Graph Centrality Measures Research Articles

Edge-based graph centrality measures with spatial analytics to support vulnerability assessment and maintenance planning in sewer networks

ABSTRACT In this study, the spatial relationship between critical pipes identified using edge-based centrality measures and pipes with higher failure probability-based on selected vulnerability indicators were analysed in sanitary sewer networks. By analysing two sub-networks, one residential and the other a central network, significant spatial associations between pipes with high centrality values and those exhibiting adverse conditions (poor CCTV grades, previous blockages, and low self-cleaning capabilities) were identified. Path-based centrality measures, particularly edge betweenness and K-path edge centrality were less influenced by weights when identifying critical pipes. In contrast, non-path-based measures like nearest neighbour edge centrality could identify more localised critical pipes within the sewer networks investigated. The results showed that the spatial patterns between critical pipes and pipes in adverse conditions were not random and could support proactive maintenance planning and the development of more resilient networks. Additionally, the impact of network structure, connectivity, and differences in the composition of pipe attributes could contribute to variations in the strength of observable spatial associations.

Network excitability of stimulation-induced spectral responses helps localize the seizure onset zone

ObjectiveWhile evoked potentials elicited by single pulse electrical stimulation (SPES) may assist seizure onset zone (SOZ) localization during intracranial EEG (iEEG) monitoring, induced high frequency activity has also shown promising utility. We aimed to predict SOZ sites using induced cortico-cortical spectral responses (CCSRs) as an index of excitability within epileptogenic networks. MethodsSPES was conducted in 27 epilepsy patients undergoing iEEG monitoring and CCSRs were quantified by significant early (10–200 ms) increases in power from 10 to 250 Hz. Using response power as CCSR network connection strengths, graph centrality measures (metrics quantifying each site’s influence within the network) were used to predict whether sites were within the SOZ. ResultsAcross patients with successful surgical outcomes, greater CCSR centrality predicted SOZ sites and SOZ sites targeted for surgical treatment with median AUCs of 0.85 and 0.91, respectively. We found that the alignment between predicted and targeted SOZ sites predicted surgical outcome with an AUC of 0.79. ConclusionsThese findings indicate that network analysis of CCSRs can be used to identify increased excitability of SOZ sites and discriminate important surgical targets within the SOZ. SignificanceCCSRs may supplement traditional passive iEEG monitoring in seizure localization, potentially reducing the need for recording numerous seizures.

Analyzing road network robustness in major Chinese cities through hierarchical stroke-based representations

ABSTRACT In this study, we explore the robustness of urban road networks, a crucial aspect of urban infrastructure whose failure can significantly disrupt urban functionality. Our approach offers a fresh perspective on network robustness by focusing on intrinsic street hierarchies within stroke-based representations across 20 major Chinese cities. These networks exhibit common complex properties, such as being scale-free and small-world. We determine street hierarchies based on the power law distribution of two key graph centrality measures: degree and betweenness. Our methodology involves a targeted attack strategy, sequentially removing roads from the highest to the lowest hierarchy in each urban street network. This process yields robustness profiles characterized by monotonic decreasing curves, which reflect changes in network connectivity and efficiency. The profiles not only provide valuable insights into urban structure and function, but also offer significant implications for practical road planning and urban resilience strategies.

Seizure onset zone (SOZ) identification using effective brain connectivity of epileptogenic networks

Objective. To demonstrate the capability of utilizing graph feature-based supervised machine learning (ML) algorithm on intracranial electroencephalogram recordings for the identification of seizure onset zones (SOZs) in individuals with drug-resistant epilepsy. Approach. Utilizing three model-free measures of effective connectivity (EC)-directed information, mutual information-guided Granger causality index (MI-GCI), and frequency-domain convergent cross-mapping (FD-CCM) - directed graphs are generated. Graph centrality measures at different sparsity are used as the classifier’s features. Main results. The centrality features achieve high accuracies exceeding 90% in distinguishing SOZ electrodes from non-SOZ electrodes. Notably, a sparse graph representation with just ten features and simple ML models effectively achieves such performance. The study identifies FD-CCM centrality measures as particularly significant, with a mean AUC of 0.93, outperforming prior literature. The FD-CCM-based graph modeling also highlights elevated centrality measures among SOZ electrodes, emphasizing heightened activity relative to non-SOZ electrodes during ictogenesis. Significance. This research not only underscores the efficacy of automated SOZ identification but also illuminates the potential of specific EC measures in enhancing discriminative power within the context of epilepsy research.

