EEG studies using graph-theoretic analysis have found aberrations in functional connectivity (FC) in dyslexics. How the visual training (VT) can change FC of the reading neural network (RNN) in developmental dyslexia is still unclear. We studied differences in local and global topological properties of FC-RNN between controls and dyslexic children before and after VT (pre-D, post-D). The minimum spanning tree method was used to construct RNN in multiple EEG frequency-bands. Pre-D had higher leaf fraction, tree hierarchy, kappa, and smaller diameter (theta-gamma), therefore more loaded RNNs than at controls. The RNN-metrics of post-D became similar to controls. In b1 and c-frequency bands, pre-D exhibited reduced degree and betweenness centrality of hubs in superior, middle, inferior frontal areas in both hemispheres compared to controls. Dyslexics relied on left anterior temporal (beta 1,gamma 1), dorsolateral prefrontal cortex (gamma 1), while in right hemisphere - occipitotemporal, parietal (beta 1), motor (beta 2,gamma 1), somatosensory cortices (gamma 1). Post-D, hubs appeared in both hemispheric middle occipital (beta), parietal (beta 1), somatosensory (gamma 1), dorsolateral prefrontal cortices (gamma 2), while in left hemisphere - at middle temporal, motor (beta 1), intermediate (gamma 2), inferior frontal cortices (gamma 1,beta 2). Language-related brain regions, more active after VT, contribute to lexical and sublexical understanding, as well areas, important for articulatory reading processes.