Problem In Network Science Research Articles

The conceptual model of the national blue economic system and its modeling principles: A supernetwork perspective

The national blue economic system is a complex system formed by the correlation of different agents, such as related blue industries, blue products, blue firms and blue provinces in a country. Its essence can be regarded as a complex system formed by the interconnection of a variety of heterogeneous networks. The supernetwork is an important method for studying such multilevel, multidimensional and multiagent correlation problems in network science. This method can effectively assess the intra- and interrelationships of each element entity. This paper incorporates the multielement entities in the national blue economic system into this multilayer network framework for systematic analysis and decomposes the development issue of the blue economy into the development issues of blue industries, blue products, blue firms and blue provinces. On this basis, this paper analyzes the conceptual model of the national blue economic system space, qualitatively describes the intra- and interexport relationships among multifactor entities in national blue economic development from the perspective of the multilayer network, and expounds the modeling principle of the national blue economic system space. This supernetwork approach provides effective new methods and tools for countries to study the development of the blue economy and formulate corresponding policies to achieve blue growth.

Directed Network Comparison Using Motifs.

Analyzing and characterizing the differences between networks is a fundamental and challenging problem in network science. Most previous network comparison methods that rely on topological properties have been restricted to measuring differences between two undirected networks. However, many networks, such as biological networks, social networks, and transportation networks, exhibit inherent directionality and higher-order attributes that should not be ignored when comparing networks. Therefore, we propose a motif-based directed network comparison method that captures local, global, and higher-order differences between two directed networks. Specifically, we first construct a motif distribution vector for each node, which captures the information of a node's involvement in different directed motifs. Then, the dissimilarity between two directed networks is defined on the basis of a matrix, which is composed of the motif distribution vector of every node and the Jensen-Shannon divergence. The performance of our method is evaluated via the comparison of six real directed networks with their null models, as well as their perturbed networks based on edge perturbation. Our method is superior to the state-of-the-art baselines and is robust with different parameter settings.

Identifying key players in complex networks via network entanglement

Empirical networks exhibit significant heterogeneity in node connections, resulting in a few vertices playing critical roles in various scenarios, including decision-making, viral marketing, and population immunization. Thus, identifying key vertices is a fundamental research problem in Network Science. In this paper, we introduce vertex entanglement (VE), an entanglement-based metric capable of quantifying the perturbations caused by individual vertices on spectral entropy, residing at the intersection of quantum information and network science. Our analytical analysis reveals that VE is closely related to network robustness and information transmission ability. As an application, VE offers an approach to the challenging problem of optimal network dismantling, and empirical experiments demonstrate its superiority over state-of-the-art algorithms. Furthermore, VE also contributes to the diagnosis of autism spectrum disorder (ASD), with significant distinctions in hub disruption indices based on VE between ASD and typical controls, promising a diagnostic role for VE in ASD assessment.

Reconstructing networks via discrete state dynamical data: A mini-review

The inference of network structure from dynamic data is one of the most challenging scientific problems in network science. To address this issue, researchers have proposed various approaches regarding different types of dynamical data. Since many real evolution processes or social phenomena can be described by discrete state dynamical systems, such as the spreading of epidemic, the evolution of opinions, and the cooperation behaviors, network reconstruction methods driven by discrete state dynamical data were also widely studied. In this letter, we provide a mini-review of recent progresses for reconstructing networks based on discrete state dynamical data. These studies encompass network reconstruction problems where the dynamical processes are known, as well as those where the dynamics are unknown, and extend to the reconstruction of higher-order networks. Finally, we discuss the remaining challenges in this field.

Statistical structural inference from edge weights using a mixture of gamma distributions

Abstract The inference of reliable and meaningful connectivity information from weights representing the affinity between nodes in a graph is an outstanding problem in network science. Usually, this is achieved by simply thresholding the edge weights to distinguish true links from false ones and to obtain a sparse set of connections. Tools developed in statistical mechanics have provided particularly effective ways to locate the optimal threshold so as to preserve the statistical properties of the network structure. Thermodynamic analogies together with statistical mechanical ensembles have been proven to be useful in analysing edge-weighted networks. To extend this work, in this article, we use a statistical mechanical model to describe the probability distribution for edge weights. This models the distribution of edge weights using a mixture of Gamma distributions. Using a two-component Gamma mixture model with components describing the edge and non-edge weight distributions, we use the Expectation–Maximization algorithm to estimate the corresponding Gamma distribution parameters and mixing proportions. This gives the optimal threshold to convert weighted networks to sets of binary-valued connections. Numerical analysis shows that it provides a new way to describe the edge weight probability. Furthermore, using a physical analogy in which the weights are the energies of molecules in a solid, the probability density function for nodes is identical to the degree distribution resulting from a uniform weight on edges. This provides an alternative way to study the degree distribution with the nodal probability function in unweighted networks. We observe a phase transition in the low-temperature region, corresponding to a structural transition caused by applying the threshold. Experimental results on real-world weighted and unweighted networks reveal an improved performance for inferring binary edge connections from edge weights.