Narratives from GPT-derived networks of news and a link to financial markets dislocations

AbstractWe introduce a novel framework to study the dynamics of news narratives, by leveraging GPT3.5 advanced text analysis capabilities and graph theory. In particular, we focus on a corpus of economic articles from The Wall Street Journal and dynamically extract the main topics of discussion over time, in a completely systematic and scalable fashion. As a simple application of the suggested approach, we show how the structure of such topics of discussion has a statistically significant relationship with the contemporaneous state of financial markets, which can be used to construct an investment strategy or monitor financial risks. Our work is based on the intrinsic ability of GPT models to track the context of sentences within a document, thanks to which we can accurately extract a ranking of the most important entities discussed within each article, and evaluate their entity-specific sentiments. Then, we create a graph for each week of data, in which nodes are the entities retrieved and edges are built from the co-occurrence of such entities within articles. Graph centrality measures are computed over time to track the most representative keywords of topics of discussion, which result in an accurate summary view of the evolution of economic narratives. Fuzzy community detection is finally used to cluster linked entities into a more detailed representation of topics. Such groups of entities are mapped to the related journal articles, which are in turn summarised to reach a highly nuanced and interpretable view of the topics discussed within each week. Linking the features of these topics to the relevant financial market time series, we find that high fragmentation within our networks’ communities relates to moments of financial markets dislocations (i.e. dates with unusually high volatility across asset classes). This result should thus motivate stronger effort within financial research to move beyond ubiquitous sentiment analysis of news and delve deeper into broader and more holistic studies of textual data.

An application of node and edge nonlinear hypergraph centrality to a protein complex hypernetwork.

The use of graph centrality measures applied to biological networks, such as protein interaction networks, underpins much research into identifying key players within biological processes. This approach however is restricted to dyadic interactions and it is well-known that in many instances interactions are polyadic. In this study we illustrate the merit of using hypergraph centrality applied to a hypernetwork as an alternative. Specifically, we review and propose an extension to a recently introduced node and edge nonlinear hypergraph centrality model which provides mutually dependent node and edge centralities. A Saccharomyces Cerevisiae protein complex hypernetwork is used as an example application with nodes representing proteins and hyperedges representing protein complexes. The resulting rankings of the nodes and edges are considered to see if they provide insight into the essentiality of the proteins and complexes. We find that certain variations of the model predict essentiality more accurately and that the degree-based variation illustrates that the centrality-lethality rule extends to a hypergraph setting. In particular, through exploitation of the models flexibility, we identify small sets of proteins densely populated with essential proteins. One of the key advantages of applying this model to a protein complex hypernetwork is that it also provides a classification method for protein complexes, unlike previous approaches which are only concerned with classifying proteins.

Hypergraphs and centrality measures identifying key features in gene expression data

Multidisciplinary approaches can significantly advance our understanding of complex systems. For instance, gene co-expression networks align prior knowledge of biological systems with studies in graph theory, emphasising pairwise gene to gene interactions. In this paper, we extend these ideas, promoting hypergraphs as an investigative tool for studying multi-way interactions in gene expression data. Additional freedoms are achieved by representing individual genes with hyperedges, and simultaneously testing each gene against many features/vertices. Further gene/hyperedge interactions can be captured and explored using the line graph representations, a technique that reduces the complexity of dense hypergraphs. Such an approach provides access to graph centrality measures, which identifies salient features within a data set. For instance dominant or hub-like hyperedges, leading to key knowledge on gene expression. The validity of this approach is established through the study of gene expression data for the plant species Senecio lautus and results will be interpreted within this biological setting.

Dispersion entropy for graph signals

We present a novel method, called Dispersion Entropy for Graph Signals, DEG, as a powerful tool for analysing the irregularity of signals defined on graphs. DEG generalizes the classical dispersion entropy concept for univariate time series, enabling its application in diverse domains such as image processing, time series analysis, and network analysis. Furthermore, DEG establishes a theoretical framework that provides insights into the irregularities observed in graph centrality measures and in the spectra of operators acting on graphs. We demonstrate the effectiveness of DEG in detecting changes in the dynamics of signals defined on both synthetic and real-world graphs, by defining a mix process on random geometric graphs or those exhibiting small-world properties. Our results indicate that DEG effectively captures the irregularity of graph signals across various network configurations, successfully differentiating between distinct levels of randomness and connectivity. Consequently, DEG provides a comprehensive framework for entropy analysis of various data types, enabling new applications of dispersion entropy not previously feasible, and uncovering nonlinear relationships between graph signals and their graph topology.

