Visualization in Connectomics - Scientific Visualization: Uncertainty, Multifield, Biomedical, and Scalable Visualization - page 223

21.8.1 Network Measures

For each of the brain connectivity types (anatomical, functional, effective), one can
extract networks from data obtained by an appropriate brain imaging modality [ 10 ,
54 ]. The next step is to characterize such networks. In the last decade, a multitude
of topological network measures have been developed in an attempt to characterize
and compare brain networks [ 11 , 45 , 78 , 90 ]. Such measures characterize aspects
of global, regional, and local brain connectivity. 2 Examples of global measures are
characteristic path length, clustering coefficient, modularity, centrality, degree dis-
tribution, etc. Some of them, such as clustering coefficient or modularity, refer to
functional segregation in the brain, i.e., the ability for specialized processing to occur
in densely interconnected groups of brain regions. Others characterize functional
integration , i.e., the ability to rapidly combine specialized information from distrib-
uted brain regions [ 78 , 90 ]. Typical measures in this class are based on the concept
of paths in the network, e.g., characteristic path length or global efficiency (aver-
age inverse shortest path length). It is believed that both anatomical and functional
brain connectivity exhibit small-world properties , i.e., they combine functionally
segregated modules with a robust number of intermodular links [ 3 , 88 ]. The degree
distribution can be used as a measure of network resilience, i.e., the capacity of the
network to withstand network deterioration due to lesions or strokes.
For characterizing networks on a local scale one uses single node features such as
in-degree and out-degree, or the local clustering coefficient. Typical regional network
measures are network motifs , which are defined as patterns of local connectivity. A
typical motif in a directed network is a triangle, consisting of feedforward and/or
feedback loops. Both anatomical and functional motifs are distinguished. The signif-
icance of a certain motif in a network is determined by its frequency of occurrence,
and the frequency of occurrence of different motifs around a node is known as the
motif fingerprint of that node.

21.8.2 Brain Network Comparison and Visualization

The comparison of different brain networks presents challenging problems. Usually
the networks differ in number and position of nodes and links, and a direct comparison
is therefore difficult. One possible approach is to compute a network measure for
each of the networks, and then compare the network measures. However, this loses
spatial information. For interpretation and diagnosis it may be essential that local
differences can be visualized in the original network representation [ 27 , 86 ]. This
asks for the development of mathematical methods, algorithms and visualization
tools for the local comparison of complex networks—not necessarily of the same
size—obtained under different conditions (time, frequency, scale) or pertaining to
different (groups of) subjects.

2 Similar approaches have been used in genomics [ 62 , 84 ] and other areas.