Martina Contisciani;Hadiseh Safdari;Caterina De Bacco
To unravel the driving patterns of networks, the most popular models rely on community detection algorithms. However, these approaches are generally unable to reproduce the structural features of the network. Therefore, attempts are always made to develop models that incorporate these network properties beside the community structure. In this article, we present a probabilistic generative model and an efficient algorithm to both perform community detection and capture reciprocity in networks. Our approach jointly models pairs of edges with exact two-edge joint distributions. In addition, it provides closed-form analytical expressions for both marginal and conditional distributions. We validate our model on synthetic data in recovering communities, edge prediction tasks and generating synthetic networks that replicate the reciprocity values observed in real networks. We also highlight these findings on two real datasets that are relevant for social scientists and behavioural ecologists. Our method overcomes the limitations of both standard algorithms and recent models that incorporate reciprocity through a pseudo-likelihood approximation. The inference of the model parameters is implemented by the efficient and scalable expectation–maximization algorithm, as it exploits the sparsity of the dataset. We provide an open-source implementation of the code online.
{"title":"Community detection and reciprocity in networks by jointly modelling pairs of edges","authors":"Martina Contisciani;Hadiseh Safdari;Caterina De Bacco","doi":"10.1093/comnet/cnac034","DOIUrl":"https://doi.org/10.1093/comnet/cnac034","url":null,"abstract":"To unravel the driving patterns of networks, the most popular models rely on community detection algorithms. However, these approaches are generally unable to reproduce the structural features of the network. Therefore, attempts are always made to develop models that incorporate these network properties beside the community structure. In this article, we present a probabilistic generative model and an efficient algorithm to both perform community detection and capture reciprocity in networks. Our approach jointly models pairs of edges with exact two-edge joint distributions. In addition, it provides closed-form analytical expressions for both marginal and conditional distributions. We validate our model on synthetic data in recovering communities, edge prediction tasks and generating synthetic networks that replicate the reciprocity values observed in real networks. We also highlight these findings on two real datasets that are relevant for social scientists and behavioural ecologists. Our method overcomes the limitations of both standard algorithms and recent models that incorporate reciprocity through a pseudo-likelihood approximation. The inference of the model parameters is implemented by the efficient and scalable expectation–maximization algorithm, as it exploits the sparsity of the dataset. We provide an open-source implementation of the code online.","PeriodicalId":15442,"journal":{"name":"Journal of complex networks","volume":"10 4","pages":"1121-1122"},"PeriodicalIF":2.1,"publicationDate":"2022-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/iel7/8016804/10070447/10070458.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49943942","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Recent developments in network neuroscience have highlighted the importance of developing techniques for analysing and modelling brain networks. A particularly powerful approach for studying complex neural systems is to formulate generative models that use wiring rules to synthesize networks closely resembling the topology of a given connectome. Successful models can highlight the principles by which a network is organized (identify structural features that arise from wiring rules versus those that emerge) and potentially uncover the mechanisms by which it grows and develops. Previous research has shown that such models can validate the effectiveness of spatial embedding and other (non-spatial) wiring rules in shaping the network topology of the human connectome. In this research, we propose variants of the action-based model that combine a variety of generative factors capable of explaining the topology of the human connectome. We test the descriptive validity of our models by evaluating their ability to explain between-subject variability. Our analysis provides evidence that geometric constraints are vital for connectivity between brain regions, and an action-based model relying on both topological and geometric properties can account for between-subject variability in structural network properties. Further, we test correlations between parameters of subject-optimized models and various measures of cognitive ability and find that higher cognitive ability is associated with an individual's tendency to form long-range or non-local connections.
