Link Overlap Research Articles

Hyper-diffusion on multiplex networks

Multiplex networks describe systems whose interactions can be of different nature, and are fundamental to understand complexity of networks beyond the framework of simple graphs. Recently it has been pointed out that restricting the attention to pairwise interactions is also a limitation, as the vast majority of complex systems include higher-order interactions that strongly affect their dynamics. Here, we propose hyper-diffusion on multiplex networks, a dynamical process in which diffusion on each single layer is coupled with the diffusion in other layers thanks to the presence of higher-order interactions occurring when there exists link overlap. We show that hyper-diffusion on a duplex network (a multiplex network with two layers) can be described by the hyper-Laplacian in which the strength of four-body interactions among every set of four replica nodes connected in both layers can be tuned by a parameter δ 11 ⩾ 0. The hyper-Laplacian reduces to the standard lower Laplacian, capturing pairwise interactions at the two layers, when δ 11 = 0. By combining tools of spectral graph theory, applied topology and network science we provide a general understanding of hyper-diffusion on duplex networks when δ 11 > 0, including theoretical bounds on the Fiedler and the largest eigenvalue of hyper-Laplacians and the asymptotic expansion of their spectrum for δ 11 ≪ 1 and δ 11 ≫ 1. Although hyper-diffusion on multiplex networks does not imply a direct ‘transfer of mass’ among the layers (i.e. the average state of replica nodes in each layer is a conserved quantity of the dynamics), we find that the dynamics of the two layers is coupled as the relaxation to the steady state becomes synchronous when higher-order interactions are taken into account and the Fiedler eigenvalue of the hyper-Laplacian is not localized in a single layer of the duplex network.

Link overlap influences opinion dynamics on multiplex networks of Ashkin-Teller spins.

Consider a multiplex network formed by two layers indicating social interactions: the first layer is a friendship network and the second layer is a network of business relations. In this duplex network each pair of individuals can be connected in different ways: they can be connected by a friendship but not connected by a business relation, they can be connected by a business relation without being friends, or they can be simultaneously friends and in a business relation. In the latter case we say that the links in different layers overlap. These three types of connections are called multilinks and the multidegree indicates the sum of multilinks of a given type that are incident to a given node. Previous opinion models on multilayer networks have mostly neglected the effect of link overlap. Here we show that link overlap can have important effects in the formation of a majority opinion. Indeed, the formation of a majority opinion can be significantly influenced by the statistical properties of multilinks, and in particular by the multidegree distribution. To quantitatively address this problem, we study a simple spin model, called the Ashkin-Teller model, including two-body and four-body interactions between nodes in different layers. Here we fully investigate the rich phase diagram of this model which includes a large variety of phase transitions. Indeed, the phase diagram or the model displays continuous, discontinuous, and hybrid phase transitions, and successive jumps of the order parameters within the Baxter phase.

Impacts of social distancing on the spread of infectious diseases with asymptomatic infection: A mathematical model

Social distancing can be divided into two categories: spontaneous social distancing adopted by the individuals themselves, and public social distancing promoted by the government. Both types of social distancing have been proved to suppress the spread of infectious disease effectively. While previous studies examined the impact of each social distancing separately, the simultaneous impacts of them are less studied. In this research, we develop a mathematical model to analyze how spontaneous social distancing and public social distancing simultaneously affect the outbreak threshold of an infectious disease with asymptomatic infection. A communication-contact two-layer network is constructed to consider the difference between spontaneous social distancing and public social distancing. Based on link overlap of the two layers, the two-layer network is divided into three subnetworks: communication-only network, contact-only network, and overlapped network. Our results show that public social distancing can significantly increase the outbreak threshold of an infectious disease. To achieve better control effect, the subnetwork of higher infection risk should be more targeted by public social distancing, but the subnetworks of lower infection risk shouldn’t be overlooked. The impact of spontaneous social distancing is relatively weak. On the one hand, spontaneous social distancing in the communication-only network has no impact on the outbreak threshold of the infectious disease. On the other hand, the impact of spontaneous social distancing in the overlapped network is highly dependent on the detection of asymptomatic infection sources. Moreover, public social distancing collaborates with infection detection on controlling an infectious disease, but their impacts can’t add up perfectly. Besides, public social distancing is slightly less effective than infection detection, because infection detection can also promote spontaneous social distancing.

