Cognition emerges from interactions within spatially distributed but synchronized brain networks. Such networks are transient and dynamic, established on the timescale of milliseconds in order to perform specific cognitive operations. But it is not known whether topological features of transient cognitive networks contribute to cognitive processing. Cognition might merely change weights of intrinsic functional networks or, conversely, cognitive processing might require qualitatively new topological arrangements. To address this question, we recorded high-density EEG when subjects performed a visual discrimination task and characterized source-space weighted functional networks with graph measures. We revealed rapid, transient, and frequency-specific reorganization of the network’s topology during cognition. Specifically, cognitive networks were characterized by strong clustering, low modularity, and strong interactions between hub-nodes. Our findings suggest that dense and clustered connectivity between the hub nodes belonging to different modules is the “network fingerprint” of cognition. Such reorganization patterns might facilitate global integration of information and provide a substrate for a “global workspace”; necessary for cognition and consciousness to occur. Thus, characterizing topology of the event-related networks opens new vistas to interpret cognitive dynamics in the broader conceptual framework of graph theory.