{"title":"Investigating cognitive ability using action-based models of structural brain networks","authors":"Viplove Arora;Enrico Amico;Joaquín Goñi;Mario Ventresca","doi":"10.1093/comnet/cnac037","DOIUrl":"https://doi.org/10.1093/comnet/cnac037","url":null,"abstract":"Recent developments in network neuroscience have highlighted the importance of developing techniques for analysing and modelling brain networks. A particularly powerful approach for studying complex neural systems is to formulate generative models that use wiring rules to synthesize networks closely resembling the topology of a given connectome. Successful models can highlight the principles by which a network is organized (identify structural features that arise from wiring rules versus those that emerge) and potentially uncover the mechanisms by which it grows and develops. Previous research has shown that such models can validate the effectiveness of spatial embedding and other (non-spatial) wiring rules in shaping the network topology of the human connectome. In this research, we propose variants of the action-based model that combine a variety of generative factors capable of explaining the topology of the human connectome. We test the descriptive validity of our models by evaluating their ability to explain between-subject variability. Our analysis provides evidence that geometric constraints are vital for connectivity between brain regions, and an action-based model relying on both topological and geometric properties can account for between-subject variability in structural network properties. Further, we test correlations between parameters of subject-optimized models and various measures of cognitive ability and find that higher cognitive ability is associated with an individual's tendency to form long-range or non-local connections.","PeriodicalId":15442,"journal":{"name":"Journal of complex networks","volume":"10 4","pages":"0245-0251"},"PeriodicalIF":2.1,"publicationDate":"2022-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49943939","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In the Internet era, rumours will spread rapidly in the network and hinder the development of all aspects of society. To create a harmonious network environment, it is essential to take punitive measures against malicious rumour mongers on social platforms. Take the measure of forbidden as an example. The forbidden one may stop spreading rumours because of being punished, or he may become a disseminator again because of paranoia. Other people who know rumours may become alert and stop propagating rumours or temporarily forget rumours. And therefore, the forbidden state is added to describe the above phenomenon, and the SIFR (Ignorant–Disseminator–Forbidden–Restorer) model is proposed. Taking the vigilance and paranoia derived from punishment measures into account, the connection edges from the forbidden to the disseminator and from the disseminator to the restorer are increased in this model. And then, the stability of SIFR model is proved by using the basic regeneration number and Routh–Hurwitz stability theorem. The simulation results demonstrate that individual paranoia may do harm to the control of rumour dissemination. While the punishment mechanism, individual forgetting mechanism and vigilance can effectively curb the spread of rumours.
{"title":"Online dynamic rumour propagation model considering punishment mechanism and individual personality characteristics","authors":"Chengai Sun;Donghang Qiao;Liqing Qiu","doi":"10.1093/comnet/cnac038","DOIUrl":"https://doi.org/10.1093/comnet/cnac038","url":null,"abstract":"In the Internet era, rumours will spread rapidly in the network and hinder the development of all aspects of society. To create a harmonious network environment, it is essential to take punitive measures against malicious rumour mongers on social platforms. Take the measure of forbidden as an example. The forbidden one may stop spreading rumours because of being punished, or he may become a disseminator again because of paranoia. Other people who know rumours may become alert and stop propagating rumours or temporarily forget rumours. And therefore, the forbidden state is added to describe the above phenomenon, and the SIFR (Ignorant–Disseminator–Forbidden–Restorer) model is proposed. Taking the vigilance and paranoia derived from punishment measures into account, the connection edges from the forbidden to the disseminator and from the disseminator to the restorer are increased in this model. And then, the stability of SIFR model is proved by using the basic regeneration number and Routh–Hurwitz stability theorem. The simulation results demonstrate that individual paranoia may do harm to the control of rumour dissemination. While the punishment mechanism, individual forgetting mechanism and vigilance can effectively curb the spread of rumours.","PeriodicalId":15442,"journal":{"name":"Journal of complex networks","volume":"10 4","pages":"22-37"},"PeriodicalIF":2.1,"publicationDate":"2022-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49943397","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We introduce hub centrality and study the relation between hub centrality and the degree of each node in the networks. We discover and verify a universal relation between them in various networks generated by the growth method, but the relation is not applied to real-world networks due to the rich-club phenomenon and the presence of local hubs. Through the study of a targeted attack and overload cascading failure, we prove that hub centrality is a meaningful parameter that gives extra insight beyond degree in real-world networks. Especially, we show that the local hubs occupy key positions in real-world networks with higher probabilities to incur global cascading failure. Therefore, we conclude that networks generated by the growth method, which do not include local hubs, have inevitable limitations to describe real-world networks.
