scholarly journals Evaluating the Cascade Effect in Interdependent Networks via Algebraic Connectivity

2015 ◽  
Vol 1 (1) ◽  
pp. 55-68 ◽  
Author(s):  
Sotharith Tauch ◽  
William Liu ◽  
Russel Pears
Keyword(s):  
Network Structure ◽  
Topological Structure ◽  
Laplacian Matrix ◽  
Network Robustness ◽  
Node Degree ◽  
Algebraic Connectivity ◽  
Interdependent Networks ◽  
Cascade Effect ◽  
Underlying Network ◽  
Average Node Degree

Understanding how the underlying network structure and interconnectivity impact on the robustness of the interdependent networks is a major challenge in complex networks studies. There are some existing metrics that can be used to measure network robustness. However, different metrics such as the average node degree interprets different characteristic of network topological structure, especially less metrics have been identified to effectively evaluate the cascade performance in interdependent networks. In this paper, we propose to use a combined Laplacian matrix to model the interdependent networks and their interconnectivity, and then use its algebraic connectivity metric as a measure to evaluate its cascading behavior. Moreover, we have conducted extensive comparative studies among different metrics such as the average node degree, and the proposed algebraic connectivity. We have found that the algebraic connectivity metric can describe more accurate and finer characteristics on topological structure of the interdependent networks than other metrics widely adapted by the existing research studies for evaluating the cascading performance in interdependent networks.

Cascading failure of interdependent networks with dependence groups obeying different distributions

2020 ◽  
Vol 31 (08) ◽  
pp. 2050107
Author(s):  
Min Zhang ◽  
Xiaojuan Wang ◽  
Lei Jin ◽  
Mei Song
Keyword(s):  
Normal Distribution ◽  
Poisson Distribution ◽  
Field Approximation ◽  
Network Robustness ◽  
Mean Field Approximation ◽  
Node Degree ◽  
Cascading Failure ◽  
Truncated Normal Distribution ◽  
Interdependent Networks ◽  
Truncated Normal

Recent work on the cascading failure of networks with dependence groups assumes that the number of nodes in each dependence group is equal. In this paper, we construct a model on interdependent networks with dependence groups against cascading failure. The size of dependence group is supposed to obey the Poisson Distribution and the Truncated Normal Distribution, respectively. By applying the tools of mean-field approximation and the generating function techniques, the cascading model is theoretically analyzed and the theoretical solutions are nearly consistent with the simulation values. Besides, we define three kinds of coupling preferences based on node degree, i.e. assortative coupling, disassortative coupling and random coupling. The connection between layers is no longer one-to-one correspondence of nodes, but fully connection of some groups. In addition, some factors affecting the network robustness are discussed and extensive simulations are realized on two-layer BA networks. The simulation results show that the coupling preference has influence on the network robustness and the network with dependence groups obeying the Truncated Normal Distribution performs better than the Poisson Distribution.

scholarly journals On minimum algebraic connectivity of graphs whose complements are bicyclic

2019 ◽  
Vol 17 (1) ◽  
pp. 1490-1502 ◽  
Author(s):  
Jia-Bao Liu ◽  
Muhammad Javaid ◽  
Mohsin Raza ◽  
Naeem Saleem
Keyword(s):  
Connected Graph ◽  
Diffusion Processes ◽  
Laplacian Matrix ◽  
Group Differences ◽  
Algebraic Connectivity ◽  
Connected Graphs ◽  
Bicyclic Graph ◽  
Smallest Eigenvalue ◽  
Unique Graph ◽  
The Stability

Abstract The second smallest eigenvalue of the Laplacian matrix of a graph (network) is called its algebraic connectivity which is used to diagnose Alzheimer’s disease, distinguish the group differences, measure the robustness, construct multiplex model, synchronize the stability, analyze the diffusion processes and find the connectivity of the graphs (networks). A connected graph containing two or three cycles is called a bicyclic graph if its number of edges is equal to its number of vertices plus one. In this paper, firstly the unique graph with a minimum algebraic connectivity is characterized in the class of connected graphs whose complements are bicyclic with exactly three cycles. Then, we find the unique graph of minimum algebraic connectivity in the class of connected graphs $\begin{array}{} {\it\Omega}^c_{n}={\it\Omega}^c_{1,n}\cup{\it\Omega}^c_{2,n}, \end{array}$ where $\begin{array}{} {\it\Omega}^c_{1,n} \end{array}$ and $\begin{array}{} {\it\Omega}^c_{2,n} \end{array}$ are classes of the connected graphs in which the complement of each graph of order n is a bicyclic graph with exactly two and three cycles, respectively.

scholarly journals Community Detection Based on Graph Representation Learning in Evolutionary Networks

2021 ◽  
Vol 11 (10) ◽  
pp. 4497
Author(s):  
Dongming Chen ◽  
Mingshuo Nie ◽  
Jie Wang ◽  
Yun Kong ◽  
Dongqi Wang ◽  
...  
Keyword(s):  
Community Detection ◽  
Network Structure ◽  
Clustering Algorithm ◽  
Laplacian Matrix ◽  
Representation Learning ◽  
Detection Algorithm ◽  
Graph Representation ◽  
Time Slice ◽  
Current Time ◽  
Evolutionary Networks

Aiming at analyzing the temporal structures in evolutionary networks, we propose a community detection algorithm based on graph representation learning. The proposed algorithm employs a Laplacian matrix to obtain the node relationship information of the directly connected edges of the network structure at the previous time slice, the deep sparse autoencoder learns to represent the network structure under the current time slice, and the K-means clustering algorithm is used to partition the low-dimensional feature matrix of the network structure under the current time slice into communities. Experiments on three real datasets show that the proposed algorithm outperformed the baselines regarding effectiveness and feasibility.

