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We propose a novel family of node centralities in social networks, named family of position centralities , which explicitly takes into account the importance of the links to assess the centrality of the nodes that support them through the Position value (Meessen, 1988). Our proposal shares with the family of Myerson centralities (Gómez et al., 2003) that it is a game-theoretic family of measures that allows to consider the functionality of the network modelled by a symmetric cooperative game. We prove that, like the Myerson centrality measures, every Position centrality measure also satisfies essential properties expected of a centrality measure. We analyse in detail the main differences between the Myerson and the position families of centrality measures. Specifically, we study the differences regarding the connection structures that share dividends and the fairness and stability properties. Along this analysis we consider the case of hub-and-spoke clusters, a prevalent model for studying transportation networks. Finally, a characterisation of the Position Attachment centrality is given, which is the Position centrality obtained when the functionality of the network is modelled by the attachment game. Some comparisons are made with the Attachment centrality introduced by Skibski et al. (2019), which is the analogue member of the family of Myerson centralities. • It is a game-theoretic centrality based on the network's topology and functionality. • It measures the node's centrality relying explicitly on the importance of edges. • It is well supported by many desirable properties. • Three key aspects distinguish it from the Myerson centrality. • The Position Attachment centrality is axiomatically characterised. [ABSTRACT FROM AUTHOR]

Epilepsy is a common neurological disorder that affects millions of people worldwide, disrupting brain networks and causing recurrent seizures. In this regard, investigating the distinctive characteristics of brain connectivity is crucial to understanding the underlying neural processes of epilepsy. However, the various graph-theory frameworks and different estimation measures may yield significant variability among the results of different studies. On this premise, this study investigates the brain network topological variations between patients with temporal lobe epilepsy (TLE) and extratemporal lobe epilepsy (ETLE) using both directed and undirected network connectivity methods as well as different graph-theory metrics. Our results reveal distinct topological differences in connectivity graphs between the two epilepsy groups, with TLE patients displaying more disassortative graphs at lower density levels compared to ETLE patients. Moreover, we highlight the variations in the hub regions across different network metrics, underscoring the importance of considering various centrality measures for a comprehensive understanding of brain network dynamics in epilepsy. Our findings suggest that the differences in brain network organization between TLE and ETLE patients could be attributed to the unique characteristics of each epilepsy type, offering insights into potential biomarkers for type-specific epilepsy diagnosis and treatment. [ABSTRACT FROM AUTHOR]

A new concept known as the orthogonal component graph associated with a finite-dimensional vector space over a finite field has been recently added as another class of algebraic graphs. In these types of graphs, the vertices will be all the possible non-zero linear combinations of orthogonal basis vectors, and any two vertices will be adjacent if the corresponding vectors are orthogonal. In this paper, we discuss the various colorings and structural properties of orthogonal component graphs. [ABSTRACT FROM AUTHOR]

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A new concept known as the orthogonal component graph associated with a finite-dimensional vector space over a finite field has been recently added as another class of algebraic graphs. In these types of graphs, the vertices will be all the possible non-zero linear combinations of orthogonal basis vectors, and any two vertices will be adjacent if the corresponding vectors are orthogonal. In this paper, we discuss the various colorings and structural properties of orthogonal component graphs. [ABSTRACT FROM AUTHOR]

With tremendous growth in the volume of published scholarly work, it becomes quite difficult for researchers to find appropriate documents relevant to their research topic. Many research paper recommendation approaches have been proposed and implemented which include collaborative filtering, content-based, metadata, link-based and multi-level citation network. In this research, a novel Research paper Recommendation system is proposed by integrating Multiple Features (RRMF). RRMF constructs a multi-level citation network and collaboration network of authors for feature integration. The structure and semantic based relationships are identified from the citation network whereas key authors are extracted from collaboration network for the study. For experimentation and analysis, AMiner v12 DBLP-Citation Network is used that covers 4,894,081 academic papers and 45,564,149 citation relationships. The information retrieval metrices including Mean Average Precision, Mean Reciprocal Rank and Normalized Discounted Cumulative Gain are used for evaluating the performance of proposed system. The research results of proposed approach RRMF are compared with baseline Multilevel Simultaneous Citation Network (MSCN) and Google Scholar. Consequently, comparison of RRMF showed 87% better recommendations than the traditional MSCN and Google Scholar. [ABSTRACT FROM AUTHOR]