{"title":"Universal behaviour of the growth method and importance of local hubs in cascading failure","authors":"Wonhee Jeong;Unjong Yu","doi":"10.1093/comnet/cnac028","DOIUrl":"https://doi.org/10.1093/comnet/cnac028","url":null,"abstract":"We introduce hub centrality and study the relation between hub centrality and the degree of each node in the networks. We discover and verify a universal relation between them in various networks generated by the growth method, but the relation is not applied to real-world networks due to the rich-club phenomenon and the presence of local hubs. Through the study of a targeted attack and overload cascading failure, we prove that hub centrality is a meaningful parameter that gives extra insight beyond degree in real-world networks. Especially, we show that the local hubs occupy key positions in real-world networks with higher probabilities to incur global cascading failure. Therefore, we conclude that networks generated by the growth method, which do not include local hubs, have inevitable limitations to describe real-world networks.","PeriodicalId":15442,"journal":{"name":"Journal of complex networks","volume":"10 4","pages":"175-308"},"PeriodicalIF":2.1,"publicationDate":"2022-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49943398","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Centrality measures are used in network science to assess the centrality of vertices or the position they occupy in a network. There are a large number of centrality measures according to some criterion. However, the generalizations of the most well-known centrality measures for weighted networks, degree centrality, closeness centrality and betweenness centrality have solely assumed the edge weights to be constants. This article proposes a methodology to generalize degree, closeness and betweenness centralities taking into account the variability of edge weights in the form of closed intervals (interval-weighted networks, IWN). We apply our centrality measures approach to two real-world IWN. The first is a commuter network in mainland Portugal, between the 23 NUTS 3 Regions. The second focuses on annual merchandise trade between 28 European countries, from 2003 to 2015.
{"title":"Centrality measures in interval-weighted networks","authors":"Hélder Alves;Paula Brito;Pedro Campos","doi":"10.1093/comnet/cnac031","DOIUrl":"https://doi.org/10.1093/comnet/cnac031","url":null,"abstract":"Centrality measures are used in network science to assess the centrality of vertices or the position they occupy in a network. There are a large number of centrality measures according to some criterion. However, the generalizations of the most well-known centrality measures for weighted networks, degree centrality, closeness centrality and betweenness centrality have solely assumed the edge weights to be constants. This article proposes a methodology to generalize degree, closeness and betweenness centralities taking into account the variability of edge weights in the form of closed intervals (interval-weighted networks, IWN). We apply our centrality measures approach to two real-world IWN. The first is a commuter network in mainland Portugal, between the 23 NUTS 3 Regions. The second focuses on annual merchandise trade between 28 European countries, from 2003 to 2015.","PeriodicalId":15442,"journal":{"name":"Journal of complex networks","volume":"10 4","pages":"55-71"},"PeriodicalIF":2.1,"publicationDate":"2022-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49943937","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We introduce a kernel Lasso (kLasso) approach which is a type of sparse optimization that simultaneously accounts for spatial regularity and structural sparsity to reconstruct spatially embedded complex networks from time-series data about nodal states. Through the design of a spatial kernel function motivated by real-world network features, the proposed kLasso approach exploits spatial embedding distances to penalize overabundance of spatially long-distance connections. Examples of both random geometric graphs and real-world transportation networks show that the proposed method improves significantly upon existing network reconstruction techniques that mainly concern sparsity but not spatial regularity. Our results highlight the promise of data and information fusion in the reconstruction of complex networks, by utilizing both microscopic node-level dynamics (e.g. time series data) and macroscopic network-level information (metadata or other prior information).
{"title":"Data fusion reconstruction of spatially embedded complex networks","authors":"Jie Sun;Fernando J Quevedo;Erik M Bollt","doi":"10.1093/comnet/cnac032","DOIUrl":"https://doi.org/10.1093/comnet/cnac032","url":null,"abstract":"We introduce a kernel Lasso (kLasso) approach which is a type of sparse optimization that simultaneously accounts for spatial regularity and structural sparsity to reconstruct spatially embedded complex networks from time-series data about nodal states. Through the design of a spatial kernel function motivated by real-world network features, the proposed kLasso approach exploits spatial embedding distances to penalize overabundance of spatially long-distance connections. Examples of both random geometric graphs and real-world transportation networks show that the proposed method improves significantly upon existing network reconstruction techniques that mainly concern sparsity but not spatial regularity. Our results highlight the promise of data and information fusion in the reconstruction of complex networks, by utilizing both microscopic node-level dynamics (e.g. time series data) and macroscopic network-level information (metadata or other prior information).","PeriodicalId":15442,"journal":{"name":"Journal of complex networks","volume":"10 4","pages":"1-11"},"PeriodicalIF":2.1,"publicationDate":"2022-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49943945","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Many complex engineering systems network together functional elements to balance demand spikes but suffer from stability issues due to cascades. The research challenge is to prove the stability conditions for any arbitrarily large and dynamic network topology with any complex balancing function. Most current analyses linearize the system around fixed equilibrium solutions. This approach is insufficient for dynamic networks with multiple equilibria, for example, with different initial conditions or perturbations. Region of attraction (ROA) estimation is needed in order to ensure that the desirable equilibria are reached. This is challenging because a networked system of non-linear dynamics requires compression to obtain a tractable ROA analysis. Here, we employ master stability-inspired method to reveal that the extreme eigenvalues of the Laplacian are explicitly linked to the ROA. This novel relationship between the ROA and the largest eigenvalue in turn provides a pathway to augmenting the network structure to improve stability. We demonstrate using a case study on how the network with multiple equilibria can be optimized to ensure stability.
