Disassortative Networks Research Articles

Granting leaders priority exit options promotes and jeopardizes cooperation in social dilemmas

Cooperation in human interactions often involves voluntary participation rather than obligatory requirements. This paper investigates the impact of voluntary exit strategies on cooperation within scale-free networks, employing spatial prisoner’s dilemma games as the framework. We analyze three distinct exit strategies: leader priority exit, fringe priority exit, and random exit, across varying dilemma strengths. Our findings reveal that in scenarios of weak dilemma strength, leader priority exit significantly diminishes cooperation, particularly when only a small subset of players is granted exit rights. In contrast, under strong dilemma strength conditions, both leader priority and random exits serve to unexpectedly bolster cooperation. This enhancement is primarily facilitated by high-degree nodes opting out, thereby enabling low-degree nodes to establish stable cooperation. Furthermore, our study underscores the pivotal role of network structure. In assortative networks, random exit emerges as the most effective strategy in promoting cooperation. On the other hand, disassortative networks exhibit a substantial increase in cooperation levels when employing leader priority exit. These results highlight the intricate interplay between exit strategies, dilemma strength, and network topology, offering critical insights for promoting cooperation in varied social contexts.

Examining indicators of complex network vulnerability across diverse attack scenarios

Complex networks capture the structure, dynamics, and relationships among entities in real-world networked systems, encompassing domains like communications, society, chemistry, biology, ecology, politics, etc. Analysis of complex networks lends insight into the critical nodes, key pathways, and potential points of failure that may impact the connectivity and operational integrity of the underlying system. In this work, we investigate the topological properties or indicators, such as shortest path length, modularity, efficiency, graph density, diameter, assortativity, and clustering coefficient, that determine the vulnerability to (or robustness against) diverse attack scenarios. Specifically, we examine how node- and link-based network growth or depletion based on specific attack criteria affect their robustness gauged in terms of the largest connected component (LCC) size and diameter. We employ partial least squares discriminant analysis to quantify the individual contribution of the indicators on LCC preservation while accounting for the collinearity stemming from the possible correlation between indicators. Our analysis of 14 complex network datasets and 5 attack models invariably reveals high modularity and disassortativity to be prime indicators of vulnerability, corroborating prior works that report disassortative modular networks to be particularly susceptible to targeted attacks. We conclude with a discussion as well as an illustrative example of the application of this work in fending off strategic attacks on critical infrastructures through models that adaptively and distributively achieve network robustness.

Systemic risk prevention policies targeting systemically important banks: Does clustering pattern matter?

It is well known that strengthening the soundness of individual banks that are too large or too interconnected is essential for maintaining financial stability. The clustering among homogeneous banks may also cause financial fragility but has received less attention. This paper discusses the policy improvement for preventing systemic risk from the perspective of the clustering pattern of systemically important banks (SIBs) based on a network optimization model. The results show that the clustering pattern of SIBs is closely related to systemic risk contagion. Remarkably, networks with fewer connections among SIBs exhibit lower systemic risk than those featuring apparent clustering of SIBs. The potential mechanism is that the systemic vulnerability of small and medium-sized banks is greatly reduced in the disassortative networks. The proposed tools based on this-inter-SIBs exposure limits and pairwise capital requirements-can guide network optimization and significantly reduce systemic risk. Furthermore, combining existing capital surcharges for SIBs (focusing on the stability of individual SIBs) and proposed network-based tools (focusing on the cluster structure of the network) will be an effective way to enhance financial stability over existing policies.

Network topologies for maximal organismal health span and lifespan.

The population dynamics of human health and mortality can be jointly captured by complex network models using scale-free network topology. To validate and understand the choice of scale-free networks, we investigate which network topologies maximize either lifespan or health span. Using the Generic Network Model (GNM) of organismal aging, we find that both health span and lifespan are maximized with a "star" motif. Furthermore, these optimized topologies exhibit maximal lifespans that are not far above the maximal observed human lifespan. To approximate the complexity requirements of the underlying physiological function, we then constrain network entropies. Using non-parametric stochastic optimization of network structure, we find that disassortative scale-free networks exhibit the best of both lifespan and health span. Parametric optimization of scale-free networks behaves similarly. We further find that higher maximum connectivity and lower minimum connectivity networks enhance both maximal lifespans and health spans by allowing for more disassortative networks. Our results validate the scale-free network assumption of the GNM and indicate the importance of disassortativity in preserving health and longevity in the face of damage propagation during aging. Our results highlight the advantages provided by disassortative scale-free networks in biological organisms and subsystems.