scholarly journals Dynamic Evolution of Securities Market Network Structure under Acute Fluctuation Circumstances

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-11
Author(s):  
Haifei Liu ◽  
Tingqiang Chen ◽  
Zuhan Hu
Keyword(s):  
Stock Market ◽  
Network Structure ◽  
Topological Structure ◽  
Securities Market ◽  
Structure Stability ◽  
Dynamic Evolution ◽  
Bear Market ◽  
Bull Market ◽  
Market Transaction ◽  
Measuring Network

This empirical research applies cointegration in the traditional measurement method first to build directed weighted networks in the context of stock market. Then, this method is used to design the indicators and the value simulation for measuring network fluctuation and studying the dynamic evolution mechanism of stock market transaction networks as affected by price fluctuations. Finally, the topological structure and robustness of the network are evaluated. The results show that network structure stability is strong in the bull market stage and weak in the bear market stage. And the convergence rate of the dynamic evolution of network fluctuation is higher in the bull market stage than in the bear market stage.

A transportation network evolution model based on link prediction

2021 ◽  
Author(s):  
Shuang Gu ◽  
Keping Li ◽  
Yan Liang ◽  
Dongyang Yan
Keyword(s):  
Network Structure ◽  
Link Prediction ◽  
Transportation Networks ◽  
Network Evolution ◽  
Evolution Model ◽  
Civil Aviation ◽  
Node Degree ◽  
Network Efficiency ◽  
Evolution Mechanism ◽  
Proposed Model

An effective and reliable evolution model can provide strong support for the planning and design of transportation networks. As a network evolution mechanism, link prediction plays an important role in the expansion of transportation networks. Most of the previous algorithms mainly took node degree or common neighbors into account in calculating link probability between two nodes, and the structure characteristics which can enhance global network efficiency are rarely considered. To address these issues, we propose a new evolution mechanism of transportation networks from the aspect of link prediction. Specifically, node degree, distance, path, expected network structure, relevance, population and GDP are comprehensively considered according to the characteristics and requirements of the transportation networks. Numerical experiments are done with China’s high-speed railway network, China’s highway network and China’s inland civil aviation network. We compare receiver operating characteristic curve and network efficiency in different models and explore the degree and hubs of networks generated by the proposed model. The results show that the proposed model has better prediction performance and can effectively optimize the network structure compared with other baseline link prediction methods.

Utilizing the average node degree to assess the temporal growth rate of Twitter

2018 ◽  
Vol 8 (1) ◽  
Author(s):  
Despoina Antonakaki ◽  
Sotiris Ioannidis ◽  
Paraskevi Fragopoulou
Keyword(s):  
Growth Rate ◽  
Node Degree ◽  
Average Node Degree ◽  
Temporal Growth Rate

scholarly journals Optimizing Pinned Nodes to Maximize the Convergence Rate of Multiagent Systems with Digraph Topologies

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-12 ◽  
Author(s):  
Yujuan Han ◽  
Wenlian Lu ◽  
Tianping Chen ◽  
Changkai Sun
Keyword(s):  
Convergence Rate ◽  
Multiagent Systems ◽  
Spanning Trees ◽  
Laplacian Matrix ◽  
Pinning Control ◽  
Left Eigenvector ◽  
Underlying Network ◽  
Eigenvalues Of The Laplacian ◽  
Eigenvalue Zero ◽  
Theoretical Results

This paper investigates how to choose pinned node set to maximize the convergence rate of multiagent systems under digraph topologies in cases of sufficiently small and large pinning strength. In the case of sufficiently small pinning strength, perturbation methods are employed to derive formulas in terms of asymptotics that indicate that the left eigenvector corresponding to eigenvalue zero of the Laplacian measures the importance of node in pinning control multiagent systems if the underlying network has a spanning tree, whereas for the network with no spanning trees, the left eigenvectors of the Laplacian matrix corresponding to eigenvalue zero can be used to select the optimal pinned node set. In the case of sufficiently large pinning strength, by the similar method, a metric based on the smallest real part of eigenvalues of the Laplacian submatrix corresponding to the unpinned nodes is used to measure the stabilizability of the pinned node set. Different algorithms that are applicable for different scenarios are develped. Several numerical simulations are given to verify theoretical results.

scholarly journals Learning Diverse Bayesian Networks

2019 ◽  
Vol 33 ◽  
pp. 7793-7800
Author(s):  
Cong Chen ◽  
Changhe Yuan
Keyword(s):  
Bayesian Networks ◽  
Bayesian Network ◽  
Network Structure ◽  
Search Algorithm ◽  
Noisy Data ◽  
Local Neighborhood ◽  
Causal Ordering ◽  
True Model ◽  
Underlying Network ◽  
Novel Method

Much effort has been directed at developing algorithms for learning optimal Bayesian network structures from data. When given limited or noisy data, however, the optimal Bayesian network often fails to capture the true underlying network structure. One can potentially address the problem by finding multiple most likely Bayesian networks (K-Best) in the hope that one of them recovers the true model. However, it is often the case that some of the best models come from the same peak(s) and are very similar to each other; so they tend to fail together. Moreover, many of these models are not even optimal respective to any causal ordering, thus unlikely to be useful. This paper proposes a novel method for finding a set of diverse top Bayesian networks, called modes, such that each network is guaranteed to be optimal in a local neighborhood. Such mode networks are expected to provide a much better coverage of the true model. Based on a globallocal theorem showing that a mode Bayesian network must be optimal in all local scopes, we introduce an A* search algorithm to efficiently find top M Bayesian networks which are highly probable and naturally diverse. Empirical evaluations show that our top mode models have much better diversity as well as accuracy in discovering true underlying models than those found by K-Best.

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