Electroencephalographic studies using graph-theoretic analysis have found aberrations in functional connectivity in dyslexics. How visual nonverbal training (VT) can change the functional connectivity of the reading network in developmental dyslexia is still unclear. We studied differences in the local and global topological properties of functional reading networks between controls and dyslexic children before and after VT. The minimum spanning tree method was used to construct the reading networks in multiple electroencephalogram (EEG) frequency bands. Compared to controls, pre-training dyslexics had a higher leaf fraction, tree hierarchy, kappa, and smaller diameter (θ—γ-frequency bands), and therefore, they had a less segregated neural network than controls. After training, the reading-network metrics of dyslexics became similar to controls. In β1 and γ-frequency bands, pre-training dyslexics exhibited a reduced degree and betweenness centrality of hubs in superior, middle, and inferior frontal areas in both brain hemispheres compared to the controls. Dyslexics relied on the left anterior temporal (β1, γ1) and dorsolateral prefrontal cortex (γ1), while in the right hemisphere, they relied on the occipitotemporal, parietal, (β1), motor (β2, γ1), and somatosensory cortices (γ1). After training, hubs appeared in both hemispheres at the middle occipital (β), parietal (β1), somatosensory (γ1), and dorsolateral prefrontal cortices (γ2), while in the left hemisphere, they appeared at the middle temporal, motor (β1), intermediate (γ2), and inferior frontal cortices (γ1, β2). Language-related brain regions were more active after visual training. They contribute to an understanding of lexical and sublexical representation. The same role has areas important for articulatory processes of reading.