scholarly journals An Asymmetric Popularity-Similarity Optimization Method for Embedding Directed Networks into Hyperbolic Space

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-16 ◽  
Author(s):  
Zongning Wu ◽  
Zengru Di ◽  
Ying Fan
Keyword(s):  
Complex Networks ◽  
Hyperbolic Space ◽  
Optimization Method ◽  
Directed Network ◽  
Network Embedding ◽  
Directed Networks ◽  
Scale Free ◽  
Exponential Expansion ◽  
Asymmetric Networks ◽  
Symmetric Networks

Network embedding is a frontier topic in current network science. The scale-free property of complex networks can emerge as a consequence of the exponential expansion of hyperbolic space. Some embedding models have recently been developed to explore hyperbolic geometric properties of complex networks—in particular, symmetric networks. Here, we propose a model for embedding directed networks into hyperbolic space. In accordance with the bipartite structure of directed networks and multiplex node information, the method replays the generation law of asymmetric networks in hyperbolic space, estimating the hyperbolic coordinates of each node in a directed network by the asymmetric popularity-similarity optimization method in the model. Additionally, the experiments in several real networks show that our embedding algorithm has stability and that the model enlarges the application scope of existing methods.

scholarly journals Eigenvalue-based entropy in directed complex networks

PLoS ONE ◽  
2021 ◽  
Vol 16 (6) ◽  
pp. e0251993
Author(s):  
Yan Sun ◽  
Haixing Zhao ◽  
Jing Liang ◽  
Xiujuan Ma
Keyword(s):  
Complex Networks ◽  
Complex Network ◽  
Network Models ◽  
Small World ◽  
Laplacian Matrix ◽  
Directed Network ◽  
Small World Network ◽  
Scale Free Network ◽  
Scale Free ◽  
Free Network

Entropy is an important index for describing the structure, function, and evolution of network. The existing research on entropy is primarily applied to undirected networks. Compared with an undirected network, a directed network involves a special asymmetric transfer. The research on the entropy of directed networks is very significant to effectively quantify the structural information of the whole network. Typical complex network models include nearest-neighbour coupling network, small-world network, scale-free network, and random network. These network models are abstracted as undirected graphs without considering the direction of node connection. For complex networks, modeling through the direction of network nodes is extremely challenging. In this paper, based on these typical models of complex network, a directed network model considering node connection in-direction is proposed, and the eigenvalue entropies of three matrices in the directed network is defined and studied, where the three matrices are adjacency matrix, in-degree Laplacian matrix and in-degree signless Laplacian matrix. The eigenvalue-based entropies of three matrices are calculated in directed nearest-neighbor coupling, directed small world, directed scale-free and directed random networks. Through the simulation experiment on the real directed network, the result shows that the eigenvalue entropy of the real directed network is between the eigenvalue entropy of directed scale-free network and directed small-world network.

scholarly journals CONTROL CONTRIBUTION IDENTIFIES TOP DRIVER NODES IN COMPLEX NETWORKS

2019 ◽  
Vol 22 (07n08) ◽  
pp. 1950014 ◽  
Author(s):  
YAN ZHANG ◽  
ANTONIOS GARAS ◽  
FRANK SCHWEITZER
Keyword(s):  
Complex Networks ◽  
Real World ◽  
Optimization Method ◽  
Directed Network ◽  
Control Range ◽  
New Information ◽  
Random Samples ◽  
Text Ranking ◽  
The Impact ◽  
Synthetic Networks

We propose a new measure to quantify the impact of a node [Formula: see text] in controlling a directed network. This measure, called “control contribution” [Formula: see text], combines the probability for node [Formula: see text] to appear in a set of driver nodes and the probability for other nodes to be controlled by [Formula: see text]. To calculate [Formula: see text], we propose an optimization method based on random samples of minimum sets of drivers. Using real-world and synthetic networks, we find very broad distributions of [Formula: see text]. Ranking nodes according to their [Formula: see text] values allows us to identify the top driver nodes that can control most of the network. We show that this ranking is superior to rankings based on other control-based measures. We find that control contribution indeed contains new information that cannot be traced back to degree, control capacity or control range of a node.

