Description Usage Arguments Details Value Author(s) References

`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.

1 2 3 4 5 | ```
gateway_coeff(g, memb, centr = c("btwn.cent", "degree", "strength"))
part_coeff(g, memb)
within_module_deg_z_score(g, memb)
``` |

`g` |
An |

`memb` |
A numeric vector of membership indices of each vertex |

`centr` |
Character string; the type of centrality to use in calculating
GC (default: |

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.

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

Christopher G. Watson, [email protected]

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.

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