dorsal/arxiv
View SchemaReciprocity and the Emergence of Power Laws in Social Networks
| Authors | Michael Schnegg |
|---|---|
| Categories | |
| ArXiv ID | physics/0603005 |
| URL | https://arxiv.org/abs/physics/0603005 |
| DOI | 10.1142/S0129183106009473 |
Abstract
Research in network science has shown that many naturally occurring and technologically constructed networks are scale free, that means a power law degree distribution emerges from a growth model in which each new node attaches to the existing network with a probability proportional to its number of links (=degree). Little is known about whether the same principles of local attachment and global properties apply to societies as well. Empirical evidence from six ethnographic case studies shows that complex social networks have significantly lower scaling exponents gamma ~ 1 than have been assumed in the past. Apparently humans do not only look for the most prominent players to play with. Moreover cooperation in humans is characterized through reciprocity, the tendency to give to those from whom one has received in the past. Both variables -- reciprocity and the scaling exponent -- are negatively correlated ($r=-0.767, sig=0.075$). If we include this effect in simulations of growing networks, degree distributions emerge that are much closer to those empirically observed. While the proportion of nodes with small degrees decreases drastically as we introduce reciprocity, the scaling exponent is more robust and changes only when a relatively large proportion of attachment decisions follow this rule. If social networks are less scale free than previously assumed this has far reaching implications for policy makers, public health programs and marketing alike.
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"abstract": "Research in network science has shown that many naturally occurring and\ntechnologically constructed networks are scale free, that means a power law\ndegree distribution emerges from a growth model in which each new node attaches\nto the existing network with a probability proportional to its number of links\n(=degree). Little is known about whether the same principles of local\nattachment and global properties apply to societies as well. Empirical evidence\nfrom six ethnographic case studies shows that complex social networks have\nsignificantly lower scaling exponents gamma ~ 1 than have been assumed in the\npast. Apparently humans do not only look for the most prominent players to play\nwith. Moreover cooperation in humans is characterized through reciprocity, the\ntendency to give to those from whom one has received in the past. Both\nvariables -- reciprocity and the scaling exponent -- are negatively correlated\n($r=-0.767, sig=0.075$). If we include this effect in simulations of growing\nnetworks, degree distributions emerge that are much closer to those empirically\nobserved. While the proportion of nodes with small degrees decreases\ndrastically as we introduce reciprocity, the scaling exponent is more robust\nand changes only when a relatively large proportion of attachment decisions\nfollow this rule. If social networks are less scale free than previously\nassumed this has far reaching implications for policy makers, public health\nprograms and marketing alike.",
"arxiv_id": "physics/0603005",
"authors": [
"Michael Schnegg"
],
"categories": [
"physics.soc-ph"
],
"doi": "10.1142/S0129183106009473",
"title": "Reciprocity and the Emergence of Power Laws in Social Networks",
"url": "https://arxiv.org/abs/physics/0603005"
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