We study the behavior of the clustering coefficient in tagged networks. The rich variety of tags associated with the nodes in the networks we considered provide additional relevant information about the entities represented by the nodes. Such specific features can be important for practical...

To provide a phenomenological theory for the various interesting transitions in restructuring networks we employ a statistical mechanical approach with detailed balance satisfied for the transitions between topological states. This enables us to establish an equivalence between the equilibrium...

Our goal is to describe the collective motion of organisms in the presence of fluctuations. Therefore, we discuss biologically inspired, inherently non-equilibrium models consisting of self-propelled particles. In our models the particles corresponding to organisms locally interact with their...

An interesting example for collective decision-making is the so-called Mexican wave during which the spectators in a stadium leap to their feet with their arms up and then sit down again following those to their left (right) with a small delay. Here we use a simple, but realistic model to...

The origin of biological motion can be traced back to the function of molecular motor proteins. Cytoplasmic dynein and kinesin transport organelles within our cells moving along a polymeric filament, the microtubule. The motion of the myosin molecules along the actin filaments is responsible for...

In the last 30 years it was found that many combinatorial systems undergo phase transitions. One of the most important examples of these can be found among the random k-satisfiability problems (often referred to as k-SAT), asking whether there exists an assignment of Boolean values satisfying a...

Benoît Mandelbrot (1924–2010) születésének 100. évfordulóján felidézzük néhány személyes találkozásunkhoz kötődő emlékeinket. A „fraktálok atyja” a munkásságán keresztül megismert csodás természeti objektumokhoz hasonlóan igen komplex személyiség volt. Nagy...

Scale-free networks are abundant in nature and society, describing such diverse systems as the world wide web, the web of human sexual contacts, or the chemical network of a cell. All models used to generate a scale-free topology are stochastic, that is they create networks in which the nodes...

Two independent approaches, the box counting and the sand box methods are used for the determination of the generalized dimensions (Dq) associated with the geometrical structure of growing deterministic fractals. We find that the multifractal nature of the geometry results in an unusually slow...

We discuss biologically inspired, inherently non-equilibrium models of self-propelled particles, in which the particles interact with their neighbors by choosing at each time step the local average direction of motion. We summarize some of the results of large-scale simulations and theoretical...