Analyzing protein–protein interaction (PPI) networks using machine learning and deep learning algorithms, alongside centrality measures, holds paramount importance in understanding complex biological systems. These advanced computational techniques enable the extraction of valuable insights from intricate network structures, shedding light on the functional relationships between proteins. By leveraging AI-driven approaches, researchers can uncover key regulatory mechanisms, identify critical nodes within the network and predict novel protein interactions with high accuracy. Ultimately, this integration of computational methodologies enhances our ability to comprehend the dynamic behavior of biological systems at a molecular level, paving the way for advancements in drug discovery, disease understanding and personalized medicine. This review paper starts by outlining various popular available PPI network databases and network centrality calculation tools. A thorough classification of various centrality measures has been identified. It primarily delves into the centrality-driven discoveries within PPI networks in biological systems and suggests using edge centrality measures and a hybrid version of node and edge centrality measures in machine learning algorithms and deep learning algorithms to predict hidden knowledge much more effectively. The review paper begins by outlining various popular available PPI network databases and network centrality calculation tools. A thorough classification of various centrality measures has been identified. A detailed view of various findings of different types of centrality measures in PPI networks is presented. [ABSTRACT FROM AUTHOR]

Abstract The explosive growth of the Web and of social networks motivates the need for analyzing the macroscopic structure of their underlying graphs. Although the characterization of the structure of a graph with respect to its pairwise connectivity has been known for over 15 years, just one subsequent study analyzed the world inside the giant strongly connected component, where it has been shown that the largest strongly connected component has its own microscopic bow-tie structure defined with respect to pairwise 2-connectivity among its vertices. In this paper, we introduce the local microscopic bow-tie structure of the largest strongly connected component, demonstrating its self-similarity property. Our experiments, conducted on the several Web graphs and social networks demonstrate clear structural differences between considered Web and social networks.

Abstract Understanding the spread of SARS-CoV-2 has been one of the most pressing problems of the recent past. Network models present a potent approach to studying such spreading phenomena because of their ability to represent complex social interactions. While previous studies have shown that network centrality measures are generally able to identify influential spreaders in a susceptible population, it is not yet known if they can also be used to predict infection risks. However, information about infection risks at the individual level is vital for the design of targeted interventions. Here, we use large-scale administrative data from the Netherlands to study whether centrality measures can predict the risk and timing of infections with COVID-19-like diseases. We investigate this issue leveraging the framework of multi-layer networks, which accounts for interactions taking place in different contexts, such as workplaces, households and schools. In epidemic models simulated on real-world network data from over one million individuals, we find that existing centrality measures offer good predictions of relative infection risks, and are correlated with the timing of individual infections. We however find no association between centrality measures and real SARS-CoV-2 test data, which indicates that population-scale network data alone cannot aid predictions of virus transmission.

Summary: The t$$ t $$‐admissibility is a min‐max problem that concerns to determine whether a graph G$$ G $$ contains a spanning tree T$$ T $$ in which the distance between any two adjacent vertices of G$$ G $$ is at most t$$ t $$ in T$$ T $$. The stretch index of G$$ G $$, σ(G)$$ \sigma (G) $$, is the smallest t$$ t $$ for which G$$ G $$ is t$$ t $$‐admissible. This problem is in P for t≤2$$ t\le 2 $$, NP‐complete for σ(G)≤t$$ \sigma (G)\le t $$, t≥4$$ t\ge 4 $$, and remaining open for t=3$$ t=3 $$. In a very recent development, Couto et al. (Inf Process Lett, 2022; 177: 106265) introduced both sequential and parallel algorithms for constructing spanning trees. Additionally, they proposed two greedy heuristics for generating a candidate solution tree, but they left unresolved the issue of how to decide between two vertices when both have equal chances of being chosen in a greedy step. This criterion is important, since different branches can yield different stretch indexes. In response to this question, we developed nine new heuristics that use the concept of vertex importance in complex networks. Our research evaluates results on several types of graphs, including Barabási‐Albert, Erdős‐Rényi, Watts‐Strogatz, and bipartite graphs. Furthermore, we introduce a new parallel algorithm that employs a method using induced cycle of the graph to compare its performance with previously proposed algorithms. We develop a deep analysis on the proposed strategies (parallel and heuristics) comparing all of them to the other ones in the literature and as a result we obtain the best results so far in order to obtain exact values (or heuristics) of stretch indexes. [ABSTRACT FROM AUTHOR]

