Ranking important nodes in complex networks by simulated annealing

In this paper, based on simulated annealing a new method to rank important nodes in complex networks is presented.First, the concept of an importance sequence（IS） to describe the relative importance of nodes in complex networks is defined. Then, a measure used to evaluate the reasonability of an IS is designed. By comparing an IS and the measure of its reasonability to a state of complex networks and the energy of the state, respectively, the method finds the ground state of complex networks by simulated annealing. In other words, the method can construct a most reasonable IS. The results of experiments on real and artificial networks show that this ranking method not only is effective but also can be applied to different kinds of complex networks.

Identification of Important FPGA Modules Based on Complex Network

The globalization of hardware designs and supply chains,as well as the integration of third-party intellectual property(IP)cores,has led to an increased focus from malicious attackers on computing hardware.However,existing defense or detection approaches often require additional circuitry to perform security verification,and are thus constrained by time and resource limitations.Considering the scale of actual engineering tasks and tight project schedules,it is usually difficult to implement designs for all modules in field programmable gate array(FPGA)circuits.Some studies have pointed out that the failure of key modules tends to cause greater damage to the network.Therefore,under limited conditions,priority protection designs need to be made on key modules to improve protection efficiency.We have conducted research on FPGA designs including single FPGA systems and multi-FPGA systems,to identify key modules in FPGA systems.For the single FPGA designs,considering the topological structure,network characteristics,and directionality of FPGA designs,we propose a node importance evaluationmethod based on the technique for order preference by similarity to an ideal solution(TOPSIS)method.Then,for the multi-FPGA designs,considering the influence of nodes in intra-layer and inter-layers,they are constructed into the interdependent network,and we propose a method based on connection strength to identify the important modules.Finally,we conduct empirical research using actual FPGA designs as examples.The results indicate that compared to other traditional indexes,node importance indexes proposed for different designs can better characterize the importance of nodes.

Brittleness Analysis and Important Nodes Discovery in Large Time-Evolving Complex Networks

The brittleness analysis and important nodes detection have been a hot spot in the complex networks.How to get the overall feature of the whole network and how to find out some important nodes are requisites to solve these problems. In this paper, we adopt the trace of the adjacency matrix and the centrality of the complex networks to give a quantitative and qualitative analysis of networks being studied. Results show that the k-shell plays a more important role than the degree centrality and the betweenness in finding important nodes, and it can also be used to give direction on the immunization and maintenance of complex networks.

Statistical Identification of Important Nodes in Biological Systems

Biological systems can be modeled and described by biological networks.Biological networks are typical complex networks with widely real-world applications.Many problems arising in biological systems can be boiled down to the identification of important nodes.For example,biomedical researchers frequently need to identify important genes that potentially leaded to disease phenotypes in animal and explore crucial genes that were responsible for stress responsiveness in plants.To facilitate the identification of important nodes in biological systems,one needs to know network structures or behavioral data of nodes(such as gene expression data).If network topology was known,various centrality measures can be developed to solve the problem;while if only behavioral data of nodes were given,some sophisticated statistical methods can be employed.This paper reviewed some of the recent works on statistical identification of important nodes in biological systems from three aspects,that is,1)in general complex networks based on complex networks theory and epidemic dynamic models;2)in biological networks based on network motifs;and 3)in plants based on RNA-seq data.The identification of important nodes in a complex system can be seen as a mapping from the system to the ranking score vector of nodes,such mapping is not necessarily with explicit form.The three aspects reflected three typical approaches on ranking nodes in biological systems and can be integrated into one general framework.This paper also proposed some challenges and future works on the related topics.The associated investigations have potential real-world applications in the control of biological systems,network medicine and new variety cultivation of crops.

A Novel Method Based on Node’s Correlation to Evaluate Important Nodes in Complex Networks

Finding the important nodes in complex networks by topological structure is of great significance to network invulnerability.Several centrality measures have been proposed recently to evaluate the performance of nodes based on their correlation,showing that the interaction between nodes has an influence on the importance of nodes.In this paper,a novel method based on node’s distribution and global influence in complex networks is proposed.The nodes in the complex networks are classified according to the distance matrix,then the correlation coefficient between pairs of nodes is calculated.From the whole perspective in the network,the global similarity centrality(GSC)is proposed based on the relevance and the shortest distance between any two nodes.The efficiency,accuracy,and monotonicity of the proposed method are analyzed in two artificial datasets and eight real datasets of different sizes.Experimental results show that the performance of GSC method outperforms those current state-of-the-art algorithms.

