Higher-order networks encode the many-body interactions existing in complex systems, such as the brain, protein complexes, and social interactions. Simplicial complexes are higher-order networks that allow a comprehensive investigation of the interplay between topology and dynamics. However, simplicial complexes have the limitation that they only capture undirected higher-order interactions while in real-world scenarios, often there is a need to introduce the direction of simplices, extending the popular notion of direction of edges. On graphs and networks the Magnetic Laplacian, a special case of connection Laplacian, is becoming a popular operator to address edge directionality. Here we tackle the challenge of handling directionality in simplicial complexes by formulating higher-order connection Laplacians taking into account the configurations induced by the simplices’ directions. Specifically, we define all the connection Laplacians of directed simplicial complexes of dimension two and we discuss the induced higher-order diffusion dynamics by considering instructive synthetic examples of simplicial complexes. The proposed higher-order diffusion processes can be adopted in real scenarios when we want to consider higher-order diffusion displaying non-trivial frustration effects due to conflicting directionalities of the incident simplices.
{"title":"Higher-order connection Laplacians for directed simplicial complexes","authors":"Xue Gong, Desmond J Higham, Konstantinos Zygalakis, Ginestra Bianconi","doi":"10.1088/2632-072x/ad353b","DOIUrl":"https://doi.org/10.1088/2632-072x/ad353b","url":null,"abstract":"Higher-order networks encode the many-body interactions existing in complex systems, such as the brain, protein complexes, and social interactions. Simplicial complexes are higher-order networks that allow a comprehensive investigation of the interplay between topology and dynamics. However, simplicial complexes have the limitation that they only capture undirected higher-order interactions while in real-world scenarios, often there is a need to introduce the direction of simplices, extending the popular notion of direction of edges. On graphs and networks the Magnetic Laplacian, a special case of connection Laplacian, is becoming a popular operator to address edge directionality. Here we tackle the challenge of handling directionality in simplicial complexes by formulating higher-order connection Laplacians taking into account the configurations induced by the simplices’ directions. Specifically, we define all the connection Laplacians of directed simplicial complexes of dimension two and we discuss the induced higher-order diffusion dynamics by considering instructive synthetic examples of simplicial complexes. The proposed higher-order diffusion processes can be adopted in real scenarios when we want to consider higher-order diffusion displaying non-trivial frustration effects due to conflicting directionalities of the incident simplices.","PeriodicalId":53211,"journal":{"name":"Journal of Physics Complexity","volume":"35 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140572522","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-03-27DOI: 10.1088/2632-072x/ad32da
Pavle Cajic, Dominic Agius, Oliver M Cliff, James M Shine, Joseph T Lizier, Ben D Fulcher
The participation coefficient is a widely used metric of the diversity of a node’s connections with respect to a modular partition of a network. An information-theoretic formulation of this concept of connection diversity, referred to here as participation entropy, has been introduced as the Shannon entropy of the distribution of module labels across a node’s connected neighbors. While diversity metrics have been studied theoretically in other literatures, including to index species diversity in ecology, many of these results have not previously been applied to networks. Here we show that the participation coefficient is a first-order approximation to participation entropy and use the desirable additive properties of entropy to develop new metrics of connection diversity with respect to multiple labelings of nodes in a network, as joint and conditional participation entropies. The information-theoretic formalism developed here allows new and more subtle types of nodal connection patterns in complex networks to be studied.
{"title":"On the information-theoretic formulation of network participation","authors":"Pavle Cajic, Dominic Agius, Oliver M Cliff, James M Shine, Joseph T Lizier, Ben D Fulcher","doi":"10.1088/2632-072x/ad32da","DOIUrl":"https://doi.org/10.1088/2632-072x/ad32da","url":null,"abstract":"The participation coefficient is a widely used metric of the diversity of a node’s connections with respect to a modular partition of a network. An information-theoretic formulation of this concept of connection diversity, referred to here as participation entropy, has been introduced as the Shannon entropy of the distribution of module labels across a node’s connected neighbors. While diversity metrics have been studied theoretically in other literatures, including to index species diversity in ecology, many of these results have not previously been applied to networks. Here we show that the participation coefficient is a first-order approximation to participation entropy and use the desirable additive properties of entropy to develop new metrics of connection diversity with respect to multiple labelings of nodes in a network, as joint and conditional participation entropies. The information-theoretic formalism developed here allows new and more subtle types of nodal connection patterns in complex networks to be studied.","PeriodicalId":53211,"journal":{"name":"Journal of Physics Complexity","volume":"38 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140312412","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-03-25DOI: 10.1088/2632-072x/ad30bf
Luca Mungo, Alexandra Brintrup, Diego Garlaschelli, François Lafond
Network reconstruction is a well-developed sub-field of network science, but it has only recently been applied to production networks, where nodes are firms and edges represent customer-supplier relationships. We review the literature that has flourished to infer the topology of these networks by partial, aggregate, or indirect observation of the data. We discuss why this is an important endeavour, what needs to be reconstructed, what makes it different from other network reconstruction problems, and how different researchers have approached the problem. We conclude with a research agenda.
