Universal power laws in the threshold network model: A theoretical analysis based on extreme value theory

摘要

We theoretically and numerically investigated the threshold network modelwith a generic weight function where there were a large number of nodes and ahigh threshold. Our analysis was based on extreme value theory, which gave us atheoretical understanding of the distribution of independent and identicallydistributed random variables within a sufficiently high range. Specifically,the distribution could be generally expressed by a generalized Paretodistribution, which enabled us to formulate the generic weight distributionfunction. By using the theorem, we obtained the exact expressions of degreedistribution and clustering coefficient which behaved as universal power lawswithin certain ranges of degrees. We also compared the theoretical predictionswith numerical results and found that they were extremely consistent.