 1 School of Computing, Ulster University, Belfast, BT15 1ED, United Kingdom 2 Scotland’s Rural College, Edinburgh, EH25 9RG, United Kingdom * Correspondence: h.zheng@ulster.ac.uk Received: 31 October 2022 Accepted: 21 November 2022 Published: 22 December 2022 Abstract: The diversity of nodes in a complex network causes each node to have varying significance, and the important nodes often have a significant impact on the structure and function of the network. Although the interpretation of the results of biological networks must always depend on the topological study of nodes, there is presently no consensus on how to use these metrics, and most network analyses always result in a basic interpretation of a limited number of metrics. To thoroughly comprehend biological networks, it is necessary to consistently understand the notion of node centrality. Therefore, for 10 typical nodal metrics in biological networks, the study first assesses their current applications, advantages, disadvantages as well as potential applications. Then, a review of previous studies is provided, and suggestions are made correspondingly for the purpose of improving biological topology algorithms. Finally, the following recommendations are made in this study: (1) a comprehensive and accurate assessment of node centrality necessitates the use of multiple metrics, including both the target node and its surroundings, and density of maximum neighbourhood component(DMNC) can be used as a complement to other node centrality metrics; (2) different centrality metrics can be applied to identify nodes with different functions, which in this study are mapped as modular surroundings, bridging roles, and susceptibility; and (3) the following groups of node centrality can often be verified against each other, including degree and maximum neighbourhood component (MNC), eccentricity, closeness and radiality; stress and betweenness.

When standard network measures fail to rank journals: A theoretical and empirical analysis

Abstract Journal rankings are widely used and are often based on citation data in combination with a network approach. We argue that some of these network-based rankings can produce misleading results. From a theoretical point of view, we show that the standard network modeling approach of citation data at the journal level (i.e., the projection of paper citations onto journals) introduces fictitious relations among journals. To overcome this problem, we propose a citation path approach, and empirically show that rankings based on the network and the citation path approach are very different. Specifically we use MEDLINE, the largest open-access bibliometric data set, listing 24,135 journals, 26,759,399 papers, and 323,356,788 citations. We focus on PageRank, an established and well-known network metric. Based on our theoretical and empirical analysis, we highlight the limitations of standard network metrics and propose a method to overcome them.

Maternal psychological distress associates with alterations in resting-state low-frequency fluctuations and distal functional connectivity of the neonate medial prefrontal cortex.

Prenatal stress exposure (PSE) has been observed to exert a programming effect on the developing infant brain, possibly with long-lasting consequences on temperament, cognitive functions and the risk for developing psychiatric disorders. Several prior studies have revealed that PSE associates with alterations in neonate functional connectivity in the prefrontal regions and amygdala. In this study, we explored whether maternal psychological symptoms measured during the 24th gestational week had associations with neonate resting-state network metrics. Twenty-one neonates (nine female) underwent resting-state fMRI scanning (mean gestation-corrected age at scan 26.95 days) to assess fractional amplitude of low-frequency fluctuation (fALFF) and regional homogeneity (ReHo). The ReHo/fALFF maps were used in multiple regression analysis to investigate whether maternal self-reported anxiety and/or depressive symptoms associate with neonate functional brain features. Maternal psychological distress (composite score of depressive and anxiety symptoms) was positively associated with fALFF in the neonate medial prefrontal cortex (mPFC). Anxiety and depressive symptoms, assessed separately, exhibited similar but weaker associations. Post hoc seed-based connectivity analyses further showed that distal connectivity of mPFC covaried with PSE. No associations were found between neonate ReHo and PSE. These results offer preliminary evidence that PSE may affect functional features of the developing brain during gestation.

Homogenous or heterogeneous? Demand effect of reviewer similarity in online video website

PurposeNowadays, online platforms which provide products or services try to implement their homegrown communities to facilitate users' social interactions. Reviewers' activities in these communities can reflect their interests. Based on the theory of homophily, the authors aim to explore the impacts of the reviewer preference similarity and opinion similarity on the rate of product diffusion.Design/methodology/approachFirst, the authors construct reviewer similarity network based on their common interests and propose typical network metrics to measure reviewer preference similarity. Second, the authors measure reviewer opinion similarity with natural language processing. Finally, based on a panel data from an online video platform in China, both the fixed-effect and random-effect panel data models are constructed.FindingsThe authors find that reviewer preference similarity has a positive effect on the product diffusion, whereas reviewer opinion similarity has a negative effect on the diffusion. Furthermore, temporal distance moderates the relationship between reviewer similarity and the product diffusion. As a double-edged sword, review preference similarity hinders product diffusion in the initial phase, whereas benefits it in the later phase. Reviewer opinion similarity is always detrimental to product diffusion, especially in the initial phase.Originality/valueThis paper extends the understanding of homophily from the micro peer level to the group level by constructing reviewers' similarity network and highlights the important role of reviewer preference similarity and opinion similarity in product diffusion. The results also provide important insights for managers to design and implement diversity strategies for better product adoption in the community context.

