Memory effect in growing trees

We show that the structure of a growing tree preserves an information on the shape of an initial graph. For the exponential trees, evidence of this kind of memory is provided by means of the iterative equations, derived for the moments of the node-node distance distribution. Numerical calculations confirm the result and allow to extend the conclusion to the Barabasi--Albert scale-free trees. The memory effect almost disappears, if subsequent nodes are connected to the network with more than one link.Comment: 9 pages, 9 figure

Heider Balance in Human Networks

Recently, a continuous dynamics was proposed to simulate dynamics of interpersonal relations in a society represented by a fully connected graph. Final state of such a society was found to be identical with the so-called Heider balance (HB), where the society is divided into two mutually hostile groups. In the continuous model, a polarization of opinions was found in HB. Here we demonstrate that the polarization occurs also in Barabasi-Albert networks, where the Heider balance is not necessarily present. In the second part of this work we demonstrate the results of our formalism, when applied to reference examples: the Southern women and the Zachary club.Comment: 9 pages, 5 figures. Presented on 8th Granada Seminar on Computational and Statistical Physics, Modeling Cooperative Behavior in the Social Sciences, Granada, Spain, 7-11 February 200

Indifferents as an interface between Contra and Pro

In most sociophysical simulations on public opinion, only two opinions are allowed: Pro and Contra. However, in all political elections many people do not vote. Here we analyse two models of dynamics of public opinion, taking into account Indifferent voters: {\it i)} the Sznajd model with symmetry Pro-Contra, {\it ii)} the outflow one move voter model, where Contra's are converted to Indifferent by their Pro neighbours. Our results on the Sznajd model are in an overall agreement with the results of the mean field approach and with those known from the initial model formulation. The simulation on the voter model shows that an amount of Contra's who remain after convertion depends on the network topology.Comment: 12 pages, 5 figure

The Sznajd dynamics on a directed clustered network

The Sznajd model is investigated in the directed Erdos--Renyi network with the clusterization coefficient enhanced to 0.3 by the method of Holme and Kim (Phys. Rev. E65 (2002) 026107). Within additional triangles, all six links are present. In this network, some nodes preserve the minority opinion. The time tau of getting equilibrium is found to follow the log-normal distribution and it increases linearly with the system size. Its dependence on the initial opinion distribution is different from the analytical results for fully connected networks.Comment: dedicated to Dietrich Stauffer for his 65-th birthda