The functional network of the brain continually adapts to changing environmental demands. The environmental changes closely connect with changes of active cognitive processes. In recent years, the network approach has emerged as a promising method for analyzing the neurophysiological mechanisms that underlie psychological functions. The present study examines topological characteristics of functional brain networks in resting state and in cognitive load, provided by the execution of the Sternberg Item Recognition Paradigm (SIRP) based on electroencephalographic data. We propose that the topological properties of the functional networks in the human brain are distinct between cognitive load and resting state with higher integration in the networks during cognitive load. It was shown that topological features of functional connectomes strongly depend on the type of cognitive process performed by the subject and change in accordance with task change. The analysis also demonstrated that functional connectivity during working memory tasks showed a faster emergence of homology groups generators, supporting the idea of a relationship between the initial stages of working memory execution and an increase in faster network integration, with connector hubs playing a crucial role.