A Study on Graph Centrality Measures of Different Diseases Due to DNA Sequencing

Rare genetic diseases are often caused by single-gene defects that affect various biological processes across different scales. However, it is challenging to identify the causal genes and understand the molecular mechanisms of these diseases. In this paper, we present a multiplex network approach to study the relationship between human diseases and genes. We construct a human disease network (HDN) and a human genome network (HGN) based on genotype–phenotype associations and gene interactions, respectively. We analyze 3771 rare diseases and find distinct phenotypic modules within each dimension that reflect the functional effects of gene mutations. These modules can also be used to predict novel gene candidates for unsolved rare diseases and to explore the cross-scale impact of gene perturbations. We compute various centrality measures for both networks and compare them. Our main finding is that diseases are weakly connected in the HDN, while genes are strongly connected in the HGN. This implies that diseases are relatively isolated from each other, while genes are involved in multiple biological processes. This result has implications for understanding the transmission of infectious diseases and the development of therapeutic interventions. We also show that not all diseases have the same potential to spread infections to other parts of the body, depending on their centrality in the HDN. Our results show that the phenotypic module formalism can capture the complexity of rare diseases beyond simple physical interaction networks and can be applied to study diseases arising from DNA (Deoxyribonucleic Acid) sequencing errors. This study provides a novel network-based framework for integrating multi-scale data and advancing the understanding and diagnosis of rare genetic diseases.

Node classification with graph neural network based centrality measures and feature selection

<span lang="EN-US">Graph neural networks (GNNs) are a new topic of research in data science where data structure graphs are used as important components for developing and training neural networks. GNN always learns the weight importance of the neighbor for perform message aggregation in which the feature vectors of all neighbors are aggregated without considering whether the features are useful or not. Using such more informative features positively affect the performance of the GNN model. So, in this paper i) after selecting a subset of features to define important node features, we present new graph features’ explanation methods based on graph centrality measures to capture rich information and determine the most important node in a network. Through our experiments, we find that selecting certain subsets of these features and adding other features based on centrality measure can lead to better performance across a variety of datasets and ii) we introduce a major design strategy for graph neural networks. Specifically, we suggest using batch renormalization as normalization over GNN layers. Combining these techniques, representing features based on centrality measures that passed to multilayer perceptron (MLP) layer which is then passed to adjusted GNN layer, the proposed model achieves greater accuracy than modern GNN models.</span>

Non-invasive mapping of epileptogenic networks predicts surgical outcome.

Epilepsy is increasingly considered a disorder of brain networks. Studying these networks with functional connectivity can help identify hubs that facilitate the spread of epileptiform activity. Surgical resection of these hubs may lead patients who suffer from drug-resistant epilepsy to seizure freedom. Here, we aim to map non-invasively epileptogenic networks, through the virtual implantation of sensors estimated with electric and magnetic source imaging, in patients with drug-resistant epilepsy. We hypothesize that highly connected hubs identified non-invasively with source imaging can predict the epileptogenic zone and the surgical outcome better than spikes localized with conventional source localization methods (dipoles). We retrospectively analysed simultaneous high-density electroencephalography (EEG) and magnetoencephalography data recorded from 37 children and young adults with drug-resistant epilepsy who underwent neurosurgery. Using source imaging, we estimated virtual sensors at locations where intracranial EEG contacts were placed. On data with and without spikes, we computed undirected functional connectivity between sensors/contacts using amplitude envelope correlation and phase locking value for physiologically relevant frequency bands. From each functional connectivity matrix, we generated an undirected network containing the strongest connections within sensors/contacts using the minimum spanning tree. For each sensor/contact, we computed graph centrality measures. We compared functional connectivity and their derived graph centrality of sensors/contacts inside resection for good (n = 22, ILAE I) and poor (n = 15, ILAE II-VI) outcome patients, tested their ability to predict the epileptogenic zone in good-outcome patients, examined the association between highly connected hubs removal and surgical outcome and performed leave-one-out cross-validation to support their prognostic value. We also compared the predictive values of functional connectivity with those of dipoles. Finally, we tested the reliability of virtual sensor measures via Spearman's correlation with intracranial EEG at population- and patient-level. We observed higher functional connectivity inside than outside resection (P < 0.05, Wilcoxon signed-rank test) for good-outcome patients, on data with and without spikes across different bands for intracranial EEG and electric/magnetic source imaging and few differences for poor-outcome patients. These functional connectivity measures were predictive of both the epileptogenic zone and outcome (positive and negative predictive values ≥55%, validated using leave-one-out cross-validation) outperforming dipoles on spikes. Significant correlations were found between source imaging and intracranial EEG measures (0.4 ≤ rho ≤ 0.9, P < 0.05). Our findings suggest that virtual implantation of sensors through source imaging can non-invasively identify highly connected hubs in patients with drug-resistant epilepsy, even in the absence of frank epileptiform activity. Surgical resection of these hubs predicts outcome better than dipoles.

