A novel vulnerability measure based on complex network communities

This article introduces a novel vulnerability measure, based on the structure of complex network communities, to assess the significance and security of network communities, influencing complex network security, connectivity, and the prevention of cascading failures. Initially, the spectral clustering algorithm is applied to identify the communities of complex networks. Determining the appropriate number of communities is crucial in the proposed vulnerability measure and security approach. The number of communities is estimated based on the characteristics of the normalized Laplace matrix within the algorithm. Subsequently, leveraging the community structure, a vulnerability measure is proposed for community evaluation by considering three aspects of internal criteria, external criteria and node location criterion. Weight parameters are also incorporated to customize the measure according to the importance of each factor in varying security scenarios. Finally, the effectiveness of the proposed vulnerability measure as a security strategy is evaluated on ten real-world complex networks from different categories. The experimental results demonstrate the effectiveness and efficiency of the proposed measure in assessing community vulnerability and consequently using appropriate maps and policies for the complex network security.