Mathematical Modeling in Social Network Analysis： Using TOPSIS to Find Node Influences in a Social Network

In a social network analysis the output provided includes many measures and metrics. For each of these measures and metric, the output provides the ability to obtain a rank ordering of the nodes in terms of these measures. We might use this information in decision making concerning disrupting or deceiving a given network. All is fine when all the measures indicate the same node as the key or influential node. What happens when the measures indicate different key nodes？ Our goal in this paper is to explore two methodologies to identify the key players or nodes in a given network. We apply TOPSIS to analyze these outputs to find the most influential nodes as a function of the decision makers＇ inputs as a process to consider both subjective and objectives inputs through pairwise comparison matrices. We illustrate our results using two common networks from the literature： the Kite network and the Information flow network from Knoke and Wood. We discuss some basic sensitivity analysis can may be applied to the methods. We find the use of TOPSIS as a flexible method to weight the criterion based upon the decision makers＇ inputs or the topology of the network.

Time sequential influence maximization algorithm based on neighbor node influence

In view of the forwarding microblogging,secondhand smoke,happiness,and many other phenomena in real life,the spread characteristic of the secondary neighbor nodes in this kind of phenomenon and network scheduling is extracted,and sequence influence maximization problem based on the influence of neighbor nodes is proposed in this paper.That is,in the time sequential social network,the propagation characteristics of the second-level neighbor nodes are considered emphatically,and k nodes are found to maximize the information propagation.Firstly,the propagation probability between nodes is calculated by the improved degree estimation algorithm.Secondly,the weighted cascade model(WCM) based on static social network is not suitable for temporal social network.Therefore,an improved weighted cascade model(IWCM) is proposed,and a second-level neighbors time sequential maximizing influence algorithm(STIM) is put forward based on node degree.It combines the consideration of neighbor nodes and the problem of overlap of influence scope between nodes,and makes it chronological.Finally,the experiment verifies that STIM algorithm has stronger practicability,superiority in influence range and running time compared with similar algorithms,and is able to solve the problem of maximizing the timing influence based on the influence of neighbor nodes.

The relative importance of structure and dynamics on node influence in reversible spreading processes

The reversible spreading processes with repeated infection widely exist in nature and human society,such as gonorrhea propagation and meme spreading.Identifying influential spreaders is an important issue in the reversible spreading dynamics on complex networks,which has been given much attention.Except for structural centrality,the nodes’dynamical states play a significant role in their spreading influence in the reversible spreading processes.By integrating the number of outgoing edges and infection risks of node’s neighbors into structural centrality,a new measure for identifying influential spreaders is articulated which considers the relative importance of structure and dynamics on node influence.The number of outgoing edges and infection risks of neighbors represent the positive effect of the local structural characteristic and the negative effect of the dynamical states of nodes in identifying influential spreaders,respectively.We find that an appropriate combination of these two characteristics can greatly improve the accuracy of the proposed measure in identifying the most influential spreaders.Notably,compared with the positive effect of the local structural characteristic,slightly weakening the negative effect of dynamical states of nodes can make the proposed measure play the best performance.Quantitatively understanding the relative importance of structure and dynamics on node influence provides a significant insight into identifying influential nodes in the reversible spreading processes.

Robustness of community networks against cascading failures with heterogeneous redistribution strategies

Network robustness is one of the core contents of complex network security research.This paper focuses on the robustness of community networks with respect to cascading failures,considering the nodes influence and community heterogeneity.A novel node influence ranking method,community-based Clustering-LeaderRank(CCL)algorithm,is first proposed to identify influential nodes in community networks.Simulation results show that the CCL method can effectively identify the influence of nodes.Based on node influence,a new cascading failure model with heterogeneous redistribution strategy is proposed to describe and analyze node fault propagation in community networks.Analytical and numerical simulation results on cascading failure show that the community attribute has an important influence on the cascading failure process.The network robustness against cascading failures increases when the load is more distributed to neighbors of the same community instead of different communities.When the initial load distribution and the load redistribution strategy based on the node influence are the same,the network shows better robustness against node failure.

Analysis of the influence of node location on transducer performance

This paper, taking the distance between the piezoelectric ceramic center and the displacement node location of the transducer as a parameter, investigates the relation of characteristic parameters of transducer, such as force factor, equivalent resistance, potential maximum electroacoustical efficiency, and loading performance, to the displacement node location. Some design considerations about the selection of node location are noted .