In recent years the Mission Design Center (MDC) at NASA Ames Research Center has been studying mission concepts involving clusters of small spacecraft capable of providing cost-effective solutions in orbit compared to space missions involving only a single larger spacecraft. Low-cost networks of small spacecraft can be a viable alternative to large budget Earth observation or space exploration missions producing significant scientific return for often moderate development efforts and short lead times. This paper is the first in a series of 3 companion papers in which we make the point that the scientific value (and hence the cost effectiveness) of small multi-spacecraft missions can be further increased if the network of spacecraft is allowed to be heterogeneous. We define Heterogeneous Spacecraft Networks (HSNs) to be networks of spacecraft having different operators or originating from different missions that are able to communicate with each other in a low-cost manner and with low impact on overall system resources. HSN incorporates both the space segment and ground segment for an end-to-end solution. In this contribution we illustrate the strength of the HSN approach by presenting a general concept for a HSN in LEO as well as a case study showcasing the value of such a network. In particular, we present a case study where we examine the feasibility of a low-cost, multi-institutional network of small spacecraft acting as a next-generation Earth Observation (EO) platform and focusing on ad-hoc data relay to maximize throughput. In the simulation we show that the downlink throughput of an HSN can be larger by an order of magnitude compared to the conventional scenario where no networking capability exists. Other benefits of using a HSN as a next-generation increment of existing capabilities include increased revisit frequencies as well as the ability to collect correlated data simultaneously from distributed locations around the globe using either conventional or fractionated spacecraft. We list key performance requirements for a HSN in order to produce a desirable scientific return and present a concept of operations (ConOps) for the practical implementation. In the ConOps we discuss the required performance of the inter-satellite and space-to-ground links and give an overview of the associated ground station network. We give an overview of the network management techniques required to operate and control the network on a day-to-day basis and address the issues of network configuration, network discovery and security, as well as fault and performance management. The paper ends with an outlook on the paradigm shift HSNs may introduce in the domain of space operations. We also list a number of promising applications making use of the strength of the concept.