Graph Image Language Techniques Supporting Advanced Classification and Cognitive Interpretation of CT Coronary Vessel Visualizations - Computational Intelligence Paradigms in Advanced Pattern Classification - page 101

where:
V is a finite, non-empty set of graph nodes with unambiguously assigned indices
Σ

is a finite, non-empty set of node labels

Γ is a finite, non-empty set of edge labels

E is a set of graph edges in the form of (v, λ ,w), where v, w ∈ V, λ∈Γ and the in-

dex v is smaller than the index w
ϕ :V →Σ is a function of node labelling

Before we define the representation of the analysed image in the form of IE
graphs, we have to introduce the following order relationship in the set of Г edge
labels: 1 ≤ 2 ≤ 3 ≤ … ≤ 24 and α ≤ β ≤ γ ≤ … ≤ μ. This way, we index all vertices
according to the ≤ relationship in the set of edge labels which connect the main
vertex marked 1 to the adjacent vertices and we index in the ascending order
(i = 2, 3, …, n). After this operation every vertex of the graph is unambiguously
assigned the appropriate index which will later be used when syntactically analys-
ing the graph representations examined. IE graphs generated using the presented
methodology, modelling the analysed coronary vascularisation with their charac-
teristic descriptions (in tables), are presented in the figure below (fig. 8.).

Fig. 8 The representation of the right and the left coronary artery using IE graphs