Overlapping communities and the prediction of missing links in multiplex networks

Multiplex networks are a representation of real-world complex systems as a set of entities (i.e. nodes) connected via different types of connections (i.e. layers). The observed connections in these networks may not be complete and the link prediction task is about locating the missing links across layers. Here, the main challenge is about collecting relevant evidence from different layers to assist the link prediction task.It is known that co-membership in communities increases the likelihood of connectivity between nodes. We discuss that co-membership in the communities of the similar layers augments the chance of connectivity. The layers are considered similar if they show significant inter-layer community overlap. Moreover, we found that although the presence of link is correlated in layers but the extent of this correlation is not the same across different communities. Our proposed, ML-BNMTF, as a link prediction method in multiplex networks, is devised based on these findings. ML-BNMTF outperforms baseline methods specifically when the global link overlap is low.

A novel genetic algorithm-based improvement model for online communities and trust networks

Social network analysis offers an understanding of our modern world, and it affords the ability to represent, analyze and even simulate complex structures. While an unweighted model can be used for online communities, trust or friendship networks should be analyzed with weighted models. To analyze social networks, it is essential to produce realistic social models. However, there are serious differences between social network models and real-life data in terms of their fundamental statistical parameters. In this paper, a genetic algorithm (GA)-based social network improvement method is proposed to produce social networks more similar to real-life data sets. First, it creates a social model based on existing studies in the literature, and then it improves the model with the proposed GA-based approach based on the similarity of the average degree, the k-nearest neighbor, the clustering coefficient, degree distribution and link overlap. This study can be used to model the structural and statistical properties of large-scale societies more realistically. The performance results show that our approach can reduce the dissimilarity between the created social networks and the real-life data sets in terms of their primary statistical properties. It has been shown that the proposed GA-based approach can be used effectively not only in unweighted networks but also in weighted networks.

Tensor-based mathematical framework and new centralities for temporal multilayer networks

Although networks provide a powerful methodology to study a variety of real-world and engineered systems, their current formulation does not typically account for multiple interaction types that vary in space and time, or address interconnected systems such as networks of networks. Unavoidably, ignoring time-dependence and multiple interactions of topological structures might lead to important temporal and structural information loss and may obscure the actual organization. To achieve a deep understanding of the time-varying and interconnected complex networked systems, in this paper, we develop a more general mathematical model, referred to as a temporal multilayer network, which explicitly incorporates time-dependence and multiple relationships of topological structures into a system, and provides a natural and reasonable description for real-world complex systems. Furthermore, using a fifth-order tensorial framework to represent temporal multilayer networks, we generalize four important topological metrics, including overlapping degree, entropy, degree correlation and link overlap, to quantitatively evaluate the temporal multilayer networks. In particular, based on the tensorial framework, we propose two iterative refinement centralities for temporal multilayer networks, referred to as TM-eigenvector and TM-PageRank centralities, which are used to quantitatively evaluate the importance of nodes in real-world complex systems. Moreover, we use the theory of multilinear algebra and matrix analysis to strictly prove the convergence of these iterative algorithms. The proposed mathematical frameworks are validated using two real-world temporal multilayer networked systems related to complex diseases, i.e., influenza and heart diseases.

Large deviation theory of percolation on multiplex networks

Recently, increasing attention has been paid to the fluctuations observed in percolation defined in single and multiplex networks. These fluctuations are extremely important to characterize the robustness of real finite networks but cannot be captured by the traditionally adopted mean-field theory of percolation. Here we propose a theoretical framework and a message passing algorithm that is able to fully capture the large deviation of percolation in interdependent multiplex networks with a locally tree-like structure. This framework is here applied to study the robustness of single instance multiplex networks and compared to the results obtained using extensive simulations of the initial damage. For simplicity the method is here developed for interdependent multiplex networks without link overlap, however it can be generalized to treat multiplex networks with link overlap.