Mechanism of investor behavior propagation in stock market

Investor behavior has a pivotal role in price dynamics. The aim of this study was to explore the characteristics and patterns of the investor behavior and network structure behind. The investor behavior propagation model was proposed, which described the intrinsic dynamic mechanism of stock market and had a good fit to the real data. It was found that the Nearest-neighbor coupled network and the disassortative network can depict the investing behavior network precisely. Combining these two aspects, the Nearest-neighbor coupled network with hub nodes was constructed. Performance was superior to other network structures and suggests that the Nearest-neighbor coupled network with hub nodes is more consistent with the real investor networks.

Identifying accurate link predictors based on assortativity of complex networks

Link prediction algorithms in complex networks, such as social networks, biological networks, drug-drug interactions, communication networks, and so on, assign scores to predict potential links between two nodes. Link prediction (LP) enables researchers to learn unknown, new as well as future interactions among the entities being modeled in the complex networks. In addition to measures like degree distribution, clustering coefficient, centrality, etc., another metric to characterize structural properties is network assortativity which measures the tendency of nodes to connect with similar nodes. In this paper, we explore metrics that effectively predict the links based on the assortativity profiles of the complex networks. To this end, we first propose an approach that generates networks of varying assortativity levels and utilize three sets of link prediction models combining the similarity of neighborhoods and preferential attachment. We carry out experiments to study the LP accuracy (measured in terms of area under the precision-recall curve) of the link predictors individually and in combination with other baseline measures. Our analysis shows that link prediction models that explore a large neighborhood around nodes of interest, such as CH2-L2 and CH2-L3, perform consistently for assortative as well as disassortative networks. While common neighbor-based local measures are effective for assortative networks, our proposed combination of common neighbors with node degree is a good choice for the LP metric in disassortative networks. We discuss how this analysis helps achieve the best-parameterized combination of link prediction models and its significance in the context of link prediction from incomplete social and biological network data.

A novel message passing neural network based on neighborhood expansion

Most message passing neural networks (MPNNs) are widely used for assortative network representation learning under the assumption of homophily between connected nodes. However, this fundamental assumption is inconsistent with the heterophily of disassortative networks (DNs) in many real-world applications. Therefore, we propose a novel MPNN called NEDA based on neighborhood expansion for disassortative network representation learning (DNRL). Specifically, our NEDA first performs neighborhood expansion to seek more informative nodes for aggregation and then performs data augmentation to speed up the optimization process of a set of parameter matrices at the maximum available training data with minimal computational cost. To evaluate the performance of NEDA comprehensively, we perform several experiments on benchmark disassortative network datasets with variable sizes, where the results demonstrate the effectiveness of our NEDA model. The code is publicly available at https://github.com/xueyanfeng/NEDA.

Resilience enhancement of renewable cyber–physical power system against malware attacks

The widespread application of cyber technologies and Renewable Energy Sources (RESs) has gradually transformed traditional power systems into renewable Cyber–Physical Power Systems (CPPSs), which are increasingly threatened by malware attacks. In this paper, we develop an original and novel simulation framework with consideration of both malware attack process and the uncertainty of RESs to quantitatively analyze the resilience of renewable CPPS. Based on the framework, we consider different stages of the resilience process and propose corresponding prevention and restoration methods to enhance the resilience of the system. The efficacy and applicability of our proposed methods are demonstrated in a test renewable CPPS formed by coupling the IEEE 39 Bus System with a scale-free communication network. Experimental results reveal that accurate RES output forecast and a disassortative communication network can improve the resilience of renewable CPPS against malware attacks.

