A network model for soil pore space is developed and applied to the analysis of biological invasion of microorganisms in soil. The model was parameterized for two soil samples with different compaction (loosely and densely packed) from images derived from an X-ray micro-tomography system. The data were then processed using 3-D imaging techniques, to construct the networks of pore structures with in the soil samples. The network structure is characterized by the measurement of features that are relevant for biological colonization through soil. These include the distribution of channel lengths, node coordination numbers, location and size of channel bottlenecks, and the topology of the largest connected cluster. The pore-space networks are then used to investigate the spread of a microorganism through soil, in which the transmissibility between pores is defined as a function of the channel characteristics. The same spreading process is investigated in artificially constructed homogeneous networks with the same average properties as the original ones. The comparison shows that the extent of invasion is lower in the original networks than in the homogeneous ones: this proves that inherent heterogeneity and correlations contribute to the resilience of the system to biological invasion.