We describe how the recently introduced method of significant subgraph mining can be employed as a useful tool in neural network comparison. It is applicable whenever the goal is to compare two sets of unweighted graphs and to determine differences in the processes that generate them. We provide an extension of the method to dependent graph generating processes as they occur, for example, in within-subject experimental designs. Furthermore, we present an extensive investigation of the error-statistical properties of the method in simulation using Erdős-Rényi models and in empirical data in order to derive practical recommendations for the application of subgraph mining in neuroscience. In particular, we perform an empirical power analysis for transfer entropy networks inferred from resting-state MEG data comparing autism spectrum patients with neurotypical controls. Finally, we provide a Python implementation as part of the openly available IDTxl toolbox. Author Summary A key objective of neuroscientifc research is to determine how different parts of the brain are connected. The end result of such investigations is always a graph consisting of nodes corresponding to brain regions or nerve cells and edges between the nodes indicating if they are connected or not. The connections may be structural (an actual anatomical connection) but can also be functional, meaning that there is a statistical dependency between the activity in one part of the brain and the activity in another. A prime example of the latter type of connection would be the information flow between brain areas. Differences in the patterns of connectivity are likely to be responsible for and indicative of various neurological disorders such as autism spectrum disorders. It is therefore important that efficient methods to detect such differences are available. The key problem in developing methods for comparing patterns of connectivity is that there is generally a vast number of different patterns (it can easily exceed the number of stars in the milky way). In this paper we describe how the recently developed method of significant subgraph mining accounts for this problem and how it can be usefully employed in neuroscientific research.

Network inference algorithms are valuable tools for the study of large-scale neuroimaging datasets. Multivariate transfer entropy is well suited for this task, being a model-free measure that captures nonlinear and lagged dependencies between time series to infer a minimal directed network model. Greedy algorithms have been proposed to efficiently deal with high-dimensional datasets while avoiding redundant inferences and capturing synergistic effects. However, multiple statistical comparisons may inflate the false positive rate and are computationally demanding, which limited the size of previous validation studies. The algorithm we present—as implemented in the IDTxl open-source software—addresses these challenges by employing hierarchical statistical tests to control the family-wise error rate and to allow for efficient parallelization. The method was validated on synthetic datasets involving random networks of increasing size (up to 100 nodes), for both linear and nonlinear dynamics. The performance increased with the length of the time series, reaching consistently high precision, recall, and specificity (>98% on average) for 10,000 time samples. Varying the statistical significance threshold showed a more favorable precision-recall trade-off for longer time series. Both the network size and the sample size are one order of magnitude larger than previously demonstrated, showing feasibility for typical EEG and magnetoencephalography experiments.