BACKGROUND: Neural networks of the brain continually adapt to changing environmental demands. The network approach in neuroscience, which focuses on the analysis of structural and functional network characteristics related to cognitive functions, is a highly promising avenue for understanding the psychophysiological mechanisms underlying the adaptive dynamics of cognitive processes. AIM: We aimed to explore how the topological features of functional connectomes in the human brain are linked to different cognitive demands. The focus was on understanding the dynamic changes in brain networks during working memory tasks to identify network characteristics inherent to working memory. METHODS: We examined the topological characteristics of functional brain networks in the resting state and cognitive load provided by the execution of the Sternberg Item Recognition Paradigm based on electroencephalographic data. Electroencephalogram traces from 67 healthy adults were processed to estimate functional connectivity using the coherence method. We propose that the topological properties of functional networks in the human brain are distinct between cognitive load and resting state, with higher integration in the networks during cognitive load. RESULTS: The topological features of functional connectomes depend on the current state of cognitive processing and change with task-induced cognitive load variation. Moreover, functional connectivity during working memory tasks showed a faster emergence of homology group 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. CONCLUSION: Collected evidence suggest that cognitive states, particularly those related to working memory, are associated with distinct topological properties of functional brain networks, highlighting the importance of network dynamics in cognitive processing.