Analytically solvable models of the scale free growing network with hierarchical structure M´ aria Markoˇ sov´ a Department of Applied Informatics, Faculty of Mathematics, Physics and Informatics Comenius University, Bratislava, Slovakia Boris Rudolf Department of Mathematics, Faculty of Electrical Engineering and Information Technology, Technical University, Bratislava, Slovakia Martin ˇ Caj´ agi and Peter N´ ather Dept. of Applied Informatics, Faculty of Mathematics, Physics and Informatics Comenius University, Bratislava, Slovakia April 19, 2013 Abstract It is well known, that the preferential node attachment leads to the scale free network structure. Less is, however, known about the local processes leading to the hierarchical node organization. Our previous studies have shown, that adding new edges in a certain pattern creates complex scale free network with hierarchy. These studies were preferably numerical. In this paper we look for a minimal analytically solvable model of growing scale free hierarchical network. By defining a minimal number of local processes leading to the hierarchical scale free structure, we suggest two analytically solvable network models, for which we derive and solve the dynamical equations. 1