New algorithms for a simple measure of network partitioning

Partitioning a network into k pieces is a fundamental problem in network science. A simple measure of partitioning a network is provided by the Maxk-Uncut problem. Given an n-vertex undirected graph G with nonnegative weights defined on edges, and a positive integer k, the Maxk-Uncut problem asks to find a k-partition of the vertices of G to maximize the total weight of edges that are not in the cut. This problem is the complement of the classic Mink-Cut problem, and has close relation to many combinatorial optimization problems, including the famous Densestk-Subgraph problem. In this paper, we propose a greedy approximation algorithm for the Maxk-Uncut problem with performance ratio 1−2(k−1)n. The algorithm is very simple, which consists of only k−1 min cut computations. The algorithm has fast running time O(kn2) and is hence implementable. The experimental results show that the algorithm has excellent practical performance.

Generalized network dismantling via a novel spectral partition algorithm

Network dismantling problem aims to find a node subset whose removal from a network results in the fragmentation of the network into subcritical connected components at the minimal overall cost. People have always been more interested in the unweighted case where each node has the same cost, while there are few results for the weighted case when nodes have different costs. It is a much more challenging problem in network science. In this paper, we present a novel strategy for this generalized network dismantling problem by characterizing the relationship between blocks and cut nodes. We firstly construct an auxiliary block-cut tree T from the original network G, where the nodes in the tree T have two types which correspond to either blocks or cut nodes of G, and edges of T only exist between two different type of nodes. Then we transform the problem of partitioning G by removing nodes to the problem of partitioning T by removing edges, both at a minimum overall cost. Finally partitioning T can be solved by a weighted spectral clustering algorithm. When we apply this new strategy on real-world networks, it performs equally or even better than the current state-of-the-art methods.

Discriminating abilities of threshold-free evaluation metrics in link prediction

Link prediction is a paradigmatic and challenging problem in network science, which attempts to uncover missing links or predict future links, based on known topology. A fundamental but still unsolved issue is how to choose proper metrics to fairly evaluate prediction algorithms. The area under the receiver operating characteristic curve (AUC) and the balanced precision (BP) are the two most popular metrics in early studies, while their effectiveness is recently under debate. At the same time, the area under the precision–recall curve (AUPR) becomes increasingly popular, especially in biological studies. Based on a toy model with tunable noise and predictability, we propose a method to measure the discriminating ability of any given metric. We apply this method to the above three threshold-free metrics, showing that AUC and AUPR are remarkably more discriminating than BP, and AUC is slightly more discriminating than AUPR. The result suggests that it is better to simultaneously use AUC and AUPR in evaluating link prediction algorithms. At the same time, it warns us that the evaluation based only on BP may be unauthentic. This article provides a starting point towards a comprehensive picture about effectiveness of evaluation metrics for link prediction.

Link prediction in multiplex networks using intralayer probabilistic distance and interlayer co-evolving factors

Multiplex networks are very flexible at showing heterogeneous relationships between identical entities. Link prediction is a fundamental problem in network science. There are many studies on link prediction in complex networks, but few studies were conducted on link prediction in multiplex networks. This study proposes a method for estimating link likelihood in multiplex networks based on the Node-Accessibility-Distribution (NAD) and the co-evolving factors of layers. The NAD is introduced as a probabilistic measure to find local and pseudo-global structural features of nodes in layers of the multiplex network. The probabilistic distance among nodes is calculated using Jensen–Shannon diversity. Since the evolution of one layer subsequently affects the dynamics of other layers, this study introduces the co-evolving factors as criteria for determining the effect of the evolution of layers in the formation of new links in the target layer. In order to estimate the co-evolving factors, logistics regression and Maximum Likelihood Estimation(MLE) are employed. The proposed method is evaluated with six real-world datasets. The results show that the proposed approach has a better average AUC and precision than the state-of-the-art methods. Based on various datasets, the AUC and precision were improved by 1% to 5% compared with the state-of-the-art.

Valid inequalities and facets for multi‐module survivable network design problem

AbstractCapacitated survivable network design (SND), that is, designing a network that can survive edge failures with minimum flow‐routing plus capacity‐installation cost, is a fundamental problem in network science and its applications. In this article, we study a highly applicable form of the SND, referred to as the multi‐module SND (MM‐SND), in which transmission capacities on edges can be sum of integer multiples of differently sized capacity modules. We formulate MM‐SND as mixed integer programs, where existing structures of the network (p‐cycles) are used to protect edge failures. We derive valid inequalities for MM‐SND through polyhedral analysis and show that the valid inequalities previously developed in the literature for the single‐module SND are special cases of these inequalities. Furthermore, we show that these inequalities define facets for the convex hull of MM‐SND in many cases. Our computational results show that these inequalities are very effective in solving MM‐SND problem instances.

