Network neuroscience explores the brain's connectome, demonstrating that dynamic neural networks support cognitive functions. This study investigates how distinct cognitive abilities-working memory and cognitive inhibitory control-are supported by unique brain network configurations constructed by estimating whole-brain networks using mutual information. The study involved 195 participants who completed the Sternberg Item Recognition task and Flanker tasks while undergoing electroencephalography recording. A mixed-effects linear model analyzed the influence of network metrics on cognitive performance, considering individual differences and task-specific dynamics. The findings indicate that working memory and cognitive inhibitory control are associated with different network attributes, with working memory relying on distributed networks and cognitive inhibitory control on more segregated ones. Our analysis suggests that both strong and weak connections contribute to cognitive processes, with weak connections potentially leading to a more stable and support networks of memory and cognitive inhibitory control. The findings indirectly support the network neuroscience theory of intelligence, suggesting different functional topology of networks inherent to various cognitive functions. Nevertheless, we propose that understanding individual variations in cognitive abilities requires recognizing both shared and unique processes within the brain's network dynamics.