Objective: Surveillance is critical for the rapid implementation of control measures for diseases caused by aerially dispersed plant pathogens, but such programs can be resource-intensive, especially for epidemics caused by long-distance dispersed pathogens. The current cucurbit downy mildew platform for monitoring, predicting and communicating the risk of disease spread in the United States is expensive to maintain. In this study, we focused on identifying sites critical for surveillance and treatment in an attempt to reduce disease monitoring costs and determine where control may be applied to mitigate the risk of disease spread. Methods: Static networks were constructed based on the distance between fields, while dynamic networks were constructed based on the distance between fields and wind speed and direction, using disease data collected from 2008 to 2016. Three strategies were used to identify highly connected field sites. First, the probability of pathogen transmission between nodes and the probability of node infection were modeled over a discrete weekly time step within an epidemic year. Second, nodes identified as important were selectively removed from networks and the probability of node infection was recalculated in each epidemic year. Third, the recurring patterns of node infection were analyzed across epidemic years. Results: Static networks exhibited scale-free properties where the node degree followed a power-law distribution. Betweenness centrality was the most useful metric for identifying important nodes within the networks that were associated with disease transmission and prediction. Based on betweenness centrality, field sites in Maryland, North Carolina, Ohio, South Carolina and Virginia were the most central in the disease network across epidemic years. Removing field sites identified as important limited the predicted risk of disease spread based on the dynamic network model. Conclusions: Combining the dynamic network model and centrality metrics facilitated the identification of highly connected fields in the southeastern United States and the mid-Atlantic region. These highly connected sites may be used to inform surveillance and strategies for controlling cucurbit downy mildew in the eastern United States. [ABSTRACT FROM AUTHOR]

We propose a new centrality measure based on a self-adaptive epidemic model characterized by an endogenous reinforcement mechanism in the transmission of information between nodes. We provide a strategy to assign to nodes a centrality score that depends, in an eigenvector centrality scheme, on that of all the elements of the network, nodes and edges, connected to it. We parameterize this score as a function of a reinforcement factor, which for the first time implements the intensity of the interaction between the network of nodes and that of the edges. In this proposal, a local centrality measure representing the steady state of a diffusion process incorporates the global information encoded in the whole network. This measure proves effective in identifying the most influential nodes in the propagation of rumors/shocks/behaviors in a social network. In the context of financial networks, it allows us to highlight strategic assets on correlation networks. The dependence on a coupling factor between graph and line graph also enables the different asset responses in terms of ranking, especially on scale-free networks obtained as minimum spanning trees from correlation networks. [ABSTRACT FROM AUTHOR]

Vaccination is a vital strategy to prevent and control the spread of infectious diseases. In this paper, we propose a vaccination strategy that starts with community detection in a dynamic epidemic network, then uses centrality measures to identify spreaders in these communities, who are then targeted for vaccination. By vaccinating the most influential individuals in each community, we aim to achieve a highly vaccinated network that can effectively contain the spread of the disease. To test the effectiveness of the methods, we evaluate them using different evaluation metrics. Our strategy is also highly scalable and adaptable to different epidemic scenarios, making it a promising approach for future epidemic control. [ABSTRACT FROM AUTHOR]

Complex systems that consist of diverse kinds of entities that interact in different ways can be modeled by multilayer networks. This paper uses the tensor formalism with the Einstein product to model this type of networks. Several centrality measures, that are well known for single-layer networks, are extended to multilayer networks using tensors and their properties are investigated. In particular, subgraph centrality based on the exponential and resolvent of a tensor are considered. Krylov subspace methods based on the tensor format are introduced for computing approximations of different measures for large multilayer networks. [ABSTRACT FROM AUTHOR]