On the use of graph centralities to compute generalized inverse of singular finite element operators: Applications to the analysis of floating substructures

SummaryThis article introduces a robust and affordable method to compute nullspace and generalized inverse of finite element operators involved in dual domain decomposition methods. The methodology relies on the operator partial factorization and on the analysis of a well chosen Schur complement. The sparse linear operator is interpreted as a network and graph centrality measures are used to select the condensation variables. Eigenvector, Katz and Page Rank centralities are evaluated. An extension to deal with symmetric indefinite systems arising from mixed finite elements is also presented. The approach is assessed on highly heterogeneous problems and one industrial application is presented: the numerical homogenization of solid propellant.

Graph-Based Heuristic Solution for Placing Distributed Video Processing Applications on Moving Vehicle Clusters

Vehicular fog computing (VFC) is envisioned as an extension of cloud and mobile edge computing to utilize the rich sensing and processing resources available in vehicles. We focus on slow-moving cars that spend a significant time in urban traffic congestion as a potential pool of onboard sensors, video cameras, and processing capacity. For leveraging the dynamic network and processing resources, we utilize a stochastic mobility model to select nodes with similar mobility patterns. We then design two distributed applications that are scaled in real-time and placed as multiple instances on selected vehicular fog nodes. We handle the unstable vehicular environment by a), Using real vehicle density data to build a realistic mobility model that helps in selecting nodes for service deployment b), Using community-detection algorithms for selecting a robust vehicular cluster using the predicted mobility behavior of vehicles. The stability of the chosen cluster is validated using a graph centrality measure, and c), Graph-based placement heuristics is developed to find the optimal placement of service graphs based on a multi-objective constrained optimization problem with the objective of efficient resource utilization. The heuristic solves an important problem of processing data generated from distributed devices by balancing the trade-off between increasing the number of service instances to have enough redundancy of processing instances to increase resilience in the service in case of node or link failure, versus reducing their number to minimize resource usage. We compare our heuristic to a mixed integer program (MIP) solution and a first-fit heuristic. Our approach performs better than these comparable schemes in terms of resource utilization and/or has a lesser service latency when compared to an edge computing-based service placement scheme.

Mobile recommender system based on smart city graph

&lt;span&gt;Mobile recommender systems have changed the way people find items, purposes of intrigue, administrations, or even new companions. The innovation behind mobile recommender systems has developed to give client inclinations and social impacts. This paper introduces a first way to build a mobile recommendation system based on smart city graphs that appear topic features, user profiles, and impacts acquired from social connections. It exploits graph centrality measures to expand customized recommendations from the semantic information represented in the graph. The graph shows and chooses graph algorithms for computing chart centrality that is the center of the mobile recommender system are exhibited. Semantic ideas, for example, semantic transcendence and likeness measures, are adjusted to the graph model. Usage challenges confronted to settle execution issues are additionally examined.&lt;/span&gt;

An effective community-based link prediction model for improving accuracy in social networks

Link prediction plays a predominant role in complex network analysis. It indicates to determine the probability of the presence of future links that depends on available information. The existing standard classical similarity indices-based link prediction models considered the neighbour nodes have a similar effect towards link probability. Nevertheless, the common neighbor nodes residing in different communities may vary in real-world networks. In this paper, a novel community information-based link prediction model has been proposed in which every neighboring node’s community information (community centrality) has been considered to predict the link between the given node pair. In the proposed model, the given social network graph can be divided into different communities and community centrality is calculated for every derived community based on degree, closeness, and betweenness basic graph centrality measures. Afterward, the new community centrality-based similarity indices have been introduced to compute the community centralities which are applied to nine existing basic similarity indices. The empirical analysis on 13 real-world social networks datasets manifests that the proposed model yields better prediction accuracy of 97% rather than existing models. Moreover, the proposed model is parallelized efficiently to work on large complex networks using Spark GraphX Big Data-based parallel Graph processing technique and it attains a lesser execution time of 250 seconds.

