262 J. Gosliga et al. Algorithm 3 Modified Bron-Kerbosch R: set of nodes to be reported P: set of nodes which can be added toR, because they are adjacent to node uvia c-edges D: set of nodes which cannot be directly added to R, because they are adjacent to uvia d-edges T: set of nodes which have already been used to initiate the ENUMERATEC-CLIQUES algorithm Ec: set of c-edges for the graph G 1: procedure ENUMERATEC-CLIQUES(R, P, D, X, T) 2: Let P be the set {u1, . . . ,uk} 3: if P =∅andX=∅then 4: report R 5: else 6: for i ←1to k do 7: P ←P\{ui} 8: N ←{v ∈V | (ui,v) ∈E} 9: for all v ∈Ddo 10: if (v,ui) ∈Ec then 11: if v ∈T then 12: X←X∪{v} 13: else 14: P ←P ∪{v} 15: end if 16: D←D\{v} 17: end if 18: end for 19: ENUMERATEC-CLIQUES(R∪{ui}, P ∩N, D∩N, X∩N, T) 20: X←X∪{ui} 21: end for 22: end if 23: end procedure Fig. 26.7 The maximum common connected induced subgraph of the two graphs shown in Fig. 26.2 The left-hand entries in node labels (A, B, C, D, E) correspond to the wind turbine, and so node and edge attributes can be found in Tables 26.1 and 26.3, whereas the right-hand entries in the node labels (A2, A3, N, M, L) correspond to the aeroplane and can be used to find node attributes from Tables 26.2 and 26.4. For example, the geometry class and shape for node in the wind turbine is ‘Beam, Aerofoil’, and for node N in the aeroplane the geometry class and shape is also ‘Beam, Aerofoil’ so there is a match. However, node D in the wind turbine represents complex geometry, while node A3 in the aeroplane represents a shell, so these do not match. The comparison is performed at the greatest possible level of resolution, if the geometry class matches, then the shape is compared. If the shape matches, then the dimensions for each are examined. If the elements match on all levels, then they are essentially identical. This is shown as a flowchart in Fig. 26.9. This is true for the case of materials as well. If the material class, specific material and material properties are all the same, then the two elements are made from the same material.
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