{"title":"Analysing region of attraction of load balancing on complex network","authors":"Mengbang Zou;Weisi Guo","doi":"10.1093/comnet/cnac025","DOIUrl":"https://doi.org/10.1093/comnet/cnac025","url":null,"abstract":"Many complex engineering systems network together functional elements to balance demand spikes but suffer from stability issues due to cascades. The research challenge is to prove the stability conditions for any arbitrarily large and dynamic network topology with any complex balancing function. Most current analyses linearize the system around fixed equilibrium solutions. This approach is insufficient for dynamic networks with multiple equilibria, for example, with different initial conditions or perturbations. Region of attraction (ROA) estimation is needed in order to ensure that the desirable equilibria are reached. This is challenging because a networked system of non-linear dynamics requires compression to obtain a tractable ROA analysis. Here, we employ master stability-inspired method to reveal that the extreme eigenvalues of the Laplacian are explicitly linked to the ROA. This novel relationship between the ROA and the largest eigenvalue in turn provides a pathway to augmenting the network structure to improve stability. We demonstrate using a case study on how the network with multiple equilibria can be optimized to ensure stability.","PeriodicalId":15442,"journal":{"name":"Journal of complex networks","volume":"10 4","pages":"2551-2556"},"PeriodicalIF":2.1,"publicationDate":"2022-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49943943","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Complex network is an important tool for studying complex systems. From the mesoscopic perspective, the complex network is composed of a large number of different types of motifs, research on the importance of motifs is helpful to analyse the function and dynamics of a complex network. However, the importance of different motifs or the same kind of motifs in the network is different, and the importance of motifs is not only affected by a single factor. Therefore, we propose a comprehensive measurement method of motif importance based on multi-attribute decision-making (MAM). We use the idea of MAM and take into account the influence of the local attribute, global attribute and location attribute of the motif on the network structure and function, and the information entropy method is used to give different weight to different attributes, finally, a comprehensive importance measure of the motif is obtained. Experimental results on the artificial network and real networks show that our method is more direct and effective for a small network.
{"title":"Motif importance measurement based on multi-attribute decision","authors":"Biao Feng;Yunyun Yang;Liao Zhang;Shuhong Xue;Xinlin Xie;Jiianrong Wang;Gang Xie","doi":"10.1093/comnet/cnac023","DOIUrl":"https://doi.org/10.1093/comnet/cnac023","url":null,"abstract":"Complex network is an important tool for studying complex systems. From the mesoscopic perspective, the complex network is composed of a large number of different types of motifs, research on the importance of motifs is helpful to analyse the function and dynamics of a complex network. However, the importance of different motifs or the same kind of motifs in the network is different, and the importance of motifs is not only affected by a single factor. Therefore, we propose a comprehensive measurement method of motif importance based on multi-attribute decision-making (MAM). We use the idea of MAM and take into account the influence of the local attribute, global attribute and location attribute of the motif on the network structure and function, and the information entropy method is used to give different weight to different attributes, finally, a comprehensive importance measure of the motif is obtained. Experimental results on the artificial network and real networks show that our method is more direct and effective for a small network.","PeriodicalId":15442,"journal":{"name":"Journal of complex networks","volume":"10 4","pages":"2856-2869"},"PeriodicalIF":2.1,"publicationDate":"2022-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49943944","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this article, we propose a method to reconstruct the active links of a power network described by a second-order Kuramoto model and subject to dynamically induced cascading failures. Starting from the assumption (realistic for power grids) that the structure of the network is known, our method reconstructs the active links from the evolution of the relevant dynamical quantities of the nodes of the system, that is, the node phases and angular velocities. We find that, to reconstruct the temporal sequence of the faults, it is crucial to use time series with a small number of samples, as the observation window should be smaller than the temporal distance between subsequent events. This requirement is in contrast with the need of using larger sets of data in the presence of noise, such that the number of samples to feed in the algorithm has to be selected as a trade-off between the prediction error and temporal resolution of the active link reconstruction.