Scale-Free Functional Brain Networks Exhibit Increased Connectivity, Are More Integrated and Less Segregated in Patients with Parkinson's Disease following Dopaminergic Treatment.

Dopaminergic treatment (DT), the standard therapy for Parkinson's disease (PD), alters the dynamics of functional brain networks at specific time scales. Here, we explore the scale-free functional connectivity (FC) in the PD population and how it is affected by DT. We analyzed the electroencephalogram of: (i) 15 PD patients during DT (ON) and after DT washout (OFF) and (ii) 16 healthy control individuals (HC). We estimated FC using bivariate focus-based multifractal analysis, which evaluated the long-term memory and multifractal strength of the connections. Subsequent analysis yielded network metrics (node degree, clustering coefficient and path length) based on FC estimated by or . Cognitive performance was assessed by the Mini Mental State Examination (MMSE) and the North American Adult Reading Test (NAART). The node degrees of the networks were significantly higher in ON, compared to OFF and HC, while clustering coefficient and path length significantly decreased. No alterations were observed in the networks. Significant positive correlations were also found between the metrics of networks and NAART scores in the HC group. These results demonstrate that DT alters the multifractal coupled dynamics in the brain, warranting the investigation of scale-free FC in clinical and pharmacological studies.

Disrupted intrinsic functional brain network in patients with late-life depression: Evidence from a multi-site dataset

BackgroundLate-life depression (LLD) is a common and serious mental disorder, whose neural mechanisms are not yet fully understood. In this study, we aimed to characterize LLD-related changes in intrinsic functional brain networks using a large, multi-site sample. MethodsUsing resting-state functional magnetic resonance imaging, the edge-based functional connectivity (FC) as well as multiple topological brain network metrics at both global and nodal levels were compared between 206 LLD patients and 210 normal controls (NCs). ResultsCompared with NCs, the LLD patients had extensive alterations in the intrinsic brain FCs, especially significant decreases in FCs within the default mode network (DMN) and within the somatomotor network (SMN). The LLD patients also showed alterations in several global brain network metrics compared with NCs, including significant decreases in global efficiency, local efficiency, clustering coefficient, and small-worldness, as well as a significantly increased characteristic path length. Moreover, significant alterations in nodal network metrics (increased nodal betweenness and decreased nodal efficiency) were found in patients with LLD, which mainly involved the DMN and SMN. Post-hoc subgroup analyses indicated that the above changes in FC strengths were present in both first-episode, drug-naïve (FEDN) and non-FEDN patients, and were correlated with depression severity in the FEDN patients. Moreover, changes in FC strengths were found in both the early/late-onset (depression starts before/after the age of 50) patients, while altered topological metrics were found in only the late-onset patients. ConclusionsThese results may help to strengthen our understanding of the underlying neural mechanisms and biological heterogeneity in LLD.

Can Ingoing Contact Chains and other cattle movement network metrics help predict herd-level bovine tuberculosis in Irish cattle herds?

We used logistic regression to investigate whether the risk of an Irish cattle herd undergoing a bovine tuberculosis (bTB) breakdown increased with the size of the Ingoing Contact Chain (ICC) of previous herd to herd cattle movements, in a sequence up to eight moves back from the most recent, direct, movement into the herd. We further examined whether taking into account the bTB test history of each herd in the chain would improve model fit. We found that measures of cattle movements directly into the herd were risk factors for subsequent bTB restrictions, and the number of herds that animals were coming from was the most important of these. However, in contrast to a previous study in Great Britain, the ICC herd count at steps more remote than direct movements into the herd did not result in better fitting models than restricting the count to direct movements. Restricting the ICC counts to herds which had previously or would in the future test positive for bTB resulted in improved model fits, but this was not the case if only the previous test status was considered. This suggests that in many cases bTB infected animals are moving out of herds before being identified through testing, and that risk-based trading approaches should not rely solely on the previous test history of source herds as a proxy for future risk. Model fit was also improved by the inclusion of variables measuring bTB history of the herd, bTB in neighbouring herds, herd size, herd type, the movement network measures “in strength” and “betweenness”, altitude, modelled badger abundance and county. Rainfall was not a good predictor. The most influential measures of bTB in nearby herds (a proxy for neighbourhood infection) were the proportion of herds with a history of bTB whose centroids were within 6 km, or whose boundaries were within 4 km, of the index herd. As well as informing national control and surveillance measures, our models can be used to identify areas where bTB rates are anomalously high, to prompt further investigation in these areas.

