The Study Of Identifying Influential Nodes In Complex Networks

Over the years, complex network systems have been all around in people’s production and living. As a young and active field of scientific research inspired largely by empirical studies of real-world networks, it have been paid attention by more and more people in marry fields such as computer sciences, social sciences, biological sciences, management sciences and so on. On the one hand, with the constant development of complex networks, people’s production and living have been improved significantly, and brought great convenience. One the other hand, there are some negative effects caused by complex networks. Such as the rapid spread of the disease, widespread blackouts accidents, as well as transportation paralysis. In order to predict, prevent and control the failures caused by complex networks, we need understand and analysis the complex network more profoundly. In the so many complex network researches, identifying influential nodes has been a popular area.Nowadays, although many centrality measures have been proposed to identify influential nodes, the rankings of identifying influential nodes may be discrepant by using a different centrality measure. Therefore, with different centrality measures, it may obtain different results. In order to address this issue, it is necessary for us to modified the existing centrality measures of identifying influential nodes.In this paper, we propose three different centrality measures to identify influential nodes. In the first measure, we introduce effective distance into the application of the shortest path problem. Effective distance is applied to replace the conventional geographic distance or binary distance. A new closeness centrality measure based on effective distance is proposed to identify influential nodes. Then, a new centrality measure based on TOPSIS is proposed. Degree centrality, closeness centrality and betweenness centrality are taken into account as the multi-attribute in TOPSIS application. TJiis new centrality measure compromise the different results by Degree centrality, closeness centrality and betweenness centrality. In our last measure, we use node information to model the assessments of occurrence, severity and detection in the application of failure mode and effects analysis (FMEA). According to the value of risk priority number (RPN), the identification of influential nodes can be determined. To show the effectiveness and practicability of the proposed measures, we apply four real networks by Susceptible-Infected (SI) model in each centrality measure.The main work of this paper is summarized as follows:(1) Proposing of a modified closeness centrality measure based on effective distanceIn many real networks, there may exist some isolated nodes and unidirectional edge. It may lead to unreachable distances.In this case, the traditional closeness centrality is useless. Inspired effective distance, a new closeness centrality based on effective distance is proposed. Effective distance is applied to replace the conventional geographic distance or binary distance.(2) Proposing of a new centrality measure based on TOPSISAs a widely used multiple attribute decision making method, TOPSIS is very useful to aggregate the differences between attributes. Due to the fact that there are many shortcomings and deficiencies in these centrality measures, it is necessary for us to propose a new centrality to compromise the results by different centrality measure. In our model, degree centrality, closeness centrality and betweenness centrality are taken into account as the multi-attribute in TOPSIS application to identify influential nodes.(3) Proposing of a new centrality measure based on FMEAFailure mode and effects analysis (FMEA) is an engineering and management technique, and it is widely used to define, identify, and eliminate known or potential failures, problems, errors, and risk from the design, process, service. A traditional FMEA is determined by the risk priority number, which is obtained by multiplying the scores of the occurrence, severity and detection. We use node information to model the assessments of occurrence, severity and detection. We think that more in-degrees a node has, higher probability a node suffer effects from other nodes. For this node, the probability of occurrence is high by the way. Meanwhile, if a node has more shorter effective distances between other nodes, we think that the node has a higher spreading ability of failure effects, which means that the node has higher failure severity. In our model, we define the entropy of nodes. Entropy can be described as the nondeterminacy of a system or unit. So we think that if the entropy score of a node is high, it means that this node is in a high complex structure. By this way, it can be deemed that it is difficult to detect the node’s failure. According to this proposed model, we can identify influential nodes by the new risk priority number. The higher RPN of a node, the more important degree it should be assigned.