<?xml version="1.0" encoding="utf-8"?>
    <rss version="2.0">
      <channel xmlns:content="http://purl.org/rss/1.0/modules/content/">
        <title>Frontiers in Complex Systems | Complex Networks section | New and Recent Articles</title>
        <link>https://www.frontiersin.org/journals/complex-systems/sections/complex-networks</link>
        <description>RSS Feed for Complex Networks section in the Frontiers in Complex Systems journal | New and Recent Articles</description>
        <language>en-us</language>
        <generator>Frontiers Feed Generator,version:1</generator>
        <pubDate>2026-04-07T13:45:46.464+00:00</pubDate>
        <ttl>60</ttl>
        <item>
        <guid isPermaLink="true">https://www.frontiersin.org/articles/10.3389/fcpxs.2025.1636222</guid>
        <link>https://www.frontiersin.org/articles/10.3389/fcpxs.2025.1636222</link>
        <title><![CDATA[Organizational regularities in recurrent neural networks]]></title>
        <pubdate>2026-01-05T00:00:00Z</pubdate>
        <category>Original Research</category>
        <author>Claus Metzner</author><author>Achim Schilling</author><author>Andreas Maier</author><author>Patrick Krauss</author>
        <description><![CDATA[Previous work has shown that the dynamical regime of Recurrent Neural Networks (RNNs)—ranging from oscillatory to chaotic and fixed point behavior—can be controlled by the global distribution of weights in connection matrices with statistically independent elements. However, it remains unclear how network dynamics respond to organizational regularities in the weight matrix, as often observed in biological neural networks. Here, we investigate three such regularities: (1) monopolar output weights per neuron, in accordance with Dale’s principle, (2) reciprocal symmetry between neuron pairs, as in Hopfield networks, and (3) modular structure, where strongly connected blocks are embedded in a background of weaker connectivity. These regularities are studied independently, but as functions of the RNN’s general connection strength and its excitatory/inhibitory bias. For this purpose, we construct weight matrices in which the strength of each regularity can be continuously tuned via control parameters, and analyze how key dynamical signatures of the RNN evolve as a function of these parameters. Moreover, using the RNN for actual information processing in a reservoir computing framework, we study how each regularity affects performance. We find that Dale monopolarity and modularity significantly enhance task accuracy, while Hopfield reciprocity tends to reduce it by promoting early saturation, limiting reservoir flexibility.]]></description>
      </item><item>
        <guid isPermaLink="true">https://www.frontiersin.org/articles/10.3389/fcpxs.2025.1620260</guid>
        <link>https://www.frontiersin.org/articles/10.3389/fcpxs.2025.1620260</link>
        <title><![CDATA[Network modelling in analysing cyber-related graphs]]></title>
        <pubdate>2025-09-16T00:00:00Z</pubdate>
        <category>Original Research</category>
        <author>Vesa Kuikka</author><author>Lauri Pykälä</author><author>Tuomas Takko</author><author>Kimmo K. Kaski</author>
        <description><![CDATA[To improve the resilience of the computer network infrastructure against cyber attacks or causal influences and find ways to mitigate their impact, we need to understand their structure and dynamics. Here, we propose a novel network-based influence-spreading modelling approach to investigate event trajectories or paths in attack and causal graphs with directed, weighted, cyclic and/or acyclic paths. In our model, we can perform probabilistic analyses that extend beyond traditional methods to visualise cyber-related graphs. The model uses a probabilistic method to combine paths that join within the graph. This analysis includes vulnerabilities, services, and exploitabilities. To demonstrate the applicability of our model, we present three cyber-related use cases: two attack graphs and one causal graph. This model can serve cyber analysts as a tool to produce quantitative metrics for prioritising tasks, summarising statistics, or analysing large-scale graphs.]]></description>
      </item><item>
        <guid isPermaLink="true">https://www.frontiersin.org/articles/10.3389/fcpxs.2025.1575210</guid>
        <link>https://www.frontiersin.org/articles/10.3389/fcpxs.2025.1575210</link>
        <title><![CDATA[Spectrum optimization of dynamic networks for reduction of vulnerability against adversarial resonance attacks]]></title>
        <pubdate>2025-05-30T00:00:00Z</pubdate>
        <category>Original Research</category>
        <author>Alp Sahin</author><author>Nicolas Kozachuk</author><author>Rick S. Blum</author><author>Subhrajit Bhattacharya</author>