{"title":"Reconstructing supply networks","authors":"Luca Mungo, Alexandra Brintrup, Diego Garlaschelli, François Lafond","doi":"10.1088/2632-072x/ad30bf","DOIUrl":"https://doi.org/10.1088/2632-072x/ad30bf","url":null,"abstract":"Network reconstruction is a well-developed sub-field of network science, but it has only recently been applied to production networks, where nodes are firms and edges represent customer-supplier relationships. We review the literature that has flourished to infer the topology of these networks by partial, aggregate, or indirect observation of the data. We discuss why this is an important endeavour, what needs to be reconstructed, what makes it different from other network reconstruction problems, and how different researchers have approached the problem. We conclude with a research agenda.","PeriodicalId":53211,"journal":{"name":"Journal of Physics Complexity","volume":"31 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140312543","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-03-21DOI: 10.1088/2632-072x/ad3262
Md Sayeed Anwar, Dibakar Ghosh, Timoteo Carletti
Synchronization has received a lot of attention from the scientific community for systems evolving on static networks or higher-order structures, such as hypergraphs and simplicial complexes. In many relevant real-world applications, the latter are not static but do evolve in time, in this work we thus discuss the impact of the time-varying nature of higher-order structures in the emergence of global synchronization. To achieve this goal, we extend the master stability formalism to account, in a general way, for the additional contributions arising from the time evolution of the higher-order structure supporting the dynamical systems. The theory is successfully challenged against two illustrative examples, the Stuart–Landau nonlinear oscillator and the Lorenz chaotic oscillator.
{"title":"Global synchronization on time-varying higher-order structures","authors":"Md Sayeed Anwar, Dibakar Ghosh, Timoteo Carletti","doi":"10.1088/2632-072x/ad3262","DOIUrl":"https://doi.org/10.1088/2632-072x/ad3262","url":null,"abstract":"Synchronization has received a lot of attention from the scientific community for systems evolving on static networks or higher-order structures, such as hypergraphs and simplicial complexes. In many relevant real-world applications, the latter are not static but do evolve in time, in this work we thus discuss the impact of the time-varying nature of higher-order structures in the emergence of global synchronization. To achieve this goal, we extend the master stability formalism to account, in a general way, for the additional contributions arising from the time evolution of the higher-order structure supporting the dynamical systems. The theory is successfully challenged against two illustrative examples, the Stuart–Landau nonlinear oscillator and the Lorenz chaotic oscillator.","PeriodicalId":53211,"journal":{"name":"Journal of Physics Complexity","volume":"69 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140312291","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-03-13DOI: 10.1088/2632-072x/ad2ec2
L A Smirnov, M I Bolotov, A Pikovsky
We explore the model of a population of nonlocally coupled identical phase oscillators on a ring (Abrams and Strogatz 2004 Phys. Rev. Lett.93 174102) and describe traveling patterns. In the continuous in space formulation, we find families of traveling wave solutions for left-right symmetric and asymmetric couplings. Only the simplest of these waves are stable, which is confirmed by numerical simulations for a finite population. We demonstrate that for asymmetric coupling, a weakly turbulent traveling chimera regime is established, both from an initial standing chimera or an unstable traveling wave profile. The weakly turbulent chimera is a macroscopically chaotic state, with a well-defined synchronous domain and partial coherence in the disordered domain. We characterize it through the correlation function and the Lyapunov spectrum.