Investigation of Flow Characteristics of Landslide Materials Through Pore Space Topology and Complex Network Analysis

AbstractUnlike embankments, earth dams, and other man‐made structures, most landslide dams are formed by rapid accumulation of rock or debris rather than mechanical compaction; thus, they are loose and pose a great risk of seepage failure. Landslide materials usually have complex pore structures with randomly distributed pores of various sizes, making the flow and transport processes very complex. Aiming at these challenges, we systematically investigated the influences of pore structure on the micro‐and macro‐scale flow characteristics of landslide materials. First, landslide materials are simplified as spherical granular packings with wide grain size distributions. Then, we use the Finite‐difference method Stokes solver to simulate the fluid flow through granular packings and calculate their permeability. We characterize the pore structure using different topological measures, including these borrowed from complex network theory. Among these measures, tortuosity and global efficiency show clear relations with permeability. The pore network modeling indicates that pore size heterogeneity and pore connectivity significantly influence the flow characteristics. The correlation between pore‐scale velocity and throat diameters follows a power‐law scaling with an exponent close to two, suggesting that the Hagen–Poiseuille law would still be valid in complex porous media. The permeability and porosity, throat radius, and tortuosity of pore structure can be related by the equation proposed by Nishiyama and Yokoyama (2017, https://doi.org/10.1002/2016JB013793). The complex network analysis reveals that the assortative network is more permeable than the disassortative network. Furthermore, pores with larger closeness centrality have higher flow efficiency, resulting in higher macroscopic permeability.

Discontinuous emergence of a giant cluster in assortative scale-free networks

A giant cluster emerges discontinuously in bond percolation in various networks when the growth of large clusters is globally suppressed. It was recently revealed that this phenomenon occurs even in a scale-free (SF) network, where hubs accelerate the growth of large clusters. The SF network used in the previous study was disassortative, though, so it is necessary to check whether the phenomenon also occurs in an assortative SF network, where each hub prefers to be connected to another hub and thus the large cluster growth is accelerated. In this paper, we find that the phenomenon, namely the discontinuous emergence of a giant cluster in bond percolation with the global suppression of large clusters, also occurs in an assortative SF network. Interestingly, the generated network is also assortative but not a SF network at the transition point, unlike the disassortative SF network generated at the transition point in the previous study. We observe similar behaviors in two additional models and discuss the results.

Role of assortativity in predicting burst synchronization using echo state network.

In this study, we use a reservoir computing based echo state network (ESN) to predict the collective burst synchronization of neurons. Specifically, we investigate the ability of ESN in predicting the burst synchronization of an ensemble of Rulkov neurons placed on a scale-free network. We have shown that a limited number of nodal dynamics used as input in the machine can capture the real trend of burst synchronization in this network. Further, we investigate the proper selection of nodal inputs of degree-degree (positive and negative) correlated networks. We show that for a disassortative network, selection of different input nodes based on degree has no significant role in the machine's prediction. However, in the case of assortative network, training the machine with the information (i.e., time series) of low degree nodes gives better results in predicting the burst synchronization. The results are found to be consistent with the investigation carried out with a continuous time Hindmarsh-Rose neuron model. Furthermore, the role of hyperparameters like spectral radius and leaking parameter of ESN on the prediction process has been examined. Finally, we explain the underlying mechanism responsible for observing these differences in the prediction in a degree correlated network.

Effects of FDI on trade among countries along the Belt and Road: A network perspective

From the network perspective, this paper explores the effect of FDI on trade and analyzes the structural effect on different sectors classified by technology levels among the Belt and Road (B&R) countries. Employing social network analysis methods, we depict the evolution of FDI networks and trade networks of B&R countries and find that both two networks are disassortative and small-world networks as well as the density and number of edges increase. Through the results of ERGM, we get three findings about the effect of FDI on trade. (1) FDI has the positive effect on trade among B&R countries from the network perspective; (2) the positive effect of FDI on trade has improved since the Belt and Road Initiative is proposed; (3) FDI promotes the exports of low technological sector, medium technological sector, and high technological sector, but the effect on medium technological sector is stronger than the other two sectors.

Basic reproduction number for the SIR epidemic in degree correlated networks

The basic reproduction number R0 is an important indicator of the severity for an epidemic outbreak, but it may not be obtained easily for heterogeneous populations especially with biased mixing contacts. Usually, explicit formula for the basic reproduction number in degree correlated networks is difficult to get, thus it is very useful to understand the relationship with their uncorrelated counterparts. It seems that the assortative mixing increases the basic reproduction number of susceptible–infected–recovered (SIR) epidemic, whereas disassortative mixing decreases it, or that assortative mixing enhances the percolation, whereas disassortative mixing weakens it. This result is obtained for degree correlated networks based on a small deviation from the uncorrelated networks, and may not be universal. In this paper, we show rigorously that the result is true for degree correlated networks with arbitrary bimodal degree distribution and for assortative mixing networks with arbitrary degree distribution. However, this may not be always true for general disassortative mixing networks. We also introduce a numerical algorithm to construct an arbitrary joint degree distribution and generate a counterexample of disassortative mixing network that the result fails. Finally, a sufficient condition is given to guarantee that the SIR model in disassortative mixing networks yields smaller R0.