A colored mean-field model for analyzing the effects of awareness on epidemic spreading in multiplex networks.

We study the impact of susceptible nodes' awareness on epidemic spreading in social systems, where the systems are modeled as multiplex networks coupled with an information layer and a contact layer. We develop a colored heterogeneous mean-field model taking into account the portion of the overlapping neighbors in the two layers. With theoretical analysis and numerical simulations, we derive the epidemic threshold which determines whether the epidemic can prevail in the population and find that the impacts of awareness on threshold value only depend on epidemic information being available in network nodes' overlapping neighborhood. When there is no link overlap between the two network layers, the awareness cannot help one to raise the epidemic threshold. Such an observation is different from that in a single-layer network, where the existence of awareness almost always helps.

Pair quenched mean-field approach to epidemic spreading in multiplex networks

• A pair-quenched mean-field approach to epidemic spreading on multiplex networks is developed. • The condition for the epidemic threshold in a static multiplex network is derived. • Gillespie algorithm-based simulations staged on various multilayered network topologies were conducted. • Theoretical results are in agreement with numerical simulations on 2-layer and 3-layer complex networks. • Our findings highlight the efficiency of the presented approach for assessing epidemic thresholds in multiplex networks. Using the law of total probability, we extend the pair quenched mean-field approach for epidemic spreading in monoplex networks to the scenario of contagion outbreaks in multiplex networks. By means of the quasi-static approximation, we derive the condition for the epidemic threshold in a static multiplex network overlapped by the randomly connected subnetwork without clustering. Our theoretical results are in good agreement with continuous-time Gillespie algorithm-based simulations for 2-layer and 3-layer multiplex networks, revealing the advantage of our model in the prediction of epidemic spreading relative to the quenched mean-field (QMF) approach. Importantly, our study demonstrates that unlike the standard QMF approach, the pair QMF model can be used to assess the influence of the link overlap on the epidemic threshold, thereby carrying vital implications for future epidemiological research and policy development.

Opinion formation on multiplex scale-free networks

Most individuals, if not all, live in various social networks. The formation of opinion systems is an outcome of social interactions and information propagation occurring in such networks. We study the opinion formation with a new rule of pairwise interactions in the novel version of the well-known Deffuant model on multiplex networks composed of two layers, each of which is a scale-free network. It is found that in a duplex network composed of two identical layers, the presence of the multiplexity helps either diminish or enhance opinion diversity depending on the relative magnitudes of tolerance ranges characterizing the degree of openness/tolerance on both layers: there is a steady separation between different regions of tolerance range values on two network layers where multiplexity plays two different roles, respectively. Additionally, the two critical tolerance ranges follow a one-sum rule; that is, each of the layers reaches a complete consensus only if the sum of the tolerance ranges on the two layers is greater than a constant approximately equaling 1, the double of the critical bound on a corresponding isolated network. A further investigation of the coupling between constituent layers quantified by a link overlap parameter reveals that as the layers are loosely coupled, the two opinion systems co-evolve independently, but when the inter-layer coupling is sufficiently strong, a monotonic behavior is observed: an increase in the tolerance range of a layer causes a decline in the opinion diversity on the other layer regardless of the magnitudes of tolerance ranges associated with the layers in question.

Message passing theory for percolation models on multiplex networks with link overlap.