Influence analysis, derived from Social Network Analysis (SNA), is extremely useful in academic literature analytic. Different Academic Social Network Sites (ASNS) have been widely examined for influence analysis in terms of co-authorship and co-citation networks. The impact of other network-based features, such as followers and followings, provided by ASNS such as ResearchGate (RG) and Academia is yet to be anatomised. As proven in ingrained social theories, the followers and followings have significant impact in influence prorogation. This research aims at examining the same in one of the widely adopted ASNS, RG. The rendering process is developed to render real-time RG information, which is modelled into graph. Standard centrality measures are implemented to identify influential users from the constructed RG graph. Each centrality measure gives a list of top- k influential RG users. The results are compared with RGScore and Total Research Interest (TRI) to discover the most effective centrality measure. Betweenness and closeness centrality measures have shown the outperforming results compared with others. A procedure is established to discover influential RG users that are commonly present in all top- k centrality results to identify dominant skills, affiliations, departments and locations from the rendered data. [ABSTRACT FROM AUTHOR]

The ranking of nodes in a network according to their centrality or ''importance'' is a classic problem that has attracted the interest of different scientific communities in the last decades. The COVID-19 pandemic has recently rejuvenated the interest in this problem, as the ranking may be used to decide who should be tested, or vaccinated, first, in a population of asymptomatic individuals. In this paper, we review classic methods for node ranking and compare their performance in a benchmark network that considers the community-based structure of society. The outcome of the ranking procedure is then used to decide which individuals should be tested, and possibly quarantined, first. Finally, we also review the extension of these ranking methods to weighted graphs and explore the importance of weights in a contact network by providing a toy model and comparing node rankings for this case in the context of disease spread. [ABSTRACT FROM AUTHOR]

Link prediction plays a crucial role in identifying future connections within complex networks, facilitating the analysis of network evolution across various domains such as biological networks, social networks, recommender systems, and more. Researchers have proposed various centrality measures, such as degree, clustering coefficient, betweenness, and closeness centralities, to compute similarity scores for predicting links in these networks. These centrality measures leverage both the local and global information of nodes within the network. In this study, we present a novel approach to link prediction using similarity score by utilizing average centrality measures based on local and global centralities, namely Similarity based on Average Degree (S A C D) , Similarity based on Average Betweenness (S A C B) , Similarity based on Average Closeness (S A C C) , and Similarity based on Average Clustering Coefficient (S A C C C) . Our approach involved determining centrality scores for each node, calculating the average centrality for the entire graph, and deriving similarity scores through common neighbors. We then applied centrality scores to these common neighbors and identified nodes with above average centrality. To evaluate our approach, we compared proposed measures with existing local similarity-based link prediction measures, including common neighbors, the Jaccard coefficient, Adamic–Adar, resource allocation, preferential attachment, as well as recent measures like common neighbor and the Centrality-based Parameterized Algorithm (C C P A) , and keyword network link prediction (K N L P) . We conducted experiments on four real-world datasets. The proposed similarity scores based on average centralities demonstrate significant improvements. We observed an average enhancement of 24% in terms of Area Under the Receiver Operating Characteristic (AUROC) compared to existing local similarity measures, and a 31% improvement over recent measures. Furthermore, we witnessed an average improvement of 49% and 51% in the Area Under Precision-Recall (AUPR) compared to existing and recent measures. Our comprehensive experiments highlight the superior performance of the proposed method. [ABSTRACT FROM AUTHOR]

This study utilized Neutrosophic Cognitive Maps (NCMs) integrated with the D-OWA operator to analyze the nutritional rights of pregnant women in Ecuador, with a focus on the crucial role of nutrition education. The innovative application of the D-OWA operator enabled the computation of a composite centrality measure by merging key centrality indicators--degree, closeness, and betweenness--each appropriately weighted according to its relevance to the analysis. This methodology provided a sophisticated evaluation of the factors impacting maternal nutrition, demonstrating how combining various centrality measures offers a deeper and more comprehensive insight into the dynamics of complex systems. The calculated composite centrality measures revealed the system's intricate structure, pinpointing critical nodes and pathways that could be targeted most effectively through interventions. The findings underscore the significant benefits of using composite centrality measures to enhance decision-making in public health and other sectors characterized by complexity and uncertainty. The potential for refining and expanding this approach in future research suggests that it could be further supported by technological advancements, enabling more efficient analysis and scalability across diverse complex systems. [ABSTRACT FROM AUTHOR]