Tumor relevant protein functional interactions identified using bipartite graph analyses

An increased surge of -omics data for the diseases such as cancer allows for deriving insights into the affiliated protein interactions. We used bipartite network principles to build protein functional associations of the differentially regulated genes in 18 cancer types. This approach allowed us to combine expression data to functional associations in many cancers simultaneously. Further, graph centrality measures suggested the importance of upregulated genes such as BIRC5, UBE2C, BUB1B, KIF20A and PTH1R in cancer. Pathway analysis of the high centrality network nodes suggested the importance of the upregulation of cell cycle and replication associated proteins in cancer. Some of the downregulated high centrality proteins include actins, myosins and ATPase subunits. Among the transcription factors, mini-chromosome maintenance proteins (MCMs) and E2F family proteins appeared prominently in regulating many differentially regulated genes. The projected unipartite networks of the up and downregulated genes were comprised of 37,411 and 41,756 interactions, respectively. The conclusions obtained by collating these interactions revealed pan-cancer as well as subtype specific protein complexes and clusters. Therefore, we demonstrate that incorporating expression data from multiple cancers into bipartite graphs validates existing cancer associated mechanisms as well as directs to novel interactions and pathways.

Identifying critical higher-order interactions in complex networks

Diffusion on networks is an important concept in network science observed in many situations such as information spreading and rumor controlling in social networks, disease contagion between individuals, and cascading failures in power grids. The critical interactions in networks play critical roles in diffusion and primarily affect network structure and functions. While interactions can occur between two nodes as pairwise interactions, i.e., edges, they can also occur between three or more nodes, which are described as higher-order interactions. This report presents a novel method to identify critical higher-order interactions in complex networks. We propose two new Laplacians to generalize standard graph centrality measures for higher-order interactions. We then compare the performances of the generalized centrality measures using the size of giant component and the Susceptible-Infected-Recovered (SIR) simulation model to show the effectiveness of using higher-order interactions. We further compare them with the first-order interactions (i.e., edges). Experimental results suggest that higher-order interactions play more critical roles than edges based on both the size of giant component and SIR, and the proposed methods are promising in identifying critical higher-order interactions.

Directional Laplacian Centrality for Cyber Situational Awareness

Cyber operations is drowning in diverse, high-volume, multi-source data. To get a full picture of current operations and identify malicious events and actors, analysts must see through data generated by a mix of human activity and benign automated processes. Although many monitoring and alert systems exist, they typically use signature-based detection methods. We introduce a general method rooted in spectral graph theory to discover patterns and anomalies without a priori knowledge of signatures. We derive and propose a new graph-theoretic centrality measure based on the derivative of the graph Laplacian matrix in the direction of a vertex. To build intuition about our measure, we show how it identifies the most central vertices in standard network datasets and compare to other graph centrality measures. Finally, we focus our attention on studying its effectiveness in identifying important IP addresses in network flow data. Using both real and synthetic network flow data, we conduct several experiments to test our measure’s sensitivity to two types of injected attack profiles and show that vertices participating in injected attack profiles exhibit noticeable changes in our centrality measures, even when the injected anomalies are relatively small, and in the presence of simulated network dynamics.

A graph centrality-based approach for candidate gene prediction for type 1 diabetes.

Type 1 diabetes mellitus (T1DM) or insulin-dependent diabetes is an autoimmune disease that may pose life-threatening situations to individuals. In most cases, cytotoxic T lymphocytes (CTLs) promotes killing of islets of Langerhans in the pancreas, which harbour insulin-producing beta cells. The trigger for autoimmune attack is still unclear; therefore, identifying and targeting candidate genes are imperative to hinder its deleterious effects. In the present study, we focused on identification of new candidate genes for T1DM. For our study, we exclusively selected immune-related genes as they play a crucial role in T1DM. We constructed and analysed a human immunome signalling network (directed network) to identify the new candidate genes through various graph centrality measures combining with Gene Ontology (GO). As a result, we identified 4 new candidate genes which may act as potential drug targets for T1DM. We further validated for their disease relevance through literature survey and pathway analysis and found that 3 out of 4 predicted genes mirrored their well-established roles as potential targets for T1DM.

Building k‐partite association graphs for finding recommendation patterns from questionnaire data

AbstractGraph‐pattern association rules have been explored for detecting frequent subgraph structures in real‐world network data, which can reveal new insights for decision‐making, recommender systems, and predictive models. However, questionnaire data have been neglected so far even though they are one of the most affordable ways to gather quantitative data. Questionnaires can cover every aspect of a topic, generating new strategies and trends for many organisations. The challenge is twofold: develop a model for handling nominal/Boolean data and ordinal data simultaneously, as well as multiple values assigned to a single item. In this article, the synergy between the well‐known Apriori algorithm and k‐partite graph modelling is proposed to discover frequent recommendation patterns from questionnaire data. Using graph centrality and similarity measures, the large number of association rules are further analysed to discover meaningful spatial structures in non‐metric spaces. Counting triangles is also used to uncover hidden thematic structures of link recommendations. We demonstrate how our proposed approach can be applied to a tourism questionnaire survey to reveal frequent patterns in k‐partite graphs, which can further be used for recommender systems.