Network Analyses

Network analyses use graph-theoretic approaches to identifying/quantifying/describing/classifying networks of any sort. For example, a network analysis could be used to identify potential bottlenecks in a city design when large numbers of people have to evacuate, or the robustness of a distributed computer network to disruption in the event that one or more redundant servers goes offline.

In our lab, we apply these analytic approaches to networks that describe functional (primarily) or anatomical (potentially) connectivity. Under certain assumptions about what functional role various network nodes play, we can test hypotheses about how the connections between these nodes relates to cognitive processing. Most of our work here will be done in MATLAB and using networks that are represented as adjacency matrices. An adjacency matrix is an NxN square matrix that has entries that indicate whether there is a connection (and potentially how strong it is) between any two of the N nodes in the network. Using the Louvain 2008 parcellation scheme, for example, we break the cortical surface up into up to 1000 regions. Each region is a node in the network, and so the adjacency matrix for this network is a 1000 x 1000 square matrix. What follows assumes that you have obtained an adjacency matrix, one way or another, and wish to carry out different types of network analyses on it.

Identify Clusters/Subnetworks

One of the first things we might wish to do is identify the network community structure of our brain networks. When visualized as a sorted connectivity matrix or rendered on a brain map, this allows us to make inferences of the nature of processing taking place during the period captured in the time series data.

Obtain Network Metrics

Though visualization of network communities is instrumental to interpreting the data, we are going to rely on the hard numbers provided by various metrics of network properties over which we can carry out any number of statistical analyses we have at our disposal.