Landscape or local? Distinct responses of flower visitor diversity and interaction networks to different land use scales in agricultural tropical highlands

Land use change has been identified as a cause for biodiversity loss and has significant effects on pollinators and their interactions with plants. Interaction network analyses complement diversity estimators by providing information on the stability and functionality of the plant-pollinator community in an ecosystem. However, how land use changes affect insect diversity, and the structure of their plant-insect interaction networks, could depend on the intensity of the disturbance but also may be a matter of scale. Our study was carried out in a tropical highland landscape dominated by intense, yet diverse, small-scale agriculture. We studied the effects of land use, at a landscape scale, and local cover and plant ecological descriptors, at a local scale; on diversity descriptors of insect pollinator communities, the abundance of the most frequent flower visitors, and their interaction networks. Seminatural vegetation favored insect flower visitors at both scales. At the landscape scale, human settlements positively influenced bee diversity, and seminatural areas favored the abundance of frequent hoverfly and bumblebee species. At the local scale, bare soil cover negatively influenced honeybee abundance while flower-rich covers positively related to bumblebee abundance. Only local scale variables had influence on network metrics. Bare soil cover was related to higher network specialization, probably due to a low rate of honeybee interactions. Flower-rich covers negatively influenced network connectance but favored modularity. These results suggest that flower resources, provided by weed areas and flowering crops, promote a high rate of interactions between trophic levels and a non-random structure in the interaction networks that may be helping to sustain network stability. Our results highlight the role of seminatural vegetation, at both scales, in maintaining stable insect pollinator communities and interactions in heterogeneous agricultural landscapes of the tropics.

HDL-ODPRs: A Hybrid Deep Learning Technique Based Optimal Duplication Detection for Pull-Requests in Open-Source Repositories

Recently, open-source repositories have grown rapidly due to volunteer contributions worldwide. Collaboration software platforms have gained popularity as thousands of external contributors have contributed to open-source repositories. Although data de-duplication decreases the size of backup workloads, this causes poor data locality (fragmentation) and redundant review time and effort. Deep learning and machine learning techniques have recently been applied to identify complex bugs and duplicate issue reports. It is difficult to use, but it increases the risk of developers submitting duplicate pull requests, resulting in additional maintenance costs. We propose a hybrid deep learning technique in this work on the basis of an optimal duplication detection is for pull requests (HDL-ODPRs) in open-source repositories. An algorithm used to extract textual data from pull requests is hybrid leader-based optimization (HLBO), which increases the accuracy of duplicate detection. Following that, we compute the similarities between pull requests by utilizing the multiobjective alpine skiing optimization (MASO) algorithm, which provides textual, file-change, and code-change similarities. For pull request duplicate detection, a hybrid deep learning technique (named GAN-GS) is introduced, in which the global search (GS) algorithm is used to optimize the design metrics of the generative adversarial network (GAN). The proposed HDL-ODPR model is validated against the public standard benchmark datasets, such as DupPR-basic and DupPR-complementary data. According to the simulation results, the proposed HDL-ODPR model can achieve promising results in comparison with existing state-of-the-art models.

Test-retest reliability of modular-relevant analysis in brain functional network.

The human brain could be modeled as a complex network via functional magnetic resonance imaging (fMRI), and the architecture of these brain functional networks can be studied from multiple spatial scales with different graph theory tools. Detecting modules is an important mesoscale network measuring approach that has provided crucial insights for uncovering how brain organizes itself among different functional subsystems. Despite its successful application in a wide range of brain network studies, the lack of comprehensive reliability assessment prevents its potential extension to clinical trials. To fill this gap, this paper, using resting-state test-retest fMRI data, systematically explored the reliabilities of five popular network metrics derived from modular structure. Considering the repeatability of network partition depends heavily on network size and module detection algorithm, we constructed three types of brain functional networks for each subject by using a set of coarse-to-fine brain atlases and adopted four methods for single-subject module detection and twelve methods for group-level module detection. The results reported moderate-to-good reliability in modularity, intra- and inter-modular functional connectivities, within-modular degree and participation coefficient at both individual and group levels, indicating modular-relevant network metrics can provide robust evaluation results. Further analysis identified the significant influence of module detection algorithm and node definition approach on reliabilities of network partitions and its derived network analysis results. This paper provides important guidance for choosing reliable modular-relevant network metrics and analysis strategies in future studies.

Encoding Impact of Network Modification on Controllability via Edge Centrality Matrix

This article develops tools to quantify the importance of agent interactions and its impact on global performance metrics for networks with scalar states modeled as linear time-invariant systems. We consider Gramian-based performance metrics and propose a novel notion of edge centrality that encodes the first-order variation in the metric with respect to the modification of the corresponding edge weight, including for those edges not present in the network. The proposed edge centrality matrix (ECM) is additive over the set of inputs, i.e., it captures the specific contribution to each edge’s centrality of the presence of any given actuator. We provide a full characterization of the ECM structure for the class of directed stem-bud networks, showing that nonzero entries are only possible at specific sub/super-diagonals determined by the network size and the length of its bud. We also provide bounds on the value of the trace, trace inverse, and log-det of the Gramian before and after single-edge modifications, and on the edge-modification weight to ensure the modified network retains stability. Simulations show the utility of the proposed edge centrality notion and validate our results.