scholarly journals Network robustness improvement via long-range links

2019 ◽  
Vol 6 (1) ◽  
Author(s):  
Vincenza Carchiolo ◽  
Marco Grassia ◽  
Alessandro Longheu ◽  
Michele Malgeri ◽  
Giuseppe Mangioni
Keyword(s):  
Complex Networks ◽  
Long Range ◽  
Real World ◽  
Network Robustness ◽  
Scale Free ◽  
Area Of Interest ◽  
Before And After ◽  
Significant Area ◽  
Better Than

AbstractMany systems are today modelled as complex networks, since this representation has been proven being an effective approach for understanding and controlling many real-world phenomena. A significant area of interest and research is that of networks robustness, which aims to explore to what extent a network keeps working when failures occur in its structure and how disruptions can be avoided. In this paper, we introduce the idea of exploiting long-range links to improve the robustness of Scale-Free (SF) networks. Several experiments are carried out by attacking the networks before and after the addition of links between the farthest nodes, and the results show that this approach effectively improves the SF network correct functionalities better than other commonly used strategies.

A Network Embedding-Enhanced Bayesian Model for Generalized Community Detection in Complex Networks

2021 ◽  
Author(s):  
Dongxiao He ◽  
Youyou Wang ◽  
Jinxin Cao ◽  
Weiping Ding ◽  
Shizhan Chen ◽  
...  
Keyword(s):  
Complex Networks ◽  
Community Detection ◽  
Bayesian Model ◽  
Network Embedding

Identifying influential spreaders in complex networks based on network embedding and node local centrality

2021 ◽  
pp. 125971
Author(s):  
Xu-Hua Yang ◽  
Zhen Xiong ◽  
Fangnan Ma ◽  
Xiaoze Chen ◽  
Zhongyuan Ruan ◽  
...  
Keyword(s):  
Complex Networks ◽  
Network Embedding

scholarly journals Cycle and flow trusses in directed networks

2016 ◽  
Vol 3 (11) ◽  
pp. 160270 ◽  
Author(s):  
Taro Takaguchi ◽  
Yuichi Yoshida
Keyword(s):  
Truss Structures ◽  
Directed Network ◽  
Unified Framework ◽  
Directed Networks ◽  
Research Fields ◽  
Wide Range ◽  
Definition Of ◽  
Information Finding ◽  
Empirical Networks ◽  
Module Structures

When we represent real-world systems as networks, the directions of links often convey valuable information. Finding module structures that respect link directions is one of the most important tasks for analysing directed networks. Although many notions of a directed module have been proposed, no consensus has been reached. This lack of consensus results partly because there might exist distinct types of modules in a single directed network, whereas most previous studies focused on an independent criterion for modules. To address this issue, we propose a generic notion of the so-called truss structures in directed networks. Our definition of truss is able to extract two distinct types of trusses, named the cycle truss and the flow truss, from a unified framework. By applying the method for finding trusses to empirical networks obtained from a wide range of research fields, we find that most real networks contain both cycle and flow trusses. In addition, the abundance of (and the overlap between) the two types of trusses may be useful to characterize module structures in a wide variety of empirical networks. Our findings shed light on the importance of simultaneously considering different types of modules in directed networks.

Direction-Aware User Recommendation Based on Asymmetric Network Embedding

2022 ◽  
Vol 40 (2) ◽  
pp. 1-23
Author(s):  
Sheng Zhou ◽  
Xin Wang ◽  
Martin Ester ◽  
Bolang Li ◽  
Chen Ye ◽  
...  
Keyword(s):  
Social Networks ◽  
Random Walk ◽  
Real World ◽  
Directed Network ◽  
Network Embedding ◽  
The Social ◽  
Benchmark Datasets ◽  
Direction Information ◽  
User Recommendation ◽  
Asymmetric Proximity