The nonzero component graph of a finite-dimensional vector space over a finite field is a graph whose vertices are the nonzero vectors in the vector space, and any two vertices are adjacent if the corresponding linear combination contains a common basis vector. In this paper, we discuss the centrality measures and entropy of the nonzero component graph and also analyze the sensitivity of the graph using the centrality measures. [ABSTRACT FROM AUTHOR]

Dialogic education advocates varied forms of interactional management by teachers. In the context of whole-class discussions, teachers are encouraged to both prompt student involvement through direct mediation, and "step back" to give students a greater sense of agency and responsibility for turn-taking when appropiate. However, it is methodologically challenging to capture the relation between teacher–student and student–student interactions through dialogue in whole-class contexts. One perspective that is especially designed for exploring complex relations in social networks but not as commonly used in dialogic education is social network analysis (SNA). Drawing on 35 whole-class discussion episodes derived from lower secondary classrooms in Norway, this study uses SNA to explore interactional patterns. Methodologically, the study provides novel examples of how SNA can be used both alone and in conjunction with the indicators of interactional productivity to describe the relation between teacher–student and student–student interactions in whole-class discussions. Empirically, a key finding is that an increase in students responding directly to each other in a student-to-student fashion is associated with a reduction in the distribution of productive interactions through dialogue. Theoretically, the study directs attention to the complexities and tensions inherent in key models and concepts in dialogic education. [ABSTRACT FROM AUTHOR]

Many object‐oriented metrics have been proposed in the literature to measure various structural properties of object‐oriented software. Furthermore, many centrality measures have been introduced to identify central nodes in large networks. However, few studies have used them to measure dependencies in software systems. In fact, centrality measures, as opposed to most traditional object‐oriented metrics that mainly focus on intrinsic properties of classes, can be used to better model the control flow and to identify the most important classes in a software system. This paper aims (1) to investigate the relationships between object‐oriented metrics and centrality measures and (2) to explore the ability of their combination to support fault‐proneness prediction from different perspectives (fault‐prone classes, fault severity, and number of faults). Many studies in the literature have addressed the prediction of fault‐prone classes, from different perspectives, using object‐oriented metrics. The main motivation here is in fact to investigate if the information captured by centrality measures is related to fault proneness and complementary to the information captured by object‐oriented metrics and to investigate if the combination of object‐oriented metrics and centrality measures improves the performance of fault‐proneness prediction significantly. We used size, complexity, and coupling object‐oriented metrics in addition to various centrality measures. We collected data from 20 different versions of five open‐source Java software systems. We first studied the relationships between selected metrics and their relationships to fault proneness. Then, we built different models to predict fault‐prone classes using several machine learning algorithms. In addition, we built models to predict if a class contains a high severity fault, and the number of faults in a class. Results indicate that using centrality measures in combination with object‐oriented metrics improves the prediction of fault‐prone classes as well as the prediction of the number of faults in a class. However, the combination has no significant impact, according to the data we collected, on the quality of the prediction of fault severity. Moreover, using centrality measures in combination with object‐oriented metrics also improves the prediction performance of fault proneness and the number of faults in both cross‐version and cross‐system validation. [ABSTRACT FROM AUTHOR]

The mathematical theory of epidemics draws upon essential concepts from epidemiology, categorizing the population into three distinct compartments: Susceptible, Infected, and Resistant individuals. This battle between a malicious, intelligent, and rational agent disseminating the threat and a defender attempting to restrict its propagation is generally modeled by a partially observable stochastic game (POSG). Despite its broad applicability, solving this game is still not feasible due to the size of the state space and thus the complexity of updating the defender's belief at each step. To circumvent this 'curse of dimensionality', we present a novel framework that takes into account the network topology through centrality measures. We demonstrate that the defender, instead of updating his belief concerning the state of the network, can apply a condensed representation of his belief regarding the state of each node at each step, without changing his optimal strategy. The defender manages a vector of size n (in a network with n nodes) instead of a vector of size $ 2^{n} $. Numerical illustrations demonstrate that using the condensed representation of the defender's belief enhances the scalability and reduces the convergence time of the algorithm. [ABSTRACT FROM AUTHOR]

