vertex_roles: Gateway coefficient, participation coefficient, and...

Description Usage Arguments Details Value Author(s) References

Description

gateway_coeff calculates the gateway coefficient of each vertex, based on community membership.

part_coeff calculates the participation coefficient of each vertex, based on community membership.

within_module_deg_z_score is a measure of the connectivity from a given vertex to other vertices in its module/community.

Usage

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gateway_coeff(g, memb, centr = c("btwn.cent", "degree", "strength"))

part_coeff(g, memb)

within_module_deg_z_score(g, memb)

Arguments

g

An igraph graph object

memb

A numeric vector of membership indices of each vertex

centr

Character string; the type of centrality to use in calculating GC (default: btwn.cent)

Details

The gateway coefficient G_i of vertex i is:

G_i = 1 - ∑_{S=1}^{N_M} ≤ft ( \frac{κ_{iS}}{κ_i} \right )^2 (g_{iS})^2

where κ_{iS} is the number of edges from vertex i to vertices in module S, and κ_i is the degree of vertex i. N_M equals the number of modules. g_{ii} is a weight, defined as:

g_{iS} = 1 - \bar{κ_{iS}} \bar{c_{iS}}

where

\bar{κ_{iS}} = \frac{κ_{iS}}{∑_j κ_{jS}}

for all nodes j in node i's module, and

\bar{c_{iS}} = c_{iS} / max(c_n)

The participation coefficient P_i of vertex i is:

P_i = 1 - ∑_{s=1}^{N_M} ≤ft ( \frac{κ_{is}}{κ_i} \right )^2

where κ_{is} is the number of edges from vertex i to vertices in module s, and κ_s is the degree of vertex i. N_M equals the number of modules.

As discussed in Guimera et al., P_i = 0 if vertex i is connected only to vertices in the same module, and P_i = 1 if vertex i is equally connected to all other modules.

The within-module degree z-score is:

z_i = \frac{κ_i - \bar{κ}_{s_i}}{σ_{κ_{s_i}}}

where κ_i is the number of edges from vertex i to vertices in the same module s_i, \bar{κ}_{s_i} is the average of κ over all vertices in s_i, and σ_{κ_{s_i}} is the standard deviation.

Value

A vector of the participation coefficients, within-module degree z-scores, or gateway coefficients for each vertex of the graph.

Author(s)

Christopher G. Watson, [email protected]

References

Vargas E.R. & Wahl L.M. (2014) The gateway coefficient: a novel metric for identifying critical connections in modular networks. Eur Phys J B, 87:161-170.

Guimera, R. and Amaral, L.A.N. (2005) Cartography of complex networks: modules and universal roles, Journal of Statistical Mechanics: Theory and Experiment, 02, P02001.


brainGraph documentation built on May 29, 2018, 9:03 a.m.