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 6  gateway_coeff(g, memb, centr = c("btwn.cent", "degree", "strength"),
A = NULL)
part_coeff(g, memb, A = NULL)
within_module_deg_z_score(g, memb, A = NULL)

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: 
A 
Numeric matrix; the adjacency matrix of the input graph. 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 withinmodule degree zscore 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, withinmodule degree zscores, or gateway coefficients for each vertex of the graph.
Christopher G. Watson, cgwatson@bu.edu
Vargas, E.R. and Wahl, L.M. (2014) The gateway coefficient: a novel metric for identifying critical connections in modular networks. Eur Phys J B, 87, 161–170. https://dx.doi.org/10.1140/epjb/e2014408007
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. https://dx.doi.org/10.1088/17425468/2005/02/P02001
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