Evidence for a Scale-Free Commercial Network in the Indus Valley Civilization: A Power Law Analysis of Harappan Seal Data

We present a quantitative analysis of the frequency distribution of unicorn seal attributes from the Harappan Civilization (c.\ 2600–1900 BCE), reinterpreting published typological data through the lens of network science. We propose an information architecture for Harappan seals in which the unicorn motif serves as a commercial network marker, the offering stand variant encodes guild identity, and the script conveys transactional and administrative metadata. Under this interpretation, the frequency distribution of offering stand styles – a proxy for guild size – is consistent with a power law ($\alpha \approx 2.3$–$2.6$ from constrained reconstruction; bin-mean estimate $\alpha \approx 2.18$), significantly outperforming an exponential fit ($R=37.3$, $p<0.001$; exponential independently ruled out via goodness-of-fit bootstrap, $p<0.001$), with no alternative heavy-tailed model fitting significantly better. The distribution of seal counts across archaeological sites similarly follows a power law ($\alpha \approx 1.55$, KS $D=0.094$, $p=0.019$ vs.\ exponential). Both distributions exhibit the heavy-tailed, hub-dominated structure characteristic of scale-free networks. These findings suggest that Harappan trade was organized as a self-organizing, scale-free commercial network, with implications for understanding the civilization’s resilience and eventual decline. Analysis of the complete unfiltered per-type frequency data independently confirms power law structure ($p=0.71$), validating the guild scale-free hypothesis across both constrained and complete methodologies. Exact per-type frequency data would further refine these estimates.