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Bipartite networks are powerful descriptions of complex systems characterized by two different classes of nodes and connections allowed only across but not within the two classes. Unveiling physical principles, building theories and suggesting physical models to predict bipartite links such as product-consumer connections in recommendation systems or drug-target interactions in molecular networks can provide priceless information to improve e-commerce or to accelerate pharmaceutical research. The prediction of nonobserved connections starting from those already present in the topology of a network is known as the link-prediction problem. It represents an important subject both in many-body interaction theory in physics and in new algorithms for applied tools in computer science. The rationale is that the existing connectivity structure of a network can suggest where new connections can appear with higher likelihood in an evolving network, or where nonobserved connections are missing in a partially known network. Surprisingly, current complex network theory presents a theoretical bottle-neck: a general framework for local-based link prediction directly in the bipartite domain is missing. Here, we overcome this theoretical obstacle and present a formal definition of common neighbour index and local-community-paradigm (LCP) for bipartite networks. As a consequence, we are able to introduce the first node-neighbourhood-based and LCP-based models for topological link prediction that utilize the bipartite domain. We performed link prediction evaluations in several networks of different size and of disparate origin, including technological, social and biological systems. Our models significantly improve topological prediction in many bipartite networks because they exploit local physical driving-forces that participate in the formation and organization of many real-world bipartite networks. Furthermore, we present a local-based formalism that allows to intuitively implement neighbourhood-based link prediction entirely in the bipartite domain.

Complex systems provide an opportunity to analyze the essence of phenomena by studying their intricate connections. The networks formed by these connections, known as complex networks, embody the underlying principles governing the system’s behavior. While complex networks have been previously applied in the field of evolutionary computation, prior studies have been limited in their ability to reach conclusive conclusions. Based on our investigations, we are against the notion that there is a direct link between the complex network structure of an algorithm and its performance, and we demonstrate this experimentally. In this paper, we address these limitations by analyzing the dynamic complex network structures of five algorithms across three different problems. By incorporating mathematical distributions utilized in prior research, we not only generate novel insights but also refine and challenge previous conclusions. Specifically, we introduce the biased Poisson distribution to describe the algorithm’s exploration capability and the biased power-law distribution to represent its exploitation potential during the convergence process. Our aim is to redirect research on the interplay between complex networks and evolutionary computation towards dynamic network structures, elucidating the essence of exploitation and exploration in the black-box optimization process of evolutionary algorithms via dynamic complex networks.

Prediction of missing links is an important part of many applications, such as friends’ recommendations on social media, reduction of economic cost of protein functional modular mining, and implementation of accurate recommendations in the shopping platform. However, the existing algorithms for predicting missing links fall short in the accuracy and the efficiency. To ameliorate these, we propose a simplified quantum walk model whose Hilbert space dimension is only twice the number of nodes in a complex network. This property facilitates simultaneous consideration of the self-loop of each node and the common neighbour information between arbitrary pair of nodes. These effects decrease the negative effect generated by the interference effect in quantum walks while also recording the similarity between nodes and its neighbours. Consequently, the observed probability after the two-step walk is utilised to represent the score of each link as a missing link, by which extensive computations are omitted. Using the AUC index as a performance metric, the proposed model records the highest average accuracy in the prediction of missing links compared to 14 competing algorithms in nine real complex networks. Furthermore, experiments using the precision index show that our proposed model ranks in the first echelon in predicting missing links. These performances indicate the potential of our simplified quantum walk model for applications in network alignment and functional modular mining of protein–protein networks.