User recommendation aims at recommending users with potential interests in the social network. Previous works have mainly focused on the undirected social networks with symmetric relationship such as friendship, whereas recent advances have been made on the asymmetric relationship such as the following and followed by relationship. Among the few existing direction-aware user recommendation methods, the random walk strategy has been widely adopted to extract the asymmetric proximity between users. However, according to our analysis on real-world directed social networks, we argue that the asymmetric proximity captured by existing random walk based methods are insufficient due to the inbalance in-degree and out-degree of nodes. To tackle this challenge, we propose InfoWalk, a novel informative walk strategy to efficiently capture the asymmetric proximity solely based on random walks. By transferring the direction information into the weights of each step, InfoWalk is able to overcome the limitation of edges while simultaneously maintain both the direction and proximity. Based on the asymmetric proximity captured by InfoWalk, we further propose the qualitative (DNE-L) and quantitative (DNE-T) directed network embedding methods, capable of preserving the two properties in the embedding space. Extensive experiments conducted on six real-world benchmark datasets demonstrate the superiority of the proposed DNE model over several state-of-the-art approaches in various tasks.

scholarly journals Complex networks of earthquakes and aftershocks

2005 ◽  
Vol 12 (1) ◽  
pp. 1-11 ◽  
Author(s):  
M. Baiesi ◽  
M. Paczuski
Keyword(s):  
Complex Networks ◽  
Time Windows ◽  
Scaling Law ◽  
Relative Strength ◽  
Modern Theory ◽  
Significant Information ◽  
Data Set ◽  
Scale Free ◽  
Main Shocks ◽  
Aftershock Sequences

Abstract. We invoke a metric to quantify the correlation between any two earthquakes. This provides a simple and straightforward alternative to using space-time windows to detect aftershock sequences and obviates the need to distinguish main shocks from aftershocks. Directed networks of earthquakes are constructed by placing a link, directed from the past to the future, between pairs of events that are strongly correlated. Each link has a weight giving the relative strength of correlation such that the sum over the incoming links to any node equals unity for aftershocks, or zero if the event had no correlated predecessors. A correlation threshold is set to drastically reduce the size of the data set without losing significant information. Events can be aftershocks of many previous events, and also generate many aftershocks. The probability distribution for the number of incoming and outgoing links are both scale free, and the networks are highly clustered. The Omori law holds for aftershock rates up to a decorrelation time that scales with the magnitude, m, of the initiating shock as tcutoff~10β m with β~-3/4. Another scaling law relates distances between earthquakes and their aftershocks to the magnitude of the initiating shock. Our results are inconsistent with the hypothesis of finite aftershock zones. We also find evidence that seismicity is dominantly triggered by small earthquakes. Our approach, using concepts from the modern theory of complex networks, together with a metric to estimate correlations, opens up new avenues of research, as well as new tools to understand seismicity.

scholarly journals A Novel Edge Rewire Mechanism Based on Multiobjective Optimization for Network Robustness Enhancement

2021 ◽  
Vol 9 ◽  
Author(s):  
Zhaoxing Li ◽  
Qionghai Liu ◽  
Li Chen
Keyword(s):  
Multiobjective Optimization ◽  
Complex Networks ◽  
Optimization Algorithm ◽  
Real World ◽  
Network Robustness ◽  
Objective Functions ◽  
Swarm Optimization ◽  
Scale Free ◽  
Scale Free Networks ◽  
The Given

A complex network can crash down due to disturbances which significantly reduce the network’s robustness. It is of great significance to study on how to improve the robustness of complex networks. In the literature, the network rewire mechanism is one of the most widely adopted methods to improve the robustness of a given network. Existing network rewire mechanism improves the robustness of a given network by re-connecting its nodes but keeping the total number of edges or by adding more edges to the given network. In this work we propose a novel yet efficient network rewire mechanism which is based on multiobjective optimization. The proposed rewire mechanism simultaneously optimizes two objective functions, i.e., maximizing network robustness and minimizing edge rewire operations. We further develop a multiobjective discrete partite swarm optimization algorithm to solve the proposed mechanism. Compared to existing network rewire mechanisms, the developed mechanism has two advantages. First, the proposed mechanism does not require specific constraints on the rewire mechanism to the studied network, which makes it more feasible for applications. Second, the proposed mechanism can suggest a set of network rewire choices each of which can improve the robustness of a given network, which makes it be more helpful for decision makings. To validate the effectiveness of the proposed mechanism, we carry out experiments on computer-generated Erdős–Rényi and scale-free networks, as well as real-world complex networks. The results demonstrate that for each tested network, the proposed multiobjective optimization based edge rewire mechanism can recommend a set of edge rewire solutions to improve its robustness.

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