In recent years bottom-up network models that aim to capture how various brain processes propagate on the brain’s structural connectivity network have been proposed. These spread models are motivated by mounting evidence that both brain activity and various neurodegenerative diseases spread along fiber pathways and ramify within wider brain circuits in a stereotyped fashion. In the case of functional activity, this gives rise to canonical functional networks. In the case of neurodegeneration, the spread is underpinned by a so-called “trans-neuronal transmission” mechanism shared by all common degenerative pathologies, for example Alzheimer’s disease, Parkinson’s disease, frontotemporal dementia, corticobasal degeneration, etc. In this talk I will describe some of these graph theoretic models of spread. First, I will summarize how conventional graph theory metrics like small-world and path length are used in neuroimaging. Then I will specifically highlight the Network-Diffusion model, which seeks to capture network spread via a diffusive process restricted on the structural connectome. We will review the basic network mathematics that governs these diffusion processes. Finally we will show several examples from neuroimaging studies, specifically addressing how the network diffusion model can capture the relationship between structural connctome and functional connectome. Examples of successful network spread modeling in Alzheimer, Parkinson, frontotemporal dementia and aphasias will be presented.