{"title":"Nonuniformly twisted states and traveling chimeras in a system of nonlocally coupled identical phase oscillators","authors":"L A Smirnov, M I Bolotov, A Pikovsky","doi":"10.1088/2632-072x/ad2ec2","DOIUrl":"https://doi.org/10.1088/2632-072x/ad2ec2","url":null,"abstract":"We explore the model of a population of nonlocally coupled identical phase oscillators on a ring (Abrams and Strogatz 2004 <italic toggle=\"yes\">Phys. Rev. Lett.</italic>\u0000<bold>93</bold> 174102) and describe traveling patterns. In the continuous in space formulation, we find families of traveling wave solutions for left-right symmetric and asymmetric couplings. Only the simplest of these waves are stable, which is confirmed by numerical simulations for a finite population. We demonstrate that for asymmetric coupling, a weakly turbulent traveling chimera regime is established, both from an initial standing chimera or an unstable traveling wave profile. The weakly turbulent chimera is a macroscopically chaotic state, with a well-defined synchronous domain and partial coherence in the disordered domain. We characterize it through the correlation function and the Lyapunov spectrum.","PeriodicalId":53211,"journal":{"name":"Journal of Physics Complexity","volume":"33 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140312289","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-03-08DOI: 10.1088/2632-072x/ad2d5b
J Menezes
We study a three-species cyclic model whose organisms are vulnerable to contamination with an infectious disease which propagates person-to-person. We consider that individuals of one species perform a self-preservation strategy by reducing the mobility rate to minimise infection risk whenever an epidemic outbreak reaches the neighbourhood. Running stochastic simulations, we quantify the changes in spatial patterns induced by unevenness in the cyclic game introduced by the mobility restriction strategy of organisms of one out of the species. Our findings show that variations in disease virulence impact the benefits of dispersal limitation reaction, with the relative reduction of the organisms’ infection risk accentuating in surges of less contagious or deadlier diseases. The effectiveness of the mobility restriction tactic depends on the deceleration level and the fraction of infected neighbours which is considered too dangerous, thus triggering the defensive strategy. If each organism promptly reacts to the arrival of the first viral vectors in its surroundings with strict mobility reduction, contamination risk decreases significantly. Our conclusions may help biologists understand the impact of defensive strategies in ecosystems during an epidemic.
{"title":"Mobility restrictions in response to local epidemic outbreaks in rock-paper-scissors models","authors":"J Menezes","doi":"10.1088/2632-072x/ad2d5b","DOIUrl":"https://doi.org/10.1088/2632-072x/ad2d5b","url":null,"abstract":"We study a three-species cyclic model whose organisms are vulnerable to contamination with an infectious disease which propagates person-to-person. We consider that individuals of one species perform a self-preservation strategy by reducing the mobility rate to minimise infection risk whenever an epidemic outbreak reaches the neighbourhood. Running stochastic simulations, we quantify the changes in spatial patterns induced by unevenness in the cyclic game introduced by the mobility restriction strategy of organisms of one out of the species. Our findings show that variations in disease virulence impact the benefits of dispersal limitation reaction, with the relative reduction of the organisms’ infection risk accentuating in surges of less contagious or deadlier diseases. The effectiveness of the mobility restriction tactic depends on the deceleration level and the fraction of infected neighbours which is considered too dangerous, thus triggering the defensive strategy. If each organism promptly reacts to the arrival of the first viral vectors in its surroundings with strict mobility reduction, contamination risk decreases significantly. Our conclusions may help biologists understand the impact of defensive strategies in ecosystems during an epidemic.","PeriodicalId":53211,"journal":{"name":"Journal of Physics Complexity","volume":"6 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140312416","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-03-06DOI: 10.1088/2632-072x/ad2698
Pietro Valigi, Izaak Neri, Chiara Cammarota
We study the spectral properties of sparse random graphs with different topologies and type of interactions, and their implications on the stability of complex systems, with particular attention to ecosystems. Specifically, we focus on the behaviour of the leading eigenvalue in different type of random matrices (including interaction matrices and Jacobian-like matrices), relevant for the assessment of different types of dynamical stability. By comparing numerical results on Erdős–Rényi and Husimi graphs with sign-antisymmetric interactions or mixed sign patterns, we propose a sufficient criterion, called strong local sign stability, for stability not to be affected by system size, as traditionally implied by the complexity-stability trade-off in conventional models of random matrices. The criterion requires sign-antisymmetric or unidirectional interactions and a local structure of the graph such that the number of cycles of finite length do not increase with the system size. Note that the last requirement is stronger than the classical local tree-like condition, which we associate to the less stringent definition of local sign stability, also defined in the paper. In addition, for strong local sign stable graphs which show stability to linear perturbations irrespectively of system size, we observe that the leading eigenvalue can undergo a transition from being real to acquiring a nonnull imaginary part, which implies a dynamical transition from nonoscillatory to oscillatory linear response to perturbations. Lastly, we ascertain the discontinuous nature of this transition.