Quantification of network structural dissimilarities based on network embedding

SummaryQuantifying structural dissimilarities between networks is a fundamental and challenging problem in network science. Previous network comparison methods are based on the structural features, such as the length of shortest path and degree, which only contain part of the topological information. Therefore, we propose an efficient network comparison method based on network embedding, which considers the global structural information. In detail, we first construct a distance matrix for each network based on the distances between node embedding vectors derived from DeepWalk. Then, we define the dissimilarity between two networks based on Jensen-Shannon divergence of the distance distributions. Experiments on both synthetic and empirical networks show that our method outperforms the baseline methods and can distinguish networks well. In addition, we show that our method can capture network properties, e.g., average shortest path length and link density. Moreover, the experiment of modularity further implies the functionality of our method.

Community detection through vector-label propagation algorithms

Community detection is a fundamental and important problem in network science, as community structures often reveal both topological and functional relationships between different components of the complex system. In this paper, we first propose a gradient descent framework of modularity optimization called vector-label propagation algorithm (VLPA), where a node is associated with a vector of continuous community labels instead of one label. Retaining weak structural information in vector-label, VLPA outperforms some well-known community detection methods, and particularly improves the performance in networks with weak community structures. Further, we incorporate stochastic gradient strategies into VLPA to avoid stuck in the local optima, leading to the stochastic vector-label propagation algorithm (sVLPA). We show that sVLPA performs better than Louvain Method, a widely used community detection algorithm, on both artificial benchmarks and real-world networks. Our theoretical scheme based on vector-label propagation can be directly applied to high-dimensional networks where each node has multiple features, and can also be used for optimizing other partition measures such as modularity with resolution parameters.

Inferring the size of a collective of self-propelled Vicsek particles from the random motion of a single unit

Inferring the size of a collective from the motion of a few accessible units is a fundamental problem in network science and interdisciplinary physics. Here, we recognize stochasticity as the commodity traded in the units’ interactions. Drawing inspiration from the work of Einstein-Perrin-Smoluchowski on the discontinuous structure of matter, we use the random motion of one unit to identify the footprint of every other unit. Just as the Avogadro’s number can be determined from the Brownian motion of a suspended particle in a liquid, the size of the collective can be inferred from the random motion of any unit. For self-propelled Vicsek particles, we demonstrate an inverse proportionality between the diffusion coefficient of the heading of any particle and the size of the collective. We provide a rigorous method to infer the size of a collective from measurements of a few units, strengthening the link between physics and collective behavior.

Overlapping community detection in networks based on Neutrosophic theory

Discovering community structure is one of the most intensively studied problems in network science. Many real networks are composed of nodes belonging to multiple communities. In this manuscript, a new overlapping community detection algorithm is proposed based on neutrosophic set (NS) theory. The proposed community detection method manages uncertainty arisen from imprecise definition of communities, by handling boundary and outlier nodes. In the first step, the proposed algorithm calculates the dissimilarity index between each pair of nodes in the network. Then, in order to keep the original distance between nodes as much as possible, the network structure is mapped into a low-dimensional space by multidimensional scaling. Finally, the neutrosophic c-means algorithm is employed to find communities in the network. The experimental results show that the proposed algorithm can detect communities on real and artificial datasets effectively and accurately.

Mean-field theory of vector spin models on networks with arbitrary degree distributions

Understanding the relationship between the heterogeneous structure of complex networks and cooperative phenomena occurring on them remains a key problem in network science. Mean-field theories of spin models on networks constitute a fundamental tool to tackle this problem and a cornerstone of statistical physics, with an impressive number of applications in condensed matter, biology, and computer science. In this work we derive the mean-field equations for the equilibrium behavior of vector spin models on high-connectivity random networks with an arbitrary degree distribution and with randomly weighted links. We demonstrate that the high-connectivity limit of spin models on networks is not universal in that it depends on the full degree distribution. Such nonuniversal behavior is akin to a remarkable mechanism that leads to the breakdown of the central limit theorem when applied to the distribution of effective local fields. Traditional mean-field theories on fully-connected models, such as the Curie–Weiss, the Kuramoto, and the Sherrington–Kirkpatrick model, are only valid if the network degree distribution is highly concentrated around its mean degree. We obtain a series of results that highlight the importance of degree fluctuations to the phase diagram of mean-field spin models by focusing on the Kuramoto model of synchronization and on the Sherrington–Kirkpatrick model of spin-glasses. Numerical simulations corroborate our theoretical findings and provide compelling evidence that the present mean-field theory describes an intermediate regime of connectivity, in which the average degree c scales as a power c ∝ N b (b < 1) of the total number N ≫ 1 of spins. Our findings put forward a novel class of spin models that incorporate the effects of degree fluctuations and, at the same time, are amenable to exact analytic solutions.

