papers.adligo.com

NodeNetworks

Author: Scott Morgan
Created: 2025-12-12
Edited: 2025-12-14
Id: 1.3.6.1.4.1.33097.1.0.12
Copywrite 2025 Adligo Inc


In the context of data structures, a NodeNetwork is composed of two or more nodes and one or more edges which connect the nodes into a network. Nodes are often depicted by circles, while edges are often represented by (curved) lines or arrows. This definition may seem synonymous with the term Graph#1.3.6.1.4.1.33097.1.0.14, and although a NodeNetwork is always technically a Graph#1.3.6.1.4.1.33097.1.0.14 a Graph#1.3.6.1.4.1.33097.1.0.14 can also be comprised of one or more NodeNetworks.

Commentary

NodeNetworks are synonymous with connected graphs only when they are not part of a NodeNetworkSet#1.3.6.1.4.1.33097.1.0.15.

Illustration 1

A NodeNetwork that is also a connected Graph

 a → b → c

Components

Nodes:

1.3.6.1.4.1.33097.1.0.12.0

Also known as a Vertex#1.3.6.1.4.1.33097.1.2.6. A point or entity in a network structure. Nodes may also have attributes, including edges which reference nodes.

Formally;

The fundamental unit of a NodeNetwork $N=(V, E)$, which is part of the set $V$.

NodeIds:

1.3.6.1.4.1.33097.1.0.12.0.0

A NodeId is simply some sort of unique identifier which can uniquely identify a Node.

Edges:

1.3.6.1.4.1.33097.1.0.12.1

An edge is simply a connection between two Nodes. Edges may also have attributes, including directionality, weight and arbitrary attributes.

Formally;

The fundamental unit of a NodeNetwork $N=(V, E)$, which is part of the set $E$.

EdgeIds:

1.3.6.1.4.1.33097.1.0.12.1.0

A EdgeId is simply some sort of unique identifier which can uniquely identify a Edge.

Attributes

Acyclic:

1.3.6.1.4.1.33097.1.0.12.7

This is a simple Boolean value that (when True) signifies if the NodeNetwork is acyclic (not having any Cycles#1.3.6.1.4.1.33097.1.0.12.5).

Directional:

1.3.6.1.4.1.33097.1.0.12.6

This is a simple Boolean value that (when True) signifies if the NodeNetwork is directional or (when False) bi-directional. Note that when this is True, bi-directionality can still exist through Edges#1.3.6.1.4.1.33097.1.0.12.1 that reference Nodes#1.3.6.1.4.1.33097.1.0.12.0 in both directions.

Associated Operations

Walks:

1.3.6.1.4.1.33097.1.0.12.2

A walk of a graph is a way of transversing the graph from one vertex to another (or to the same vertex) by following a sequence of edges. Walks may be reduced to paths.

Attributes of Associated Operations

Paths:

1.3.6.1.4.1.33097.1.0.12.3

A path is a walk whose vertices are distinct (i.e., each vertex appears at most once in the walk).

Circuts:

1.3.6.1.4.1.33097.1.0.12.4

A Circut (or closed walk) means a walk (v0,e1,v1,e2,v2,…,ek,vk) with vk = v0.

Cycles:

1.3.6.1.4.1.33097.1.0.12.5

A cycle means a circut (v0,e1,v1,e2,v2,…,ek,vk) such that

Questions Comments:

Citations

https://en.wikipedia.org/wiki/Graph_theory

https://medium.com/basecs/a-gentle-introduction-to-graph-theory-77969829ead8

https://arxiv.org/pdf/2308.04512