SPATIALLY - EMBEDDED COMPLEX NETWORK ESTIMATION USING FRACTAL DIMENSION

V magistrskem delu opišemo dve zelo zanimivi področji računalništva, kompleksne mreže in fraktale. S kompleksnimi mrežami lahko na preprost in enostaven način predstavimo sestavljene in težko opisljive strukture. Vozlišča v našem primeru predstavljajo objekte v prostoru, povezave med njimi pa interakcije. Zato govorimo o prostorskovpetih mrežah. Drugi del magistrskega dela predstavljajo fraktali, ki s svojo lastnostjo samopodobnosti vzbujajo veliko pozornosti v svetu računalništva. Dejanske fraktale je težko opisati in prepoznati, eden od načinov pa je s pomočjo fraktalne dimenzije. S fraktalno dimenzijo lahko opišemo kakršnekoli fraktale, dimenzija pa je značilno manjša od prostora, v katerega so vpeti. V tem magistrskem delu predstavimo postopek ocenjevanja fraktalnosti mrež. Razvita metoda temelji na štetju zasedenih škatelj. Z rezultati pokažemo njeno učinkovitost pri razpoznavi fraktalnih struktur, skritih v prostorskovpetih mrežah.In this thesis we describe two very interesting areas of computer science: complex networks and fractals. With the complex networks we can, in an easy and simple manner, present composite structures and structures that are difficult to describe. In our case, the nodes present the objects in space, while the connections between them present interactions. We talk about spatially embedded networks. The second part of the thesis consider fractals, which with their characteristic of self-similarity raise a lot of attention in the world of computer science. The actual fractals are difficult to describe and to recognize, one of the ways to do so is with the help of fractal dimension. With the fractal dimension we can describe any kinds of fractals and the dimension is smaller than the space in which they are embedded. With the implementation of the box-counting algorithm we have assessed the fractality of the spatially embedded networks. We show that spatially embedded networks have fractal properties