Quantifying dissimilarities between heterogeneous networks with community structure

Quantifying dissimilarities between networks is a fundamental and challenging problem in network science. Current metrics for network comparison either assume the homogeneous distribution of nodal degrees or ignore the community structure of the network. Here we propose an efficient measure for comparing heterogeneous networks with communities from the perspective of probability distribution functions, which incorporates the nodal distance distribution, the clustering coefficient distribution and the alpha centrality distribution. Comparison between community benchmarks shows that the proposed measure returns non-zero values only when the networks are non-isomorphic.

Parameter and topology identification of delayed hypernetworks with stochastic perturbation

In the past two decades, large interconnected systems have been modeled as single-layer networks. In fact, various networks may interact and influence with each other to form the hypernetworks. As one of the most important problems in network science, topology identification of complex network has been widely studied in single-layer networks. On the contrary, topology identification of hypernetwork has received little attention. For a hypernetwork, different layers may have different delay, and noise is usually unavoidable. Therefore, the delayed hypernetwork with stochastic perturbation is put forward in this manuscript. By using synchronization-based identification method, the schemes to identify the unknown topology and system parameters are proposed. It is found that the unknown topology and system parameters of the drive network can be correctly identified, regardless of whether the topology of the response network is the same as that of the drive network. Numerical examples are illustrated to verify the effectiveness of the proposed algorithm. In addition, it is found that the identification time increases with the varying interval of coupling strengths, and the interval of the time delays and stochastic perturbations have opposite effects on the identification time.

A modified label propagation algorithm for community detection in attributed networks

Community detection is an important problem in network science that discovers highly clustered groups of nodes having similar properties. Label propagation algorithm (LPA) is one of the popular clustering techniques that has attracted much attention due to its efficiency and non-dependence on parameters. Despite its advantages, an important limitation of LPA is the randomness in grouping nodes that leads to instability and the formation of large communities. In this study, we propose four variants based on LPA to overcome the random community allocation problem, henceforth generating better clusters. These variants utilize link strength and node attribute information to enhance the quality of detected communities. Furthermore, the proposed variants require no parameter for categorical attributes and only one parameter (constant for all the networks) for continuous attributes. Finally, the best results are obtained by Variant I having a maximum Normalized Mutual Information score of 0.86, 0.88 on the two synthetic networks.

Netrd: A library for network reconstruction and graph distances

Over the last two decades, alongside the increased availability of large network datasets, we have witnessed the rapid rise of network science. For many systems, however, the data we have access to is not a direct description of the underlying network. More and more, we see the drive to study networks that have been inferred or reconstructed from non-network data---in particular, using time series data from the nodes in a system to infer likely connections between them. Selecting the most appropriate technique for this task is a challenging problem in network science. Different reconstruction techniques usually have different assumptions, and their performance varies from system to system in the real world. One way around this problem could be to use several different reconstruction techniques and compare the resulting networks. However, network comparison is also not an easy problem, as it is not obvious how best to quantify the differences between two networks, in part because of the diversity of tools for doing so. The netrd Python package seeks to address these two parallel problems in network science by providing, to our knowledge, the most extensive collection of both network reconstruction techniques and network comparison techniques (often referred to as graph distances) in a single library (https://github.com/netsiphd/netrd). In this article, we detail the two main functionalities of the netrd package. Along the way, we describe some of its other useful features. This package builds on commonly used Python packages and is already a widely used resource for network scientists and other multidisciplinary researchers. With ongoing open-source development, we see this as a tool that will continue to be used by all sorts of researchers to come.

Unsupervised learning for community detection in attributed networks based on graph convolutional network

Community detection has emerged during the last decade as one of the most challenging problems in network science, which has been revisited with network representation learning recently and has attracted considerable attention. Many approaches have been proposed in recent years, including the latest methods based on graph convolutional network (GCN). Here, we propose a new network representation learning method based on GCN for community detection in attributed networks without prior label information. Inspired by the message pass mechanism of GCN and the local self-organizing property of community structure, we integrate a label sampling model and GCN into an unsupervised learning framework to uncover underlying community structures by fusing topology and attribute information. The label sampling model constructs a balanced training set by structural center location and neighbor node expansion to train the GCN. The experiments on various real-world networks give a comparison view to evaluate the proposed method. The experimental results demonstrate the proposed method performs more efficiently with a comparative performance over current state-of-the-art community detection algorithms.