Both cities and markets are well understood as complex systems which are amenable to analysis using physically inspired methods. Cities have shown fascinating universality with size, while labour markets modelled as networks have considerable explanatory power. Labour markets are a particularly attractive domain of study in this context due to societal importance, the influx of high-resolution data as well as exogenous influence of automation. While much previous work has studied the economic characteristics of cities as a function of size and examined the exposure of urban economies to automation, this has often been from a static perspective. In this work, we examine the diffusive properties of labour markets and examine their variance across cities. More specifically, we identify the occupations which are most important in promoting the diffusion of beneficial or deleterious properties. To this end, we propose a new measure of node centrality empSI. We find that these properties of influence vary considerably with city size.