The Internet topology is of high importance in designing networks and architectures, evaluating performance, and economics. Interconnections between domains (ASes), routers, and points of presence (PoPs), have been measured, analyzed, and modeled. However, existing models have some serious shortcomings, related to ease, accuracy and completeness of measurements, and limited applicability to emerging research areas. To this end, in this paper, we propose a novel approach towards capturing the inter-domain Internet topology. Motivated by the recent interest in the Internet eXchange Points (IXPs), we introduce a network graph model based on IXPs and their AS memberships. The proposed model aims to complement previous modeling efforts, shed light on unexplored characteristics of the Internet topology, and support new research directions. We also collect and make available Internet connectivity data, analyze main topological properties, and discuss application-related issues.