{"title":"Reconstruction of cascading failures in dynamical models of power grids","authors":"Alessandra Corso;Lucia Valentina Gambuzza;Federico Malizia;Giovanni Russo;Vito Latora;Mattia Frasca","doi":"10.1093/comnet/cnac035","DOIUrl":"https://doi.org/10.1093/comnet/cnac035","url":null,"abstract":"In this article, we propose a method to reconstruct the active links of a power network described by a second-order Kuramoto model and subject to dynamically induced cascading failures. Starting from the assumption (realistic for power grids) that the structure of the network is known, our method reconstructs the active links from the evolution of the relevant dynamical quantities of the nodes of the system, that is, the node phases and angular velocities. We find that, to reconstruct the temporal sequence of the faults, it is crucial to use time series with a small number of samples, as the observation window should be smaller than the temporal distance between subsequent events. This requirement is in contrast with the need of using larger sets of data in the presence of noise, such that the number of samples to feed in the algorithm has to be selected as a trade-off between the prediction error and temporal resolution of the active link reconstruction.","PeriodicalId":15442,"journal":{"name":"Journal of complex networks","volume":"10 4","pages":"175-308"},"PeriodicalIF":2.1,"publicationDate":"2022-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49943938","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Graph embedding is a transformation of nodes of a graph into a set of vectors. A good embedding should capture the graph topology, node-to-node relationship and other relevant information about the graph, its subgraphs and nodes. If these objectives are achieved, an embedding is a meaningful, understandable, compressed representations of a network that can be used for other machine learning tools such as node classification, community detection or link prediction. In this article, we do a series of extensive experiments with selected graph embedding algorithms, both on real-world networks as well as artificially generated ones. Based on those experiments, we formulate the following general conclusions. First, we confirm the main problem of node embeddings that is rather well-known to practitioners but less documented in the literature. There exist many algorithms available to choose from which use different techniques and have various parameters that may be tuned, the dimension being one of them. One needs to ensure that embeddings describe the properties of the underlying graphs well but, as our experiments confirm, it highly depends on properties of the network at hand and the given application in mind. As a result, selecting the best embedding is a challenging task and very often requires domain experts. Since investigating embeddings in a supervised manner is computationally expensive, there is a need for an unsupervised tool that is able to select a handful of promising embeddings for future (supervised) investigation. A general framework, introduced recently in the literature and easily available on GitHub repository, provides one of the very first tools for an unsupervised graph embedding comparison by assigning the ‘divergence score’ to embeddings with a goal of distinguishing good from bad ones. We show that the divergence score strongly correlates with the quality of embeddings by investigating three main applications of node embeddings: node classification, community detection and link prediction.
{"title":"Evaluating node embeddings of complex networks","authors":"Arash Dehghan-Kooshkghazi;Bogumił Kamiński;Łukasz Kraiński;Paweł Prałat;François Théberge;Ali Pinar","doi":"10.1093/comnet/cnac030","DOIUrl":"https://doi.org/10.1093/comnet/cnac030","url":null,"abstract":"Graph embedding is a transformation of nodes of a graph into a set of vectors. A good embedding should capture the graph topology, node-to-node relationship and other relevant information about the graph, its subgraphs and nodes. If these objectives are achieved, an embedding is a meaningful, understandable, compressed representations of a network that can be used for other machine learning tools such as node classification, community detection or link prediction. In this article, we do a series of extensive experiments with selected graph embedding algorithms, both on real-world networks as well as artificially generated ones. Based on those experiments, we formulate the following general conclusions. First, we confirm the main problem of node embeddings that is rather well-known to practitioners but less documented in the literature. There exist many algorithms available to choose from which use different techniques and have various parameters that may be tuned, the dimension being one of them. One needs to ensure that embeddings describe the properties of the underlying graphs well but, as our experiments confirm, it highly depends on properties of the network at hand and the given application in mind. As a result, selecting the best embedding is a challenging task and very often requires domain experts. Since investigating embeddings in a supervised manner is computationally expensive, there is a need for an unsupervised tool that is able to select a handful of promising embeddings for future (supervised) investigation. A general framework, introduced recently in the literature and easily available on GitHub repository, provides one of the very first tools for an unsupervised graph embedding comparison by assigning the ‘divergence score’ to embeddings with a goal of distinguishing good from bad ones. We show that the divergence score strongly correlates with the quality of embeddings by investigating three main applications of node embeddings: node classification, community detection and link prediction.","PeriodicalId":15442,"journal":{"name":"Journal of complex networks","volume":"10 4","pages":"56001-1098"},"PeriodicalIF":2.1,"publicationDate":"2022-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49943946","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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