Graph

Graph consists of Graph Nodes ¬

Graph Node is a Graph Object ®

Graph consists of Direct Links ¬

Link is based on Graph Nodes –

<Each link is based on two graph nodes exactly.>

Direct Link is a Link º

{It’s a link connecting nodes in a graph directly.}

Indirect Link is a Link º

<A link is to be either direct or indirect.>

Graph consists of Indirect Links ¬

{Indirect links for a graph are calculated from its direct links.}

<If the graph is undirected, two graph nodes are linked indirectly if they are linked and there is no a direct link between them.>

<If the graph is directed, a graph node A is linked to a graph node B indirectly if there is a path from A to B and there is no a direct link from A to B.>

Graph. Undirected Graph

Undirected Graph is a Graph º

<Undirected graph consists of undirected links only.>

Undirected Link is a Link º

Undirected Link has Graph Nodes –

<Undirected link has the same graph nodes as its link.>

Graph. Directed Graph

Directed Graph is a Graph º

<Directed graph consists of directed links only.>

Directed Link is a Link º

<The link is based on source and target graph node, and vice versa.>

Directed Link is going from a Source Graph Node ®

Directed Link is going to a Target Graph Node ®

Source Graph Node is a Graph Node º

Target Graph Node is a Graph Node º

Graph. Connected Graph

Graph Node pertains to a Connected Sub-Graph º

<If the graph node pertains to an undirected graph, all linked graph nodes pertains to the same connected sub-graph. All graph nodes not forced to pertain to the same sub-graph by the previous constraint, are to pertain to different connected sub-graphs. A graph not linked with others is a separate connected sub-graph.>

<If the graph node pertains to a directed graph, all graph nodes of one graph node cycle pertains to the same connected sub-graph. Two graph nodes A and B are in one sub-graph, if there is a direct or indirect link (A->B) and a direct or indirect link (B->A). Graph nodes not combined with others are separate connected sub-graphs.>

Connected Graph is a Graph º

<All graph nodes of a connected graph pertains to the same connected sub-graph. All such graphs are connected.>

Connected Sub-Graph is a Connected Graph º

Graph has Connected Sub-Graphs ¬

<The connected sub-graphs are of the same type as the graph.>

<Each connected sub-graph has copies of those direct links of the graph that have both graph nodes as pertaining to the connected sub-graph. During coping objects of appropriate graph nodes are retained.>

<Graph has those connected sub-graphs to which its nodes pertain.>

Graph. Sub-Graph Graph

Sub-Graph Graph is a Directed Graph º

Directed Graph has a Sub-Graph Graph º

<Node objects of the sub-graph graph are connected sub-graphs of the directed graph. Sub-graph A is linked to a sub-graph B if any node of A is directly linked to any node of B within the directed graph.>