Simplicial Complexes In Complex Systems In Search For Alternatives Yi Zhao by Yi Zhao, Slobodan Maletić 9789811226311, 9811226318 instant download after payment.

So far we have seen that the richness of complexity phenomena necessitates the richness of tools for tackling the problems which emerge from real-world phenomena, and as well the widespread application of mathematical formalisms which rely on the simplicial complexes. In this chapter we will give an introduction to simplicial complexes, which includes defining them, definition of their properties, and quantities which characterize them. As we mentioned earlier, whenever its convenient we will avoid formal mathematical definition, and reach out to the intuitive graphical or real world examples. Although the way of defining simplices is a bit unusual, our intention is to point the equivalence of three definitions, or in other words, that the same mathematical object can be defined in three different ways. The versatility of descriptions of simplicial complex originates from three distinct aspects from which we can treat them: combinatorial, geometrical, and topological. Therefore, we hope that by the end of this chapter the reader will have at least intuitive image which will help for easy flowing through the forthcoming chapters.