A Combinatorial Model for Improved Calculation of Network Stability

The stability and vulnerability of networks is of paramount importance in communications sciences and also in a variety of other fields. The theoretical basisof calculating parameters describing networks and as such optimizing networks,has proven to be valuable and has created a wealth of research in this field[1, 6, 8, 9, 10]However, for many such parameters and studies, very high orders of computation are required [4, 5, 7] rendering them difficult to apply to large scaleprojects and thus limiting their application. Research upon novel methods andprograms to study and calculate the stability of a network is therefore necessaryin order to improve their efficacy and applicability.In this article, we present our research on the stability of networks usinga combinatorial approach obtaining optimization models with the ability tocalculate, demonstrate and optimize the stability and vulnerability of networks.Due to the linearity of these models and the limited number of binary variablespresent, computation order is decreased for most cases and calculations can becompleted faster which can be used for larger projects. Due to the optimizationnature of this model, in addition to the calculation of parameters describing thestability of a network, it can be used to optimize the design of a network bymaximizing such a parameter simultaneous to other constrictions required forany specific network design required.