Mycorrhizal networks (MNs), or the networks of fungal mycelia that connect plants to each other, are vital in contributing to the well-being of ecosystems. They not only assist in the transport of nutrients across an ecosystem, but also help protect an ecosystem from disease and adverse conditions. However, more research into these networks is needed and modelling these networks as graphs can help us achieve this. By applying centrality analysis and performing k-core partitioning on these networks, we are able to identify the trees that are most important and central to a MN and observe the effects of removing these trees. We also perform random partitioning on these networks and compare the results to the k-core partitioning results. We found that these networks are fairly resilient to the removal of a single keystone individual, but this can disrupt the interconnectedness of a MN in a dry (xeric) moisture regime. We also found that these networks are less resilient to k-core partitioning. In a network of trees divided up by age cohorts, the maximal k-core subgraph contained a mix of trees that mostly belonged to older cohorts and were linked to one specific fungal genet. This could influence conservation efforts for not only a few older trees, but also some younger trees and potentially specific fungal genets. When removing the maximal k-core subgraphs for networks in dry (xeric) and moist (mesic) moisture regimes, the network became disconnected for the xeric graph and still somewhat connected for the mesic graph. So, mycorrhizal networks could possibly be more resilient to this k-core partitioning in an area where the soil is moist rather than dry.