Robustness Analysis of Flight Conflict Networks Based on Degree Correlation

Analyzing the composition and robustness of flight conflicts is beneficial to find the vulnerable sources of conflicts and dissipate flight conflicts, and effectively improve the safety and operational efficiency of air traffic. Therefore, this paper proposes a flight conflict network robustness evaluation method based on degree correlation. Firstly, a flight conflict network is constructed by using the velocity obstacle method, and it is classified into three types of assortative, disassortative and neutral conflict networks according to the degree correlation of the network. Several common robustness metrics in complex networks are explored, and a comprehensive robustness metric is proposed. The relationship between degree correlation and robustness of conflict networks under different node removal methods is analyzed by simulation experiments. The results show that the false alarm rate of the flight conflict network is decreased by 37.5% compared with the traditional state network. The degree correlation of the flight conflict network is closely related to the robustness. The assortative and disassortative conflict networks demonstrate stronger vulnerability with degree and betweenness removal, respectively, and the stronger the correlation the more obvious the vulnerability. The robustness of the neutral conflict network does not differ significantly under the two removal methods. Compared with random deletion, target removal can significantly decrease the network robustness.

Fuzzy Clustering in Assortative and Disassortative Networks

Despite the significance of assortativity as a property of networks that paves for the emergence of new structural types, surprisingly, there has been little research done on assortativity. Assortative networks are perhaps among the most prominent examples of complex networks believed to be governed by common phenomena, thereby producing structures far from random. Further, certain vertices possess high centrality and can be regarded as significant and influential vertices that can become cluster centers that connect with high membership to many of the surrounding vertices. We propose a fuzzy clustering method to meaningfully characterize assortative, as well as disassortative, networks by adapting the Bonacichi’s power centrality to seek the high degree centrality vertices to become cluster centers. Moreover, we leverage our novel modularity function to determine the optimal number of clusters, as well as the optimal membership among clusters. However, due to the difficulty of finding real-world assortative network datasets that come with ground truths, we evaluated our method using synthetic data but possibly bearing resemblance to real-world network datasets as they were generated by the Lancichinetti–Fortunato–Radicchi benchmark. Our results show our non-hierarchical method outperforms a known hierarchical fuzzy clustering method, and also performs better than a well-known membership-based modularity function. Our method proved to perform beyond satisfactory for both assortative and disassortative networks.

Supervised temporal link prediction in large-scale real-world networks

Link prediction is a well-studied technique for inferring the missing edges between two nodes in some static representation of a network. In modern day social networks, the timestamps associated with each link can be used to predict future links between so-far unconnected nodes. In these so-called temporal networks, we speak of temporal link prediction. This paper presents a systematic investigation of supervised temporal link prediction on 26 temporal, structurally diverse, real-world networks ranging from thousands to a million nodes and links. We analyse the relation between global structural properties of each network and the obtained temporal link prediction performance, employing a set of well-established topological features commonly used in the link prediction literature. We report on four contributions. First, using temporal information, an improvement of prediction performance is observed. Second, our experiments show that degree disassortative networks perform better in temporal link prediction than assortative networks. Third, we present a new approach to investigate the distinction between networks modelling discrete events and networks modelling persistent relations. Unlike earlier work, our approach utilises information on all past events in a systematic way, resulting in substantially higher link prediction performance. Fourth, we report on the influence of the temporal activity of the node or the edge on the link prediction performance, and show that the performance differs depending on the considered network type. In the studied information networks, temporal information on the node appears most important. The findings in this paper demonstrate how link prediction can effectively be improved in temporal networks, explicitly taking into account the type of connectivity modelled by the temporal edge. More generally, the findings contribute to a better understanding of the mechanisms behind the evolution of networks.