Capacitated stochastic coloured Petri net-based approach for computing two-terminal reliability of multi-state network

Classical network reliability problems assume both net- works and components have only binary states, fully working or fully failed states. But many actual networks are multi-state, such as communication networks and transportation networks. The nodes and arcs in the networks may be in intermediate states which are not fully working either fully failed. A simulation ap- proach for computing the two-terminal reliability of a multi-state network is described. Two-terminal reliability is defined as the probability that d units of demand can be supplied from the source to sink nodes under the time threshold T. The capacities of arcs may be in a stochastic state following any discrete or continuous distribution. The transmission time of each arc is also not a fixed number but stochastic according to its current capacity and de- mand. To solve this problem, a capacitated stochastic coloured Petri net is proposed for modelling the system behaviour. Places and transitions respectively stand for the nodes and arcs of a net- work. Capacitated transition and self-modified token colour with route information are defined to describe the multi-state network. By the simulation, the two-terminal reliability and node importance can be estimated and the optimal route whose reliability is highest can also be given. Finally, two examples of different kinds of multi- state networks are given.

A compound objective reconfiguration of distribution networks using hierarchical encoded particle swarm optimization

With the development of automation in smart grids,network reconfiguration is becoming a feasible approach for improving the operation of distribution systems.A novel reconfiguration strategy was presented to get the optimal configuration of improving economy of the system,and then identifying the important nodes.In this strategy,the objectives increase the node importance degree and decrease the active power loss subjected to operational constraints.A compound objective function with weight coefficients is formulated to balance the conflict of the objectives.Then a novel quantum particle swarm optimization based on loop switches hierarchical encoded was employed to address the compound objective reconfiguration problem.Its main contribution is the presentation of the hierarchical encoded scheme which is used to generate the population swarm particles of representing only radial connected solutions.Because the candidate solutions are feasible,the search efficiency would improve dramatically during the optimization process without tedious topology verification.To validate the proposed strategy,simulations are carried out on the test systems.The results are compared with other techniques in order to evaluate the performance of the proposed method.

Method to Quantifying the Logical Node Importance for IEC 61850 Based Substation Automation Systems

The problem of logical node(LN)importance quantification in an IEC 61850 based substation automation system(SAS)is investigated in this paper.First,a weighted and directed static complex network model is established by analyzing the characteristics of SAS,according to IEC 61850.Then,we propose a method,which combines topology value and information adjunction value by introducing a first-order linear feedback controller to quantify the value of LNs.On this basis,some definitions for equivalent network conversion are proposed to greatly reduce the complexity of the original network topology.Also,the absolute value and relative value are introduced to quantify LN importance from the perspective of the node’s necessity and influence,respectively.Finally,simulation results of the case study demonstrate that the proposed method is effective and provides a broader and clearer perspective for viewing the logical node importance for IEC61850 based SAS.

Evaluation method of node importance for power grid considering inflow and outflow power

The effective identifications of important nodes in power grid are foundations of differentiated management and stable operation of power grid. However, the current studies on this field are not thorough enough. This paper applies the model based on co-citation(MBCC)-hypertext induced topic selection(HITS) algorithm used in web page ranking to power grid and proposes an index to determine node importance of power grid from the perspectives of inflow and outflow power. MBCC-HITS algorithm is modified considering load, power source, and line flow comprehensively for the differences between Internet and power grid in this paper. Then a method for evaluating node importance is proposed using the modified algorithm. Lastly, the rationality and validity of the proposed method are verified by comparisons with other methods in case studies of IEEE 14-bus and 118-bus systems.

A New Evaluation Method of Node Importance in Directed Weighted Complex Networks

Current researches on node importance evaluation mainly focus on undirected and unweighted networks, which fail to reflect the real world in a comprehensive and objective way. Based on directed weighted complex network models, the paper introduces the concept of in-weight intensity of nodes and thereby presents a new method to identify key nodes by using an importance evaluation matrix. The method not only considers the direction and weight of edges, but also takes into account the position importance of nodes and the importance contributions of adjacent nodes. Finally, the paper applies the algorithm to a microblog-forwarding network composed of 34 users, then compares the evaluation results with traditional methods. The experiment shows that the method proposed can effectively evaluate the node importance in directed weighted networks.