WB_EEG_CalcNetMeasures is a tool to calculate network measures based on graph theory using BCT toolbox. MATLAB .mat file will be imported as EEG_results structure using WeBrain tool ‘WB_EEG_CalcNetwork’. EEG_reuslts should contain connection matrix M (EEG_results.M) and EEG result type (EEG_results.type) at least. First two dimensions of EEG_results.M should be channels/nodes × channels/nodes, and EEG_results.type should be ‘network’. More details of network measures can be seen in relative paper (Rubinov and Sporns, 2010) and BCT toolbox: https://sites.google.com/site/bctnet/Home.

Parameters

nettype: the type of compatible associated network. Default is using nettype saved in EEG_results (‘[]’）. Nettype can be :

‘BU’: binary undirected network;

‘BD’: binary directed network;

‘WU’: weighted undirected network;

‘WD’: weighted directed network.

proportion: proportions of weights to preserve (proportional thresholding). ONLY used for nettype ‘BD’ or ‘BU’. Default is ‘[0.1:0.1:0.9]’. Range: proportion = 1 (all weights preserved) to proportion = 0 (no weights preserved).

flag: flag = 1: calculate network measures for networks (EEG_results.M) of all epochs

flag = 0: calculate network measures for mean networks (EEG_results.M_mean) across epochs (default).

Links:

BCT toolbox

https://sites.google.com/site/bctnet/Home

Outputs

For each subject, output is a MATLAB .mat file (netmeasure_*.mat) in which is a cell NetMeasure including network measures and parameters.

NetMeasure: a cell array which contains network measures (1×frequencies, proportions×frequencies or proportions×epochs×frequencies)

NetMeasure.nettype: the type of compatible associated network;

NetMeasure.degree: node degree;

NetMeasure.indegree: node indegree;

NetMeasure.outdegree: node outdegree;

NetMeasure.Kn: mean degree of network;

NetMeasure.Kcost: cost of network;

NetMeasure.Kn_in: mean indegree of network;

NetMeasure.Kn_out: mean outdegree of network;

NetMeasure.strength: node strength;

NetMeasure.strength_m: mean node strength of network;

NetMeasure.instrength: node instrength;

NetMeasure.outstrength: node outstrength;

NetMeasure.instrength_m: mean node instrength of network;

NetMeasure.outstrength_m: mean node outstrength of network;

NetMeasure.Cn: node clustering coefficient. The clustering coefficient is the fraction of triangles around a node and is equivalent to the fraction of node’s neighbors that are neighbors of each other;

NetMeasure.Cn_m: mean clustering coefficient of network;

NetMeasure.Ln: characteristic path length of network. The reachability matrix describes whether pairs of nodes are connected by paths (reachable). The distance matrix contains lengths of shortest paths between all pairs of nodes. The characteristic path length is the average shortest path length in the network;

NetMeasure.Eglob: global efficiency of network. The global efficiency is the average inverse shortest path length in the network, and is inversely related to the characteristic path length;

NetMeasure.Eloc: node local efficiency. The local efficiency is the global efficiency computed on the neighborhood of the node, and is related to the clustering coefficient.

NetMeasure.Eloc_m: mean local efficiency of network;

NetMeasure.BC: node betweenness centrality. Node betweenness centrality is the fraction of all shortest paths in the network that contain a given node. Nodes with high values of betweenness centrality participate in a large number of shortest paths;

NetMeasure.BC_m: mean node betweenness centrality of network;

NetMeasure.assort_coef: assortativity coefficient (undirected graph: strength/strength correlation). The assortativity coefficient is a correlation coefficient between the degrees of all nodes on two opposite ends of a link. A positive assortativity coefficient indicates that nodes tend to link to other nodes with the same or similar degree;

NetMeasure.assort_coef1: assortativity coefficient (directed graph: out-strength/in-strength correlation);

NetMeasure.assort_coef2: assortativity coefficient (directed graph: in-strength/out-strength correlation);

NetMeasure.assort_coef3: assortativity coefficient (directed graph: out-strength/out-strength correlation);

NetMeasure.assort_coef4: assortativity coefficient (directed graph: in-strength/in-strength correlation);

NetMeasure.rich_club.rich_coef: rich-club coefficients at level (degree) k, 1×levels. The rich club coefficient at level k is the fraction of edges that connect nodes of degree k or higher out of the maximum number of edges that such nodes might share;

NetMeasure.rich_club.proportion: proportions (0<p<1) of the strongest weights; 1×proportions

NetMeasure.rich_club.rich_coef_proportion: rich-club coefficients of each proportion; proportions × levels

NetMeasure.rich_club.Nk: number of nodes with degree > k;

NetMeasure.rich_club.Ek: number of edges remaining in subgraph with degree > k.

## WB_EEG_CalcNetMeasures

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