The Brain Network Analysis is oriented to apply and develop algorithms able to extract relevant features from cerebral complex networks. 

Since a graph is a mathematical representation of a network, which is essentially reduced to nodes and connections between them, a way to characterize topological properties of real complex networks was proposed using a graph theoretical approach (Strogatz et al., 2001; Wang and Chen, 2003; Sporns et al., 2004). 

In particular for the brain, it was realized that functional connectivity networks estimated from EEG or magnetoencephalographic (MEG) recordings can be analyzed with tools which have been already generated for the treatments of graphs as mathematical objects (Stam et al., 2004).

My study aims at objectively and concisely describing the characteristics of the cortical networks estimated by MVAR models from High Resolution EEG signals. By means of tools derived from the graph theory specific indexes related to the topology of the functional networks estimated from MVAR models on High Resolution EEG signals could be obtained.  

Among these, the Indegree (i.e. the number of connections incoming to a node) and the Outdegree (i.e. the number of connections outgoing from a node) indexes, indicate how much a cortical region is influenced by other areas and how many potential functional targets does it have, respectively. Anhoter useful parmater is the Efficiency, a quantity recently introduced in (Latora and Marchiori, 2001) to measure how efficiently the nodes of the network communicate. 

The main experimental questions regard the possibility to detect some differences in the network’s efficiency between groups or conditions during motor or cognitive tasks. Moreover, is of interest to check if the efficiencies values could change along different frequency contents. Finally, the contrast with random graphs could elicit the significance of the cortical networks estimated allowing to assert the particular structure of such real biological systems.

The following figure show values of global and local efficiency obtained from the comparison of a Spinal Cord Injured (SCI) group of patients and a Control group of healthy subjects during a motor task (Human Brain Mapping, in press).