Cognitive interventions that involve executive functions (EF)-demanding activities are effective in changing task-related brain activity in children from homes with low socioeconomic status (SES). However, less is known about the efficiency of EF-based interventions in modifying segregation and integration properties of the functional neural organization during a resting state. Further, the consideration of the initial cognitive performance in the design of interventions and its role in the outcome of cognitive training has been poorly studied. The present study aimed to examine the impact of two individualized cognitive interventions with EF-demanding activities on brain connectivity in preschoolers (n = 79) from low-SES homes in Argentina using complex network analysis. At baseline, participants were classified as high- or low-performers based on their performance in an inhibitory control task, and then they were assigned into intervention and control groups within each performance level. Before and after the intervention, the neural activity of each child was recorded at rest using a mobile electroencephalogram device. We found significant intervention-related changes in global efficiency, global strength, and the strength of long-range connections in the [theta] frequency band in the intervention low-performing group. These findings support the idea that patterns of processing crucial information in the brain may be modified in children from low-SES homes through an EF-based intervention. Finally, these findings show different intervention-related effects on neural activity between children with low and high initial cognitive performance and add new evidence about the interaction between individual characteristics and intervention approaches.