The child brain is a small-world network, which is hypothesized to change toward more ordered configurations with development. In graph theoretical studies, comparing network topologies under different conditions remains a critical point. Constructing a minimum spanning tree (MST) might present a solution, since it does not require setting a threshold and uses a fixed number of nodes and edges. In this study, the MST method is introduced to examine developmental changes in functional brain network topology in young children. Resting-state electroencephalography was recorded from 227 children twice at 5 and 7 years of age. Synchronization likelihood (SL) weighted matrices were calculated in three different frequency bands from which MSTs were constructed, which represent constructs of the most important routes for information flow in a network. From these trees, several parameters were calculated to characterize developmental change in network organization. The MST diameter and eccentricity significantly increased, while the leaf number and hierarchy significantly decreased in the alpha band with development. Boys showed significant higher leaf number, betweenness, degree and hierarchy and significant lower SL, diameter, and eccentricity than girls in the theta band. The developmental changes indicate a shift toward more decentralized line-like trees, which supports the previously hypothesized increase toward regularity of brain networks with development. Additionally, girls showed more line-like decentralized configurations, which is consistent with the view that girls are ahead of boys in brain development. MST provides an elegant method sensitive to capture subtle developmental changes in network organization without the bias of network comparison.