Water distribution systems (WDSs) are complex networks with numerous interconnected junctions and pipes. The robustness and reliability of these systems are critically dependent on their network structure, necessitating detailed analysis for proactive leak detection to maintain integrity and functionality. This study addresses gaps in traditional WDS analysis by integrating hydraulic measures with graph theory to improve sensitivity analysis for leak detection. Through case studies of five distinct WDSs, we investigate the relationship between hydraulic measures and graph theory metrics. Our findings demonstrate the collective impact of these factors on leak detection and system efficiency. The research provides enhanced insights into WDS operational dynamics and highlights the significant potential of graph theory to bolster network resilience and reliability. [ABSTRACT FROM AUTHOR]

Social networking sites offer a vast platform for sharing various types of content, such as information, photos, videos, and audio clips. However, the credibility of the information shared on these sites is a significant concern since there is no prior verification process as the information spreads across the networks. This increases the chances of disseminating false or misleading information, often called rumors. The spread of rumors in today's information environment creates severe problems for the credibility of information and public confidence. The quick spread of rumors, frequently conveyed via social media and other online platforms, can affect public opinion and potentially have real-world repercussions. Maintaining the integrity of information ecosystems and averting the potentially damaging impacts of disinformation require detecting and mitigating rumors. In today's social media and online communication age, it is crucial to identify rumors to prevent their spread and mitigate their potential negative impact. In this study, our primary goal is to discover and identify individual sources of rumors. This work addresses two aspects of rumor management: firstly, identifying the difference between rumors and facts, and secondly, tracking the source of the rumor. In conjunction with the attributes, state-of-the-art methods such as SVM, AdaBoost, Random Forest, Logistic Regression, and Graph Convolutional Networks (GCN) are used to accomplish these goals. This approach contributes to the broader goal of combating disinformation and preserving the Accuracy of information. [ABSTRACT FROM AUTHOR]

A distance based on the exponential kernel of the adjacency matrix of a graph and representing how well two vertices connect to each other in a graph is defined and studied. This communicability cosine distance (CCD) is a Euclidean spherical distance accounting for the cosine of the angles spanned by the position vectors of the graph vertices in this space. The Euclidean distance matrix (EDM) of CCD is used to quantify the similarity between vertices in graphs and networks as well as to define a local vertex invariant—a closeness centrality measure, which discriminate very well vertices in small graphs. It allows to distinguish all nonidentical vertices, also characterizing all identity (asymmetric) graphs–those having only the identity automorphism–among all connected graphs of up to 9 vertices. It also characterizes several other classes of identity graphs. We also study real-world networks in term of both the discriminating power of the new centrality on their vertices as well as in ranking their vertices. We analyze some dictionary networks as well as the network of copurshasing of political books, remarking some of the main advantages of the new approaches studied here. [ABSTRACT FROM AUTHOR]

Objective Surveillance is critical for the rapid implementation of control measures for diseases caused by aerially dispersed plant pathogens, but such programs can be resource-intensive, especially for epidemics caused by long-distance dispersed pathogens. The current cucurbit downy mildew platform for monitoring, predicting and communicating the risk of disease spread in the United States is expensive to maintain. In this study, we focused on identifying sites critical for surveillance and treatment in an attempt to reduce disease monitoring costs and determine where control may be applied to mitigate the risk of disease spread. Methods Static networks were constructed based on the distance between fields, while dynamic networks were constructed based on the distance between fields and wind speed and direction, using disease data collected from 2008 to 2016. Three strategies were used to identify highly connected field sites. First, the probability of pathogen transmission between nodes and the probability of node infection were modeled over a discrete weekly time step within an epidemic year. Second, nodes identified as important were selectively removed from networks and the probability of node infection was recalculated in each epidemic year. Third, the recurring patterns of node infection were analyzed across epidemic years. Results Static networks exhibited scale-free properties where the node degree followed a power-law distribution. Betweenness centrality was the most useful metric for identifying important nodes within the networks that were associated with disease transmission and prediction. Based on betweenness centrality, field sites in Maryland, North Carolina, Ohio, South Carolina and Virginia were the most central in the disease network across epidemic years. Removing field sites identified as important limited the predicted risk of disease spread based on the dynamic network model. Conclusions Combining the dynamic network model and centrality metrics facilitated the identification of highly connected fields in the southeastern United States and the mid-Atlantic region. These highly connected sites may be used to inform surveillance and strategies for controlling cucurbit downy mildew in the eastern United States.

