With decades of proven success, lasers have become central to many technologies used in manufacturing, communications, medicine and entertainment. Yet laser research continues, advancing current laser technology and developing new types of non-conventional light sources for new applications. We have just pioneered nanophotonic lasers on a graph, formed by nanostructured polymer waveguide meshes, akin to nano-scale spider webs. These are efficient lasers, with a complex emission spectrum composed of many different colours emitting in many directions, that can be understood and tailored using network theory. They also have a unique sensitivity to the illumination profile, which we can use to control the lasing spectrum, and for example reach single colour emission. We now want to push this research into III-V semiconductor laser platform, where lasers are more robust and can be designed with specific topologies. We will employ machine learning and mathematical graph theory to tailor the lasing characteristics, and achieve deterministic spectral, temporal and directional control of the lasing emission. Our goal is to develop tuneable and multi-function lasers, which can be easily integrated into next-generation lab-on-chip devices, able to support the growth of future on-chip optical computation, information technology and diagnostic tools for healthcare. Being able to switch on and off their emission could enable data processing with >10 GHz speeds, and it could act as an optical transistor for analogue optical computing, as re-programmable processing units for neuromorphic computing, for data security, novel imaging and diagnostics technologies taking advantage of their very narrow spectral lines and high sensitivity.