Fungal mycelia that grow out of woody resources into soil, in search of spatially and temporally heterogeneously distributed resources, form a responsive network. These networks are extensive and long-lived, eventually covering several m2 to many hectares, the largest recorded to date - a genet of Armillaria ostoyae - spans 965 hectares, with a maximum separation of 3810 m and estimated as 1900-8650 years old. The extent of connectivity within the system is, however, unknown. Though persistent, established systems are dynamic both in terms of: (1) continued extension at growing fronts; and (2) renewed mycelial growth from mature cords enabling colonization of the newly arrived resources. Within the mycelial networks there is considerable scope for communication, since hyphae maintain continuity with their immediate ancestors and if contact is made with neighbouring regions can become connected via de novo formation of cross-links (anastomoses). There is thus both radial and tangential connectivity, resulting in systems with many connected loops. The mycelium has evolved differently in different species resulting in a range of network architectures, imparting different ecological characteristics. The mycelial architecture of different species, and to some extent the same individual in different environmental scenarios, appears to be adapted differently for differing balances of exploration, transport efficiency, and resilience to damage. Highly interconnected mycelia are costly to construct but offer alternate transport/information routes and consequently resilience to damage. Sparse networks, with fewer interconnections, can extend further for a given construction cost, but risk the loss of pathways if part of the network becomes damaged. Graph theory and statistical mechanics provide tools for analysing networks. Here we take a network-based approach to the analysis of mycelia as transport, information and foraging systems.