This paper proposes a method to analyze the feasibility of monitoring missions of infrastructure networks (eg. railways, roads, power lines, etc.) by Unmanned Aerial Vehicles (UAVs). The method consists in evaluating the risk at ground for people due to an UAV flying over each part of the network. Based on a risk categorization defined by probability and exposition time, several metrics are developed to analyze the feasibility of flights in terms of risk. More specifically, these metrics are related to the cumulative length of feasible flight segments and their connectedness. A decision making process is then defined to automatically classify all the lines of the network in a comprehensive and synthetic way. The whole method takes into account flight regulation and flight operation constraints as well as considerations relative to business interests in asset management of the infrastructure network. An illustration is proposed through a benchmark example on the French railway network.