Multiplex networks describe a large variety of complex systems, including infrastructures, transportation networks, and biological systems. Most of these networks feature a significant link overlap. It is therefore of particular importance to characterize the mutually connected giant component in these networks. Here we provide a message passing theory for characterizing the percolation transition in multiplex networks with link overlap and an arbitrary number of layers M. Specifically we propose and compare two message passing algorithms that generalize the algorithm widely used to study the percolation transition in multiplex networks without link overlap. The first algorithm describes a directed percolation transition and admits an epidemic spreading interpretation. The second algorithm describes the emergence of the mutually connected giant component, that is the percolation transition, but does not preserve the epidemic spreading interpretation. We obtain the phase diagrams for the percolation and directed percolation transition in simple representative cases. We demonstrate that for the same multiplex network structure, in which the directed percolation transition has nontrivial tricritical points, the percolation transition has a discontinuous phase transition, with the exception of the trivial case in which all the layers completely overlap.

Composite operators in cubic field theories and link-overlap fluctuations in spin-glass models

We present a complete characterization of the fluctuations and correlations of the squared overlap in the Edwards-Anderson Spin-Glass model in zero field. The analysis reveals that the energy-energy correlations (and thus the specific heat) have a different critical behavior than the fluctuations of the link overlap in spite of the fact that the average energy and average link overlap have the same critical properties. More precisely the link-overlap fluctuations are larger than the specific heat according to a computation at first order in the $6-\epsilon$ expansion. An unexpected outcome is that the link-overlap fluctuations have a subdominant power-law contribution characterized by an anomalous logarithmic prefactor which is missing in the specific heat. In order to compute the $\epsilon$ expansion we consider the problem of the renormalization of quadratic composite operators in a generic multicomponent cubic field theory: the results obtained have a range of applicability beyond spin-glass theory.

Link overlap, viability, and mutual percolation in multiplex networks

Many real-world complex systems are best modeled by multiplex networks. The multiplexity has proved to have broad impact on the system’s structure and function. Most theoretical studies on multiplex networks to date, however, have largely ignored the effect of the link overlap across layers despite strong empirical evidences for its significance. In this article, we investigate the effect of the link overlap in the viability of multiplex networks, both analytically and numerically. After a short recap of the original multiplex viability study, the distinctive role of overlapping links in viability and mutual connectivity is emphasized and exploited for setting up a proper analytic framework. A rich phase diagram for viability is obtained and greatly diversified patterns of hysteretic behavior in viability are observed in the presence of link overlap. Mutual percolation with link overlap is revisited as a limit of multiplex viability problem, and the controversy between existing results is clarified. The distinctive role of overlapping links is further demonstrated by the different responses of networks under random removals of overlapping and non-overlapping links, respectively, as well as under several link-removal strategies. Our results show that the link overlap facilitates the viability and mutual percolation; at the same time, the presence of link overlap poses a challenge in analytical approaches to the problem.

Ising ferromagnet in dimension five: Link and spin overlaps

In the simple [hyper]cubic five-dimension, near-neighbor-interaction Ising ferromagnet, extensive simulation measurements are made of the link overlap and the spin overlap distributions. These "two replica" measurements are standard in the spin glass context but are not usually recorded in ferromagnet simulations. The moments and moment ratios of these distributions (the variance, the kurtosis, and the skewness) show clear critical behaviors at the known ordering temperature of the ferromagnet. Analogous overlap effects can be expected quite generally in Ising ferromagnets in any dimension. The link overlap results in particular, with peaks at criticality in the kurtosis and the skewness, also have implications for spin glasses.

SOCIAL DYNAMICS IN A LARGE-SCALE ONLINE GAME

Complex systems — when treated as systems accessible to natural sciences — pose tremendous requirements on data. Usually these requirements obstruct a scientific understanding of social phenomena on scientific grounds. Due to developments in IT, new collective human behavior, new dimensions of data sources are beginning to open up. Here we report on a complete data set of an entire society, consisting of over 350,000 human players of a massive multiplayer online game. All actions of all players over three years are recorded, including communication behavior and social ties. In this work we review the first steps undertaken in analyzing this vast data set, focusing on social dynamics on friend-, enemy- and communication networks. This new data-driven approach to social science allows to study socio-economic behavior of humans and human groups in specific environments with unprecedented precision. We propose two new empirical social laws which relate the network properties of link weight, overlap and betweenness centrality in a nonlinear way, and provide strong quantitative evidence for classical social balance assumptions, the weak ties hypothesis and triadic closure. In our analysis of large-scale multirelational networks we discover systematic deviations between positive and negative tie networks. Exploring such virtual "social laboratories" in the light of complexity science has the potential to lead to the discovery of systemic properties of human societies, with unforeseen impact on managing human-induced crises.