{"title":"Local sign stability and its implications for spectra of sparse random graphs and stability of ecosystems","authors":"Pietro Valigi, Izaak Neri, Chiara Cammarota","doi":"10.1088/2632-072x/ad2698","DOIUrl":"https://doi.org/10.1088/2632-072x/ad2698","url":null,"abstract":"We study the spectral properties of sparse random graphs with different topologies and type of interactions, and their implications on the stability of complex systems, with particular attention to ecosystems. Specifically, we focus on the behaviour of the leading eigenvalue in different type of random matrices (including interaction matrices and Jacobian-like matrices), relevant for the assessment of different types of dynamical stability. By comparing numerical results on Erdős–Rényi and Husimi graphs with sign-antisymmetric interactions or mixed sign patterns, we propose a sufficient criterion, called <italic toggle=\"yes\">strong local sign stability</italic>, for stability not to be affected by system size, as traditionally implied by the complexity-stability trade-off in conventional models of random matrices. The criterion requires sign-antisymmetric or unidirectional interactions and a local structure of the graph such that the number of cycles of finite length do not increase with the system size. Note that the last requirement is stronger than the classical local tree-like condition, which we associate to the less stringent definition of <italic toggle=\"yes\">local sign stability</italic>, also defined in the paper. In addition, for strong local sign stable graphs which show stability to linear perturbations irrespectively of system size, we observe that the leading eigenvalue can undergo a transition from being real to acquiring a nonnull imaginary part, which implies a dynamical transition from nonoscillatory to oscillatory linear response to perturbations. Lastly, we ascertain the discontinuous nature of this transition.","PeriodicalId":53211,"journal":{"name":"Journal of Physics Complexity","volume":"28 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140312298","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-02-28DOI: 10.1088/2632-072x/ad269b
Santiago Lamata-Otín, Jesús Gómez-Gardeñes, David Soriano-Paños
Yet often neglected, dynamical interdependencies between concomitant contagion processes can alter their intrinsic equilibria and bifurcations. A particular case of interest for disease control is the emergence of discontinuous transitions in epidemic dynamics coming from their interactions with other simultaneous processes. To address this problem, here we propose a framework coupling a standard epidemic dynamics with another contagion process, presenting a tunable parameter shaping the nature of its transitions. Our model retrieves well-known results in the literature, such as the existence of first-order transitions arising from the mutual cooperation of epidemics or the onset of abrupt transitions when social contagions unidirectionally drive epidemics. We also reveal that negative feedback loops between simultaneous dynamical processes might suppress abrupt phenomena, thus increasing systems robustness against external perturbations. Our results render a general perspective toward finding different pathways to abrupt phenomena from the interaction of contagion processes.
{"title":"Pathways to discontinuous transitions in interacting contagion dynamics","authors":"Santiago Lamata-Otín, Jesús Gómez-Gardeñes, David Soriano-Paños","doi":"10.1088/2632-072x/ad269b","DOIUrl":"https://doi.org/10.1088/2632-072x/ad269b","url":null,"abstract":"Yet often neglected, dynamical interdependencies between concomitant contagion processes can alter their intrinsic equilibria and bifurcations. A particular case of interest for disease control is the emergence of discontinuous transitions in epidemic dynamics coming from their interactions with other simultaneous processes. To address this problem, here we propose a framework coupling a standard epidemic dynamics with another contagion process, presenting a tunable parameter shaping the nature of its transitions. Our model retrieves well-known results in the literature, such as the existence of first-order transitions arising from the mutual cooperation of epidemics or the onset of abrupt transitions when social contagions unidirectionally drive epidemics. We also reveal that negative feedback loops between simultaneous dynamical processes might suppress abrupt phenomena, thus increasing systems robustness against external perturbations. Our results render a general perspective toward finding different pathways to abrupt phenomena from the interaction of contagion processes.","PeriodicalId":53211,"journal":{"name":"Journal of Physics Complexity","volume":"102 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140010937","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-02-23DOI: 10.1088/2632-072x/ad2971
Satori Tsuzuki, Daichi Yanagisawa, Eri Itoh, Katsuhiro Nishinari
We analyzed agent behavior in complex networks: Barabási–Albert, Erdos–Rényi, and Watts–Strogatz models under the following rules: agents (a) randomly select a destination among adjacent nodes; (b) exclude the most congested adjacent node as a potential destination and randomly select a destination among the remaining nodes; or (c) select the sparsest adjacent node as a destination. We focused on small complex networks with node degrees ranging from zero to a maximum of approximately 20 to study agent behavior in traffic and transportation networks. We measured the hunting rate, that is, the rate of change of agent amounts in each node per unit of time, and the imbalance of agent distribution among nodes. Our simulation study reveals that the topological structure of a network precisely determines agent distribution when agents perform full random walks; however, their destination selections alter the agent distribution. Notably, rule (c) makes hunting and imbalance rates significantly high compared with random walk cases (a) and (b), irrespective of network types, when the network has a high degree and high activity rate. Compared with the full random walk in (a) and (b) increases the hunting rate while decreasing the imbalance rate when activity is low; however, both increase when activity is high. These characteristics exhibit slight periodic undulations over time. Furthermore, our analysis shows that in the BA, ER, and WS network models, the hunting rate decreases and the imbalance rate increases when the system disconnects randomly selected nodes in simulations where agents follow rules (a)–(c) and the network has the ability to disconnect nodes within a certain time of all time steps. Our findings can be applied to various applications related to agent dynamics in complex networks.
