Fig 1.
Clique and neighbourhood complex of star graph on 5 vertices S5.
Fig 2.
(a)* Rural agricultural system in Southern-Madagascar described as a social–ecological network [4], (b) Pairwise network representation of the social-ecological system, Ei’s and Si’s represent ecological and social units respectively.
Table 1.
Dimension of different simplicial complexes corresponding to complete graphs.
Fig 3.
Plot of simmelian brokerage and topological dimension of clique complex C(NM).
Table 2.
Table showing the q-analysis of the simplicial complex (neighbourhood complex).
The first column is the different connectivity levels of the complex. The second column is the number of q-connected components at each level, while the third column reports the names of the simplices making up each q-connected component.
Fig 4.
(a) 1-nearness in the simplices of dimension 2 formed by the combination of social and ecological units (b) 1-nearness in the simplices of dimension 2 formed by the ecological units alone.
Fig 5.
1-nearness between facet of dimension 2 and a simplex of dimension 3.
Both the simplices shared a 1-dimensional face {S5, E14} with each other.
Fig 6.
2-nearness between two simplices of dimension 3, red shaded simplex is the common to both the simplices.
In (A) 3-simplices {E10, E13, E14, S5} and {E13,E14,S5,S3} shared a common 2 dimensional simplex {E13, E14, S5}. In (B) 2-simplex {S3, E7, S4} is shared by two 3-simplices.
Fig 7.
Simplex S3 of dimension 11 corresponding to social unit S3, whose structure is given as: S3 = {E2, E3, E4, E5, E6, E7, E8, E9, E13, E14, S4, S5}, it consist 12 vertices.
Fig 8.
(a) Neighbourhood complex of pairwise network NM of dimension 11 (b) Clique complex of pairwise network NM of dimension 3.
Table 3.
Table showing the q-analysis of the simplicial complex (neighbourhood complex).
The first column is the different connectivity levels of the complex. The second column is the number of q-connected components at each level, while the third column reports the names of the simplices making up each q-connected component.
Table 4.
Different structural vectors of clique complex and neighbourhood complex of NM.
The dimension of all the structural vectors of clique complex is 4, whereas dimension of all the structural vectors of neighbourhood complex is 12.
Fig 9.
Plot of first and second structural vectors of (a) Clique complex and (b) Neighbourhood complex.
Table 5.
List of top simplices with eccentricity values in both simplicial complexes.