Toothpick arrangements - Colegiul National C. Negruzzi (Iași - Roumanie)

The paper deals with counting techniques for triangles, squares and rectangles in various types of regular grids and lattices. The study of the number of such polygons or network motifs is of great interest in Graph Theory, when dealing with the complexity of large networks or with finding patterns in large scale graphs, with millions of edges. It has been shown that the distribution of the number of polygons (triangles, squares) in a large scale network can be used to create successful spam filters or to provide useful tools in assessing the content quality in social networks