{"title":"Effects of topological structure and destination selection strategies on agent dynamics in complex networks","authors":"Satori Tsuzuki, Daichi Yanagisawa, Eri Itoh, Katsuhiro Nishinari","doi":"10.1088/2632-072x/ad2971","DOIUrl":"https://doi.org/10.1088/2632-072x/ad2971","url":null,"abstract":"We analyzed agent behavior in complex networks: Barabási–Albert, Erdos–Rényi, and Watts–Strogatz models under the following rules: agents (a) randomly select a destination among adjacent nodes; (b) exclude the most congested adjacent node as a potential destination and randomly select a destination among the remaining nodes; or (c) select the sparsest adjacent node as a destination. We focused on small complex networks with node degrees ranging from zero to a maximum of approximately 20 to study agent behavior in traffic and transportation networks. We measured the hunting rate, that is, the rate of change of agent amounts in each node per unit of time, and the imbalance of agent distribution among nodes. Our simulation study reveals that the topological structure of a network precisely determines agent distribution when agents perform full random walks; however, their destination selections alter the agent distribution. Notably, rule (c) makes hunting and imbalance rates significantly high compared with random walk cases (a) and (b), irrespective of network types, when the network has a high degree and high activity rate. Compared with the full random walk in (a) and (b) increases the hunting rate while decreasing the imbalance rate when activity is low; however, both increase when activity is high. These characteristics exhibit slight periodic undulations over time. Furthermore, our analysis shows that in the BA, ER, and WS network models, the hunting rate decreases and the imbalance rate increases when the system disconnects randomly selected nodes in simulations where agents follow rules (a)–(c) and the network has the ability to disconnect nodes within a certain time of all time steps. Our findings can be applied to various applications related to agent dynamics in complex networks.","PeriodicalId":53211,"journal":{"name":"Journal of Physics Complexity","volume":"14 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140011037","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-02-23DOI: 10.1088/2632-072x/ad28fe
Stefan Klus, Maia Trower
Graphs and networks play an important role in modeling and analyzing complex interconnected systems such as transportation networks, integrated circuits, power grids, citation graphs, and biological and artificial neural networks. Graph clustering algorithms can be used to detect groups of strongly connected vertices and to derive coarse-grained models. We define transfer operators such as the Koopman operator and the Perron–Frobenius operator on graphs, study their spectral properties, introduce Galerkin projections of these operators, and illustrate how reduced representations can be estimated from data. In particular, we show that spectral clustering of undirected graphs can be interpreted in terms of eigenfunctions of the Koopman operator and propose novel clustering algorithms for directed graphs based on generalized transfer operators. We demonstrate the efficacy of the resulting algorithms on several benchmark problems and provide different interpretations of clusters.
{"title":"Transfer operators on graphs: spectral clustering and beyond","authors":"Stefan Klus, Maia Trower","doi":"10.1088/2632-072x/ad28fe","DOIUrl":"https://doi.org/10.1088/2632-072x/ad28fe","url":null,"abstract":"Graphs and networks play an important role in modeling and analyzing complex interconnected systems such as transportation networks, integrated circuits, power grids, citation graphs, and biological and artificial neural networks. Graph clustering algorithms can be used to detect groups of strongly connected vertices and to derive coarse-grained models. We define transfer operators such as the Koopman operator and the Perron–Frobenius operator on graphs, study their spectral properties, introduce Galerkin projections of these operators, and illustrate how reduced representations can be estimated from data. In particular, we show that spectral clustering of undirected graphs can be interpreted in terms of eigenfunctions of the Koopman operator and propose novel clustering algorithms for directed graphs based on generalized transfer operators. We demonstrate the efficacy of the resulting algorithms on several benchmark problems and provide different interpretations of clusters.","PeriodicalId":53211,"journal":{"name":"Journal of Physics Complexity","volume":"257 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140011036","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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