Having further formalized the properties of our nodes and edges, we will now update our undirected graph model of our reference network topology.

The Node-index property

We start by adding an additional property for nodes in the graph. The “node-index” property is an integer that must be unique to each node on the graph. Here, it is a functional stand-in for the autonomous system number (ASN) of a BGP router as well as all networks that it originates into BGP.

The node index is depicted in the graph in black text, centered in the node.

The Symmetric-perimeter Zone (SPZ) Property

The symmetric perimeter zone property of each node is represented on the graph by the color used to depict the node (the shading of the actual circle). The visual figure of the graph includes a key for mapping each color to an explicit value for the SPZ property of the nodes of that color.

Those values are formatted to reflect the hierarchical nature of the SPN zone structure (as discussed in the previous section), with the addition of an “implicit root” value of 0.

This implicit root (“0.”) does not exist in any “real” sense, but provides namespace headroom for us to contemplate representation of completely disjoint graphs (that is, networks).

SP zone values

The color coding of SP zones in the visual representation of the graph is visually convenient, but the property those colors represent have their own internal semantics:

  • Each node has an “SP zone” property consisting of a decimal-delimited sequence of octets in decimal notation.
  • The first octet is always “0”, representing the nominal/implicit “root” of the SP zone hierarchy.
  • The second octet designates the instance-index of the graph-local top/root level of the SP zone hierarchy of which the labeled node is a member.
  • The 3rd octet (if present) designates the instance-index of the 2nd-level branch of the graph-local SP zone hierarchy of which the node is a member.
  • 4th, 5th, etc… octets represent successively deeper branches in the SP Zone tree.
    • only the first three octets are used in the model presented here.

The Path-Affinity-Group (PAG) Property

Implicit Root of PAG Hierarchy

The path-affinity-group (PAG) property of edges is revised to include an implicit “root” at the top of the PAG hierarchy (also “0”). Similarly to the implicit root of the SPZ hierarchy, this presents on the graph only as a prepended value of “0.” in the PAG values, and exists to provide “headroom” for representation of disjoint PAG hierarchies within the same graph.

The implicit root of the site hierarchy is a(n implicit) node, connected to an (implicit) edge that is connected to each site node at the root/top of our graph’s site hierarchy.

PAG Values

The value of each edge’s PAG property is explicitly labeled on that edge in the visual depiction of the graph. PAG values provide a unique identifier for each fork in the PAG hierarchy within which an edge is located, as well as an indicator of whether the labeled edge is present in one, or in two different levels of the PAG hierarchy.

Edge’s PAG values are constructed as follows

  • Each edge has a PAG property whose value is a sequence a decimal-point delimited sequence of octets in decimal notation.
  • The first octet is always “0”, representing the nominal/implicit “root” of the SP zone hierarchy.
  • The second octet is always “1”, representing the actual edges in the current graph.
    • The PAG value “0.1” in our model refers to the wide-area network’s edges
    • A PAG value of “0.2” would refer to a graph that is completely disjoint from the “0.1” graph
  • A value of “0” in the final octet indicates that both ends of the edge are present in the PAG value prior to the final octet.
  • A non-zero integer in the final octet of an edge’s PAG value indicates that the edge spans two adjacent hierarchical levels in the PAG hierarchy.
    • The PAG value up-to/including the penultimate octet represents the “parent” end of an edge (the section of the path-affinity group that contains the child/sub-group.)
    • The final octet represents the “child” end of an edge.
    • The non-zero integers are unique index values for isolated areas in the same depth of the PAG hierarchy.
  • Additional octets may be included (if additional levels of the PAG hierarchy are present)

All-together now

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