Designing Information Secure Networks with Graph Theory

Graph theory studies the properties of graphs and networks. Graphs are an excellent tool for designing, analysing and optimizing data networks. In a data network there are unequal components, which need different amount of information security depending on their properties. Information security includes all measures which try to prevent destruction, manipulation or stealing of information. But at the same time the information must be available for those who have the permission to access it. Computer network can be modeled with graph, where vertices are components of network such as computer, switch or database. With edges we can illustrate allowed connections between those components. Every vertex has importance value; the smaller value means that the protection of the component is more important. Software-defined networking (SDN) is a quite new approach to designing, creating and controlling computer networks. In a software-defined network all components can be directly connected. The main result of this Thesis is the algorithm twintrees, which makes software defined networks more secure and reliable, where it is hard for malware to advance. Security levels make the network segmented, which protects critical parts from threats which could spread from the less protected parts of the network. It takes time for malware to spread from higher levels to lower levels and thus it is easier to react to threat before any catastrophic happens. The algorithm, which this Thesis represents, transfers full graphs to 2-edge-connected graphs by combining two independent spanning trees. For software designed network the 2-edge-connectivity is an excellent property. With this property it is possible to remove any connection between two components so that the network remains still connected.