Table 1 Two components core definitions for various kind of networks

Two-mode

X₁⊆V₁,X₂⊆V₂

BHA-core subgraph \(G^{\prime }=G_{W_{1},W_{2}}\) of \(G_{X_{1},X_{2}}\) s.t.

in G^′

degrees in W₁ at least h and

degrees in W₂ at least a

Directed

X₁⊆V,X₂⊆V

BHA-core subgraph \(G^{\prime }=G_{W_{1},W_{2}}\) of \(G_{X_{1},X_{2}}\) s.t.

in G^′

outdegrees in W₁ at least h and

indegrees in W₂ at least a

Undirected

X₁⊆V,X₂⊆V

StSa-core subgraph G^′=G_St,Sa of \(G_{X_{1},X_{2}}\) s.t.

in G^′

degrees in St at least k and

degrees in Sa at least 1