Nontrivial link overlap distribution in three-dimensional Ising spin glasses

We investigate the distributions of the link overlap, $P(Q)$, in three-dimensional Ising spin glasses. We use clustering methodology to identify a set of pairs of states from different Gibbs states and calculate its contribution to $P(Q)$. We find that the distribution over this set does not become trivial as the system size increases.

Analysis of a large-scale weighted network of one-to-one human communication

We construct a connected network of 3.9 million nodes from mobile phone call records, which can be regarded as a proxy for the underlying human communication network at the societal level. We assign two weights on each edge to reflect the strength of social interaction, which are the aggregate call duration and the cumulative number of calls placed between the individuals over a period of 18 weeks. We present a detailed analysis of this weighted network by examining its degree, strength, and weight distributions, as well as its topological assortativity and weighted assortativity, clustering and weighted clustering, together with correlations between these quantities. We give an account of motif intensity and coherence distributions and compare them to a randomized reference system. We also use the concept of link overlap to measure the number of common neighbours any two adjacent nodes have, which serves as a useful local measure for identifying the interconnectedness of communities. We report a positive correlation between the overlap and weight of a link, thus providing strong quantitative evidence for the weak ties hypothesis, a central concept in social network analysis. The percolation properties of the network are found to depend on the type and order of removed links, and they can help understand how the local structure of the network manifests itself at the global level. We hope that our results will contribute to modelling weighted large-scale social networks, and believe that the systematic approach followed here can be adopted to study other weighted networks.

Overlap Equivalence in the Edwards-Anderson Model

We study the relative fluctuations of the link overlap and the square standard overlap in the three-dimensional Gaussian Edwards-Anderson model with zero external field. We first analyze the correlation coefficient and find that the two quantities are uncorrelated above the critical temperature. Below the critical temperature we find that the link overlap has vanishing fluctuations for fixed values of the square standard overlap and large volumes. Our data show that the conditional variance scales to zero in the thermodynamic limit. This implies that, if one of the two random variables tends to a trivial one (i.e., deltalike distributed), then the other does also, and as a consequence, the "trivial-nontrivial" picture should be dismissed. Our results show that the two overlaps are completely equivalent in the description of the low temperature phase of the Edwards-Anderson model.

Effects of changing the boundary conditions on the ground state of Ising spin glasses

We compute and analyze couples of ground states of 3D spin glass systems with the same quenched noise but periodic and anti-periodic boundary conditions for different lattice sizes. We discuss the possible different behaviors of the system, we analyze the average link overlap, the probability distribution of window overlaps (among ground states computed with different boundary conditions) and the spatial overlap and link overlap correlation functions. We establish that the picture based on Replica Symmetry Breaking correctly describes the behavior of 3D Spin Glasses.

Influence of critical behavior on the spin-glass phase

We have argued in recent papers that Monte Carlo results for the equilibrium properties of the Edwards-Anderson spin glass in three dimensions, which had been interpreted earlier as providing evidence for replica symmetry breaking, can be explained quite simply within the droplet model once finite size effects and proximity to the critical point are taken into account. In this paper, we show that similar considerations are sufficient to explain the Monte Carlo data in four dimensions. In particular, we study the Parisi overlap and the link overlap for the four-dimensional Ising spin glass in the Migdal-Kadanoff approximation. Similar to what is seen in three dimensions, we find that temperatures well below those studied in Monte Carlo simulations have to be reached before the droplet model predictions become apparent. We also show that the double-peak structure of the link overlap distribution function is related to the difference between domain-wall excitations that cross the entire system and droplet excitations that are confined to a smaller region.