        <description><![CDATA[Resonance is a well-known phenomenon that happens in systems with second order dynamics. In this paper, we address the fundamental question of making a network robust to signal being periodically pumped into it at or near a resonant frequency by an adversarial agent with the aim of saturating the network with the signal. Toward this goal, we develop the notion of network vulnerability, which is measured by the expected resonance amplitude on the network under a stochastically modeled adversarial attack. Assuming a second order dynamics model based on the network graph Laplacian and a known stochastic model for the adversarial attack, we propose two methods for minimizing the network vulnerability–one through direct optimization of the spectrum of the network graph, and another through optimization of an auxiliary network graph attached to the main network. We provide theoretical foundations for these methods as well as extensive numerical results analyzing the effectiveness of both methods in reducing the network vulnerability.]]></description>
      </item><item>
        <guid isPermaLink="true">https://www.frontiersin.org/articles/10.3389/fcpxs.2024.1516812</guid>
        <link>https://www.frontiersin.org/articles/10.3389/fcpxs.2024.1516812</link>
        <title><![CDATA[Exploring the thermodynamic description of a simulation of flocking birds]]></title>
        <pubdate>2025-02-03T00:00:00Z</pubdate>
        <category>Original Research</category>
        <author>Alexander V. Mantzaris</author><author>George-Rafael Domenikos</author>
        <description><![CDATA[This study presents an approach to analyzing a simulation of birds flocking as a thermodynamic system. The simulation of birds is produced using standard agent-based modeling and the thermodynamic variables for the states of the trajectory using statistical mechanics. The energy of the birds is defined, and from the distribution function, the entropy, internal energy, temperature, heat flux, and pressure are defined. The trajectory of the entropy decreases as the flocks increase clustering among each other, becoming denser. As a result, internal energy generally decreases (with minor oscillations), and an overall steady decrease of the cumulative heat flux is also observed. Pressure is observed to decrease as the simulation progresses with the increase of the volume. Overall, the system displays consistency with the expected trajectories of all the thermodynamics variables in a cooling process. Thus, through this thermodynamic definition, a more in-depth representation of the state space of the system is achieved. This description offers information about both the microscopic and macroscopic behaviors of the flocks and, importantly, an understanding about the exchange of energy/information between the flock and the external environment through the heat flux.]]></description>
      </item><item>
        <guid isPermaLink="true">https://www.frontiersin.org/articles/10.3389/fcpxs.2024.1479417</guid>
        <link>https://www.frontiersin.org/articles/10.3389/fcpxs.2024.1479417</link>
        <title><![CDATA[Recurrence resonance - noise-enhanced dynamics in recurrent neural networks]]></title>
        <pubdate>2024-10-08T00:00:00Z</pubdate>
        <category>Original Research</category>
        <author>Claus Metzner</author><author>Achim Schilling</author><author>Andreas Maier</author><author>Patrick Krauss</author>
        <description><![CDATA[Understanding how neural networks process information is a fundamental challenge in neuroscience and artificial intelligence. A pivotal question in this context is how external stimuli, particularly noise, influence the dynamics and information flow within these networks. Traditionally, noise is perceived as a hindrance to information processing, introducing randomness and diminishing the fidelity of neural signals. However, distinguishing noise from structured input uncovers a paradoxical insight: under specific conditions, noise can actually enhance information processing. This intriguing possibility prompts a deeper investigation into the nuanced role of noise within neural networks. In specific motifs of three recurrently connected neurons with probabilistic response, the spontaneous information flux, defined as the mutual information between subsequent states, has been shown to increase by adding ongoing white noise of some optimal strength to each of the neurons. However, the precise conditions for and mechanisms of this phenomenon called ‘recurrence resonance’ (RR) remain largely unexplored. Using Boltzmann machines of different sizes and with various types of weight matrices, we show that RR can generally occur when a system has multiple dynamical attractors, but is trapped in one or a few of them. In probabilistic networks, the phenomenon is bound to a suitable observation time scale, as the system could autonomously access its entire attractor landscape even without the help of external noise, given enough time. Yet, even in large systems, where time scales for observing RR in the full network become too long, the resonance can still be detected in small subsets of neurons. Finally, we show that short noise pulses can be used to transfer recurrent neural networks, both probabilistic and deterministic, between their dynamical attractors. Our results are relevant to the fields of reservoir computing and neuroscience, where controlled noise may turn out a key factor for efficient information processing leading to more robust and adaptable systems.]]></description>
