Network measures
In the Network Measures section, it is possible to compute some network metrics on the previously extracted connectivity measures.
Currently, you can compute:
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Betweenness Centrality
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Clustering Coefficient
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Eigenvector Centrality
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GeneRank Centrality
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Katz Centrality
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Strength
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Subgraph Centrality
In particular, it is possible to select the connectivity measure and the network measure to extract: Athena will automatically extract the connectivity matrix (averaged between the epochs) from each subject, in order to use it as the adjacency matrix on which execute the computations.
Furthermore, it is also possible to normalize by dividing the vector corresponding to each frequency band for its maximum value, obtaining a network measure matrix which values are between 0 and 1.
At the end of the computation, the resulting matrix (locations x bands) related to each subject will be saved in a subfolder of the chosen connectivity measure, named Networks, and in particular inside a subdirectory which will have the name of the analyzed network measure.
Each resulting file will be a .mat file which contains a single variable named data, representing the metrics matrix, while the files will be named as the subject name.
Following, you can find a brief introduction on the adjacency matrix and the network measures, but if you already feel comfortable with them, you can go further and extract some network measure on your connectivity data, or go back to the analysis list.
Considering a graph in which its elements (nodes) are linked or not, the adjacency matrix is a square matrix used to represent the connections between them.
In particular, the elements of the matrix indicate whether two nodes are adjacent or not in the graph.
This matrix can be seen as a grid (nodes x nodes), in which each element represents a "value" to the connection between the node corresponding to the row index and the one corresponding to the column index.
If the graph is undirected, all these connection are bidirectional, so its value from the node A to the node B will be the same from the node B to the node A: the matrix will be symmetrix.
Furthermore, in simple graph, there is no connection between a node and itself, so the corresponding adjacency matrix will have only zeros on its principal diagonal.
These symmetry and zero-diagonal symmetry are the same as the matrix related to an undirected connectivity measure, which so can be used as adjacency matrix in order to evaluate some network metrics on it.
The network metrics are used to study structural and functional brain networks, because they allows to verify changes in their topological organization, in particular for brain disorders such as the Alzheimer’s Disease and the multiple sclerosis.
In general, the topology of networks can be:
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binary or weighted
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directed or undirected
Actually, Athena is able to manage binary undirected network metrics, as they are applied to functional connectivity measures.
Most of the analyzed network measures are centrality measures, as the centrality of a given node represents its importance and influence in the network.
There are many different centrality measures, which can have different meanings, so it is necessary to identify the centrality measures which is the most appropriate for the analysis which has to be computed.
Considering the brain networks, the centrality of a node of that network is proportional to the effectiveveness of that node in the information transmission of the brain network.
An example of the use of these measures in brain network analysis is the identification of hub brain regions: the centrality values related to all brain regions are esimated, then a threshold is used as minimum value to determine the hub nodes.
The Strength (Degree centrality) of a node in a given network is given by the its total degree.
This network metric measures the ability of a node to communicate with other nodes in the same network.
Essentially, the node which shows an higher strenght (degree) value is the most central node, and it is in that sense "the most important node".
In brain network analysis, this centrality measure represents the direct impact of the brain region on other adjacent brain regions.
The Eigenvector Centrality takes into consideration the importance of neighbours of a node in the network, giving each node a score which is proportional to the sum of the score of its neighbours.
In that sense, a node is important if it is linked to other important nodes.
In particular, it evaluates the principal eigenvector (which corresponds to the principal eigenvalue) and, since the eigenvector centralities correspond to the principal eigenvector, the node which shows the higher corresponding eigenvector centrality is considered as the most important one in the network.
The Betweenness Centrality measures the number of shortest paths which include the considered node in the newtork.
In particular, its value corresponds the fraction of all shortest paths in the network that contain a given node.
In brain network analysis, this network metric measures the impact of the brain region on the flow of information across the whole brain network.
The Clustering Coefficient measures of the degree to which nodes in the network tend to cluster together.
In particular, its value corresponds to the fraction of node’s neighbors that are neighbors of each other.
The Katz centrality considert both the number of neighbours and the further connections of a node in the network, so it considers a node as important if it has universal connections to other nodes in the network.
This network measure considers also an attenuation factor, which has to be included between 0 and the inverse of the maximum eigenvalue of the adjacency matrix (for this reason, the fraction of this maximum value can be inserted as input, and the corresponding value will be automatically computed).
The PageRank Centrality measures the transitive influence or connectivity of the nodes of a network, by iteratively distributing one node’s rank (based on degree) over its neighbours or by traversing the network in a random way and counting the frequency of hitting each node during these walks.
This network metric is a variant of the Eigenvector Centrality, while the GeneRank Centrality is an adaptation used for biological connectivity matrices.
The Subgraph centrality measures the centrality of a node by considering the participation of each node in all the possible subgraphs of the network, by counting (inderectly) the number of closed walks in the network which start and end at a given node in the network.
So, this network metric evaluates the centrality of a node as th weighted sum of closed walks of different lengths in the network starting and ending at the node itself.