The core of network transport capability is its flexibility, which represents the capability of the urban centralized heating system (UCHS) of managing the balance between heating demand, energy storage and multiple heating sources (including renewable-energy-based sources). This study carries out the flexibility analysis of UCHS by proposing an index of heating network flexibility (HNF) and formulating its evaluation methodology. HNF quantifies UCHS's capability of delivering heat to substations under different operating scenarios and enhancement measures. We take a northeastern Chinese city as an example to show the effectiveness of flexibility analysis by investigating the impact of network topological structure change and adding booster pumps. Both measures change overall flexibility. Results show that system-wide measure such as adding a new pipeline does not solve imbalance of flexible transport capability among substations even when it is added next to heating sources. The local measure such as booster pumps has more impact on flexibility enhancement but is only effective to part of substations. The index of flexibility could be used in the design and operation of large-scale complex multi-source UCHS. (C) 2019 Elsevier Ltd. All rights reserved.