There is a paucity of graph-theoretic methods applied to task-based data in schizophrenia (SCZ). Tasks are useful for modulating brain network dynamics, and topology. Understanding how changes in task conditions impact inter-group differences in topology can elucidate unstable network characteristics in SCZ. Here, in a group of patients and healthy controls (n = 59 total, 32 SCZ), we used an associative learning task with four distinct conditions (Memory Formation, Post-Encoding Consolidation, Memory Retrieval, and Post-Retrieval Consolidation) to induce network dynamics. From the acquired fMRI time series data, betweenness centrality (BC), a metric of a node’s integrative value was used to summarize network topology in each condition. Patients showed 1) differences in BC across multiple nodes and conditions; 2) decreased BC in more integrative nodes, but increased BC in less integrative nodes; 3) discordant node ranks in each of the conditions, and 4) complex patterns of stability and instability of node ranks across conditions. These analyses reveal that task conditions induce highly variegated patterns of network dys-organization in SCZ. We suggest that the dys-connection syndrome that is schizophrenia, is a contextually evoked process, and that the tools of network neuroscience should be oriented toward elucidating the limits of this dys-connection.