In most supply chains (SCs), transaction relationships between suppliers and customers are commonly considered to be an extrapolation from a linear perspective. However, this traditional linear concept of an SC is egotistic and oversimplified and does not sufficiently reflect the complex and cyclical structure of supplier-customer relationships in current economic and industrial situations. The interactional relationships and topological characteristics between suppliers and customers should be analyzed using supply networks (SNs) rather than traditional linear SCs. Therefore, this paper reconceptualizes SCs as SNs in complex adaptive systems (CAS), and presents three main contributions. First, we propose an integrated framework of CAS network by synthesizing multi-level network analysis from the network-, community- and vertex-perspective. The CAS perspective enables us to understand the advances of SN properties. Second, in order to emphasize the CAS properties of SNs, we conducted a real-world SN based on the Japanese industry and describe an advanced investigation of SN theory. The CAS properties help in enriching the SN theory, which can benefit SN management, community economics and industrial resilience. Third, we propose a quantitative metric of entropy to measure the complexity and robustness of SNs. The results not only support a specific understanding of the structural outcomes relevant to SNs, but also deliver efficient and effective support to the management and design of SNs.

Determining the core structure of complex network systems allows us to simplify them. Using h- bridge and h -strength measurements in a weighted network, we extract the h- backbone core structure. We find that focusing on the h -backbone in a network allows greater simplification because it has fewer edges and thus fewer adjacent nodes. We examine three practical applications: the co-citation network in an information system, the open flight network in a social system, and coauthorship in network science publications.

In this paper, the low energy cost synchronization control strategy of Markovian switching complex systems/networks is mainly studied and analyzed through multiple perspectives. Firstly, in order to achieve synchronization of Markovian switching complex networks with low energy cost, a control scheme based on the optimal node selection strategy that does not depend on the network coupling strength is improved, and a finite-time controller with a simpler structure is constructed. Secondly, based on the event-triggered control strategy an effective trigger event is designed to achieve the low energy cost synchronization of Markovian switching complex networks on the basis of reducing the information transmission and interaction between networks. Finally, the two control strategies mentioned in this paper are compared and analyzed from multiple perspectives through numerical simulations to better guide practical engineering.

In multilayer complex networks, the uncertainty in node states leads to intricate behaviors. It is, therefore, of great importance to be able to estimate the states of target nodes in these systems, both for theoretical advancements and practical applications. This paper introduces a state observer-based approach for the state estimation of such networks, focusing specifically on a class of complex dynamic networks with nodes that correspond one-to-one. Initially, a chaotic system is employed to model the dynamics of each node and highlight the essential state components for analysis and derivation. A network state observer is then constructed using a unique diagonal matrix, which underpins the driver and response-layer networks. By integrating control theory and stability function analysis, the effectiveness of the observer in achieving synchronization between complex dynamic networks and target systems is confirmed. Additionally, the efficacy and precision of the proposed method are validated through simulation.

Complex network systems’ models are designed to perfectly emulate real-world networks through the use of simulation and link prediction. Complex network systems are defined by nodes and their connections where both have real-world features that result in a heterogeneous network in which each of the nodes has distinct characteristics. Thus, incorporating real-world features is an important component to achieve a simulation which best represents the real-world. Currently very few complex network systems implement real-world features, thus this study proposes feature selection methods which utilise unsupervised filtering techniques to rank real-world node features alongside a wrapper function to test combinations of the ranked features. The chosen method was coined FS-SNS which improved 8 out of 10 simulations of real-world networks. A consistent threshold of included features was also discovered which saw a threshold of 4 features to achieve the most accurate simulation for all networks. Through these findings the study also proposes future work and discusses how the findings can be used to further the Digital Twin and complex network system field.

This paper studies H∞ and H2 almost state or output synchronization of homogeneous multi-agent systems (MAS) with partial-state coupling via static protocols in the presence of external disturbances. We provide solvability conditions for designing static protocols. We characterize three classes of agents for which we can design linear static protocols for state or output synchronization of a MAS such that the impact of disturbances on the network disagreement dynamics, expressed in terms of the H∞ and H2 norms of the corresponding closed-loop transfer function, is reduced to arbitrarily small value. Meanwhile, the static protocol only needs rough information on the network graph, that is a lower bound for the real part and an upper bound for the modulus of the non-zero eigenvalues of the Laplacian matrix associated with the network graph. Our study focuses on three classes of agents which are squared-down passive, squared-down passifiable via output feedback and squared-down minimum-phase with relative degree 1.