      </item><item>
        <guid isPermaLink="true">https://www.frontiersin.org/articles/10.3389/fcpxs.2024.1409101</guid>
        <link>https://www.frontiersin.org/articles/10.3389/fcpxs.2024.1409101</link>
        <title><![CDATA[Editorial: Insights in complex networks]]></title>
        <pubdate>2024-04-17T00:00:00Z</pubdate>
        <category>Editorial</category>
        <author>Claudio Castellano</author><author>Victor M. Preciado</author>
        <description></description>
      </item><item>
        <guid isPermaLink="true">https://www.frontiersin.org/articles/10.3389/fcpxs.2024.1331320</guid>
        <link>https://www.frontiersin.org/articles/10.3389/fcpxs.2024.1331320</link>
        <title><![CDATA[The projection method: a unified formalism for community detection]]></title>
        <pubdate>2024-02-26T00:00:00Z</pubdate>
        <category>Methods</category>
        <author>Martijn Gösgens</author><author>Remco van der Hofstad</author><author>Nelly Litvak</author>
        <description><![CDATA[We present the class of projection methods for community detection that generalizes many popular community detection methods. In this framework, we represent each clustering (partition) by a vector on a high-dimensional hypersphere. A community detection method is a projection method if it can be described by the following two-step approach: 1) the graph is mapped to a query vector on the hypersphere; and 2) the query vector is projected on the set of clustering vectors. This last projection step is performed by minimizing the distance between the query vector and the clustering vector, over the set of clusterings. We prove that optimizing Markov stability, modularity, the likelihood of planted partition models and correlation clustering fit this framework. A consequence of this equivalence is that algorithms for each of these methods can be modified to perform the projection step in our framework. In addition, we show that these different methods suffer from the same granularity problem: they have parameters that control the granularity of the resulting clustering, but choosing these to obtain clusterings of the desired granularity is nontrivial. We provide a general heuristic to address this granularity problem, which can be applied to any projection method. Finally, we show how, given a generator of graphs with community structure, we can optimize a projection method for this generator in order to obtain a community detection method that performs well on this generator.]]></description>
      </item><item>
        <guid isPermaLink="true">https://www.frontiersin.org/articles/10.3389/fcpxs.2023.1344094</guid>
        <link>https://www.frontiersin.org/articles/10.3389/fcpxs.2023.1344094</link>
        <title><![CDATA[Cooperation and the social brain hypothesis in primate social networks]]></title>
        <pubdate>2024-01-22T00:00:00Z</pubdate>
        <category>Original Research</category>
        <author>Neil G. MacLaren</author><author>Lingqi Meng</author><author>Melissa Collier</author><author>Naoki Masuda</author>
        <description><![CDATA[The social brain hypothesis posits that species with larger brains tend to have greater social complexity. Various lines of empirical evidence have supported the social brain hypothesis, including evidence from the structure of social networks. Cooperation is a key component of group living, particularly among primates, and theoretical research has shown that particular structures of social networks foster cooperation more easily than others. Therefore, we hypothesized that species with a relatively large brain size tend to form social networks that better enable cooperation. In the present study, we combine data on brain size and social networks with theory on the evolution of cooperation on networks to test this hypothesis in non-human primates. We have found a positive effect of brain size on cooperation in social networks even after controlling for the effect of other structural properties of networks that are known to promote cooperation.]]></description>
      </item><item>
        <guid isPermaLink="true">https://www.frontiersin.org/articles/10.3389/fcpxs.2023.1281714</guid>
        <link>https://www.frontiersin.org/articles/10.3389/fcpxs.2023.1281714</link>
        <title><![CDATA[Topology and spectral interconnectivities of higher-order multilayer networks]]></title>
        <pubdate>2023-11-20T00:00:00Z</pubdate>
        <category>Original Research</category>
        <author>Elkaïoum M. Moutuou</author><author>Obaï B. K. Ali</author><author>Habib Benali</author>