Connectivity and growth: Financial centres in investment banking networks

We investigate the effect of urban network connectivity on the growth of financial centres. While existing research recognises the importance of network connectivity to firms, clusters as well as city regions, large-sample empirical evidence is currently scarce, particularly in the context of financial services. We contribute to this debate by studying underwriting of equity and debt securities, which represent some of the core activities of financial centres. We operationalise our analysis using a proprietary dataset collated from Dealogic Equity Capital Market and Debt Capital Market databases covering over 1.7 million interactions of investment banks with issuers across 540 cities globally during the 1993–2016 period. We estimate our regression equations using the system generalised method of moments estimator, which allows us to obtain consistent coefficient estimates on potentially endogenous regressors, including network connectivity variables. We identify a clear pattern of a positive association between network centrality of financial centres and their growth. We distinguish between intracity and intercity network connectivity and find that financial centres with a larger number of intercity network ties and assortative intracity networks grow faster, while intracity network density does not appear to affect financial centre growth. Our results on intercity network ties are broadly consistent with established knowledge of cluster networks. In contrast, our findings on financial centres' intracity networks contradict previous research that suggests that dense and disassortative intracluster networks aid economic performance of clusters.

Herding in Open-end Funds: Evidence from China

This paper aims to detect the herding of Chinese open-end fund managers and examine the role that structural features of their industry play in their herding. The herding behaviour is investigated by employing the cross-sectional absolute deviation (CSAD) model, drawing on the Chinese open-end fund market for the 2007–2020 period.Our findings suggest that the presence of herding has been confirmed in all other types of funds except for income funds, with their herding being mainly driven by non-fundamental factors. Most types of funds show more pronounced herding when the market is rising and the fund flow is positive. Up markets foster positive fund flows, which promote herding to a certain extent. The structural characteristics of fund networks of common asset holdings produce an impact on the fund herding. Herding is observed in the network with larger centrality index and the disassortative network. Moreover, we also find that herding in most types of funds is more pronounced under conditions of high volatility and high economic policy uncertainty, and the fund herding tends to grow inversely with fund-size.

Experimental analyses on 2-hop-based and 3-hop-based link prediction algorithms

Link prediction is a significant and challenging task in network science. The majority of known methods are similarity-based, which assign similarity indices for node pairs and assume that two nodes of larger similarity have higher probability to be connected by a link. Due to their simplicity, interpretability and high efficiency, similarity-based methods, in particular those based only on local information, have found successful applications on disparate fields. An intuitive consensus is that two nodes sharing common neighbors are likely to have a link, while some recent evidences indicate that the number of 3-hop paths more accurately predicts missing links than the number of common neighbors. In this paper, we implement extensive experimental comparisons between 2-hop-based and 3-hop-based similarity indices on 137 real networks. Overall speaking, the class of Cannistraci–Hebb indices performs the best among all considered candidates. In addition, 3-hop-based indices outperform 2-hop-based indices on ROC-AUC, and 3-hop-based indices and 2-hop-based indices are competitive on precision. Further statistical results show that 3-hop-based indices are more suitable for disassortative networks with lower densities and lower average clustering coefficients.

Evolutionary compromise game on assortative mixing networks

Different from the cooperative game, in reality, heterogeneous individuals who choose to cooperate usually need to make a consistent strategic decision instead of directly entering the process of dividing payoffs. During the process of making consensus decisions, subjective psychology is a key factor affecting the final result, especially when individuals have similar abilities. Considering the subjective attitudes and objective abilities, this paper proposes a compromise game to model the dynamic change of subjective compromise value of individuals, which is a kind of psychological game. Here, the compromise value represented by parameter α is the strategy in game, which ranges from 0 to 1. And in terms of the continuous nature of compromise value α, we use particle swarm optimization to update strategies. Moreover, the subjective attitudes are profoundly affected by social surroundings, and thus we simulate this model on diverse assortative mixing networks by regulating the assortativity coefficient r. Simulations show that the compromise value of individuals gradually decreases as the assortativity of networks increases, and the compromise values of high-degree individuals are much higher than that of low-degree individuals in networks. Through the simulation results, we find that the subjective compromise of individual is greatly relevant with environment, which is important for the development of individuals. When meeting the individuals who have the similar ability, individuals from disassortative network tend to persist himself compared with individuals from assortative networks.