Identifying crucial nodes in complex networks is a key factor for various domains, especially for identifying influential nodes with high spreading ability. This is fundamental in applications like viral marketing. To find influential nodes number of dedicated centrality measures have been developed. CentiServer serves as a source of information about most of them making the researcher's life easier. Unfortunately, for most of them, there are no implementations available. Moreover, popular network-oriented Python libraries like networkx or igraph come with just a few implementations of the most popular ones making it harder to use and compare them. To alleviate this problem, NetCenLib has been introduced to fill that gap and become a common place for researchers to put their algorithm implementations to be easily used by the research community.

Over the last decade, we have witnessed the emergence of numerous online social media platforms and a growing research interest in understanding their underlying structures and mechanisms. This paper investigates the formation and evolution of the EcoNation social media platform, which is designed to foster collaboration for environmental sustainability.

The emerging cryptocurrency market is one of the largest financial markets in the world, with a market capitalization that is already surpassing the gross domestic product of many developed economies. Cryptocurrencies are increasingly being adopted as a means of transaction and ownership in the digital domain, particularly in areas like decentralized finance and non-fungible tokens. Known for its high volatility, this market offers investors the potential for higher returns than traditional financial markets like stocks, foreign exchange, and commodities. However, it remains underexplored in academic research. In this paper, we propose the use of social network analysis to effectively model and analyze the cryptocurrency market and conduct a comprehensive numerical study to explore its key properties, including correlation structure, topological characteristics, stability, and influence. Furthermore, we propose the use of centrality measures as novel indicators to improve the accuracy of cryptocurrency price movement predictions. Our research introduces a novel method for understanding and navigating the cryptocurrency market, enabling investors to integrate advanced analytical tools into their decision-making processes.

In the realm of network science, determining crucial nodes within a social network is an ongoing concern. As a result, it garners a lot of attention, and various centrality measures for the identification of crucial nodes have been proposed thus far. Degree and k-shell decomposition are the classic centrality measures that rely on neighboring nodes. However, degree, k-shell, and combination of degree and k-shell measures assign the identical value to the vast count of nodes, which creates a problem in distinguishing these nodes. Therefore, in this paper, for the purpose of solving the above problem, we propose an index based on three different components: degree, improved k-shell measure, and eigenvector centrality called the degree k-shell eigenvector (DKE) index. In addition, we propose an enhanced gravity model called the DKE-based gravity model (DKEGM) on the basis of universal gravity law and the proposed index for determining crucial nodes in social networks. The proposed gravity model incorporates different aspects of nodes, which include count of neighbors, location of nodes, influence of neighbors, and path information between the nodes. Numerous experiments are executed on eight real networks using the SIR model, Kendall tau, ranking monotonicity, and distinct metric to examine the effectiveness of the DKEGM with respect to the other measures. The empirical outcomes show the effectiveness of the DKEGM in terms of accuracy, distinguishing ability, and efficiency.

Centrality measures are widely utilized in complex networks to assess the importance of nodes. The choice of measure depends on the network type, leading to diverse node rankings. This paper aims to compare various centrality measures by examining their correlations. We specifically focus on the Pearson correlation coefficient and Spearman correlation. Pearson correlation considers node centrality values, while Spearman correlation is based on node ranks. Our study encompasses different network topologies, including random, scale-free, and small-world networks. We investigate how these network structures influence correlation values. The main part of the paper describes the relationship between correlations and network model parameters. Additionally, we explore the impact of global network characteristics on correlations, as well as their direct connection to network parameters. Through a systematic review of literature-based centrality measures, we have identified and selected the most commonly employed ones to investigate their correlation including degree centrality, betweenness centrality, eigenvector centrality, and closeness centrality. Our findings reveal that correlations in random networks are minimally affected by network structure, whereas restructuring significantly impacts correlations in other networks. In particular, we show a notable impact of structural parameter variations on correlations within small-world networks. Furthermore, we demonstrate the substantial influence of fundamental network characteristics such as spectral gap, global efficiency, and majorization gap on correlations. We show that amongst the various properties, the spectral gap stands out as the most valuable indicator for estimating correlations.