        <description><![CDATA[Multilayer networks have permeated all areas of science as an abstraction for interdependent heterogeneous complex systems. However, describing such systems through a purely graph-theoretic formalism presupposes that the interactions that define the underlying infrastructures are only pairwise-based, a strong assumption likely leading to oversimplification. Most interdependent systems intrinsically involve higher-order intra- and inter-layer interactions. For instance, ecological systems involve interactions among groups within and in-between species, collaborations and citations link teams of coauthors to articles and vice versa, and interactions might exist among groups of friends from different social networks. Although higher-order interactions have been studied for monolayer systems through the language of simplicial complexes and hypergraphs, a systematic formalism incorporating them into the realm of multilayer systems is still lacking. Here, we introduce the concept of crossimplicial multicomplexes as a general formalism for modeling interdependent systems involving higher-order intra- and inter-layer connections. Subsequently, we introduce cross-homology and its spectral counterpart, the cross-Laplacian operators, to establish a rigorous mathematical framework for quantifying global and local intra- and inter-layer topological structures in such systems. Using synthetic and empirical datasets, we show that the spectra of the cross-Laplacians of a multilayer network detect different types of clusters in one layer that are controlled by hubs in another layer. We call such hubs spectral cross-hubs and define spectral persistence as a way to rank them, according to their emergence along the spectra. Our framework is broad and can especially be used to study structural and functional connectomes combining connectivities of different types and orders.]]></description>
      </item><item>
        <guid isPermaLink="true">https://www.frontiersin.org/articles/10.3389/fcpxs.2023.1275934</guid>
        <link>https://www.frontiersin.org/articles/10.3389/fcpxs.2023.1275934</link>
        <title><![CDATA[Crisis spreading in multinational firms’ network: the dual influence of local interactions]]></title>
        <pubdate>2023-11-16T00:00:00Z</pubdate>
        <category>Original Research</category>
        <author>Maria Tsouchnika</author><author>Michael Kanetidis</author><author>Panos Argyrakis</author><author>Celine Rozenblat</author>
        <description><![CDATA[This study investigates the characteristics of multinational firm’s interactions within and across activity sectors and the impact of intra-urban connections, during crisis propagation. By employing data that reflect ownership relations aggregated on the city level, we constructed the partial-multiplex, directed network of cities, divided into five layers by activity sector. The network was examined in two states: one excluding intra-urban interactions and one including them. The difference between these two states highlight the significant role of intra-urban networking processes in the global economy. The five layers differ both structurally and in terms of vulnerability during crisis propagation. The Knowledge Intensive Services (KIS) layer is the densest and most populous layer of all and its firms are more likely to be owners than subsidiaries. Using a simple stochastic Susceptible-Infected-Recovered (SIR) model, we simulated a crisis diffusion on the network of cities. Our results revealed that in the absence of intra-urban connections, KIS was both the most vulnerable and most influential layer in crisis propagation. The inclusion of intra-urban links sets off a complex interplay of factors that affect diffusion outcomes in nuanced ways: while it generally enhances the impact of the crisis and the influence across layers becomes rather homogeneous it can also have a protective effect, in cases of very dense and well-connected layers, such as KIS.]]></description>
      </item><item>
        <guid isPermaLink="true">https://www.frontiersin.org/articles/10.3389/fcpxs.2023.1298265</guid>
        <link>https://www.frontiersin.org/articles/10.3389/fcpxs.2023.1298265</link>
        <title><![CDATA[Coevolutionary dynamics of group interactions: coevolving nonlinear voter models]]></title>
        <pubdate>2023-11-10T00:00:00Z</pubdate>
        <category>Mini Review</category>
        <author>Byungjoon Min</author>
        <description><![CDATA[We survey the coevolutionary dynamics of network topology and group interactions in opinion formation, grounded on a coevolving nonlinear voter model. The coevolving nonlinear voter model incorporates two mechanisms: group interactions implemented through nonlinearity in the voter model and network plasticity demonstrated as the rewiring of links to remove connections between nodes in different opinions. We show that the role of group interactions, implemented by the nonlinearity can significantly impact both the dynamical outcomes of nodes’ state and the network topology. Additionally, we review several variants of the coevolving nonlinear voter model considering different rewiring mechanisms, noise of flipping nodes’ state, and multilayer structures. We portray the various aspects of the coevolving nonlinear voter model as an example of network coevolution driven by group interactions, and finally, present the implications and potential directions for future research.]]></description>
      </item>
      </channel>
    </rss>