Software systems running in an enterprise consist of countless components, having complex dependencies, are hosted on physical or virtualized environments, and are scattered across the infrastructure of an enterprise, ranging from on-premise data centers up to public cloud deployments. The resulting topology of the current IT landscape of an enterprise is often extremely complex. We show that information about this complex ecosystem can be captured in a graph-based structure, the enterprise topology graph. We argue that by using such a graph-based representation many challenges in Enterprise Architecture Management (EAM) can be tackled through the aid of graph processing algorithms. However, the high complexity of an enterprise topology graph is the main obstacle to this approach. An enterprise topology graph may consist of millions of nodes, each representing an element of the enterprise IT landscape. Further, these nodes comprise a large variety of properties and relationships, making the topology hardly manageable by human users and software tools. To address this complexity problem, we propose different mechanisms to make enterprise topology graphs manageable. Segmentation techniques, tailored to specific use cases, extract manageable segments from the enterprise topology graph. Based on a set of formally defined transformation operations we then demonstrate the power of the approach in three application scenarios.