dorsal/arxiv
View SchemaThe Heider balance - a continuous approach
| Authors | Krzysztof Kulakowski, Przemyslaw Gawronski, Piotr Gronek |
|---|---|
| Categories | |
| ArXiv ID | physics/0501073 |
| URL | https://arxiv.org/abs/physics/0501073 |
| DOI | 10.1142/S012918310500742X |
| Journal | Int. J. Mod. Phys. C 16 (2005) 707 |
Abstract
The Heider balance (HB) is investigated in a fully connected graph of $N$ nodes. The links are described by a real symmetric array r(i,j), i,j=1,...,N. In a social group, nodes represent group members and links represent relations between them, positive (friendly) or negative (hostile). At the balanced state, r(i,j)r(j,k)r(k,i)>0 for all the triads (i,j,k). As follows from the structure theorem of Cartwright and Harary, at this state the group is divided into two subgroups, with friendly internal relations and hostile relations between the subgroups. Here the system dynamics is proposed to be determined by a set of differential equations. The form of equations guarantees that once HB is reached, it persists. Also, for N=3 the dynamics reproduces properly the tendency of the system to the balanced state. The equations are solved numerically. Initially, r(i,j) are random numbers distributed around zero with a symmetric uniform distribution of unit width. Calculations up to N=500 show that HB is always reached. Time to get the balanced state varies with the system size N as N^{-1/2}. The spectrum of relations, initially narrow, gets very wide near HB. This means that the relations are strongly polarized. In our calculations, the relations are limited to a given range around zero. With this limitation, our results can be helpful in an interpretation of somestatistical data.
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"abstract": "The Heider balance (HB) is investigated in a fully connected graph of $N$\nnodes. The links are described by a real symmetric array r(i,j), i,j=1,...,N.\nIn a social group, nodes represent group members and links represent relations\nbetween them, positive (friendly) or negative (hostile). At the balanced state,\nr(i,j)r(j,k)r(k,i)\u003e0 for all the triads (i,j,k). As follows from the structure\ntheorem of Cartwright and Harary, at this state the group is divided into two\nsubgroups, with friendly internal relations and hostile relations between the\nsubgroups. Here the system dynamics is proposed to be determined by a set of\ndifferential equations. The form of equations guarantees that once HB is\nreached, it persists. Also, for N=3 the dynamics reproduces properly the\ntendency of the system to the balanced state. The equations are solved\nnumerically. Initially, r(i,j) are random numbers distributed around zero with\na symmetric uniform distribution of unit width. Calculations up to N=500 show\nthat HB is always reached. Time to get the balanced state varies with the\nsystem size N as N^{-1/2}. The spectrum of relations, initially narrow, gets\nvery wide near HB. This means that the relations are strongly polarized. In our\ncalculations, the relations are limited to a given range around zero. With this\nlimitation, our results can be helpful in an interpretation of somestatistical\ndata.",
"arxiv_id": "physics/0501073",
"authors": [
"Krzysztof Kulakowski",
"Przemyslaw Gawronski",
"Piotr Gronek"
],
"categories": [
"physics.soc-ph",
"physics.comp-ph"
],
"doi": "10.1142/S012918310500742X",
"journal_ref": "Int. J. Mod. Phys. C 16 (2005) 707",
"title": "The Heider balance - a continuous approach",
"url": "https://arxiv.org/abs/physics/0501073"
},
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