We start our examination of network forms by considering the ideal network that would allow us to completely describe the spread of any infectious pathogen. Such a network would be derived from an omniscient knowledge of individual behaviour. We define G i, j (t) to be a time-varying, real, and high-dimensional variable that informs about the strength of all potential transmission routes from individual i to individual j at time t. Any particular infectious disease can then be represented as a function ( f pathogen ) translating this high-dimensional variable into an instantaneous probabilistic transmission rate (a single real variable). In this ideal, G subsumes all possible transmission networks, from sexual relations to close physical contact, face-to-face conversations, or brief encounters, and quantifies the time-varying strength of this contact. The disease function then picks out (and combines) those elements of G that are relevant for transmission of this pathogen, delivering a new (single-valued) timevarying infection-specific matrix (T i, j (t) = f pathogen (G i, j (t))). This infection-specific matrix then allows us to define the stochastic dynamics of the infection process for a given pathogen. (For even greater generality, we may want to let the pathogen-specific function f also depend on the time since an individual was infected, such that time-varying infectivity or even time-varying transmission routes can be accommodated.)