GRAPHTACULAR
This Graph has Vertices that have Kernels which are given Strands.
Strands passed into Kernels, which contain a reference to the Vertex that is inside.
Vertices have references to the matrix they are inside.
So a Kernel can operate in terms of all the Vertices in the graph it's in.
The Graph is structured like this:
public class Graph
{
// registry
public List<Vertex> AllVertices = new List<Vertex>();
// registry count
public int size = 0;
// adjacency matrix
public List<List<int>> Matrix = new List<List<int>>();
// vertex-guid to matrix position translation
public Dictionary<Guid, int> MatrixKey = new Dictionary<Guid, int>();
A Vertex looks something like this:
public class Vertex
{
public Guid ID = Guid.NewGuid();
public BaseKernel K { get; set; }
public Graph cluster { get; set; }
public Vertex(BaseKernel k)
{
K = k;
}
}
A Vertex has a Kernel object which gives it the ability to execute functions on itself.
A Strand is a series of instructions, in this case, the seed vertex is given the entire strand, which generates a linked list with a blob on the end:
public void Flower()
{
int n = 1;
// flowers
flower.Add(n, new object[] { "KbranchUndirected", 1, 1 }); n++;
flower.Add(n, new object[] { "KbranchUndirected", 1, 1 }); n++;
flower.Add(n, new object[] { "KbranchUndirected", 1, 1 }); n++;
flower.Add(n, new object[] { "KbranchUndirected", 1, 1 }); n++;
flower.Add(n, new object[] { "KbranchUndirected", 1, 1 }); n++;
flower.Add(n, new object[] { "KbranchUndirected", 1, 1 }); n++;
flower.Add(n, new object[] { "KbranchUndirected", 1, 1 }); n++;
flower.Add(n, new object[] { "KbranchUndirected", 1, 1 }); n++;
flower.Add(n, new object[] { "KcompleteCluster", 4, 7 }); n++;
flower.Add(n, new object[] { null });
}
The strand is passed to the Kernel, which parses it and calls logic on its shell Vertex:
switch (ss[0])
{
case "KbranchUndirected":
KbranchUndirected(strand, step, Convert.ToInt32(ss[1]), Convert.ToInt32(ss[2]));
break;
case "KcompleteCluster":
KcompleteCluster(strand, step, Convert.ToInt32(ss[1]), Convert.ToInt32(ss[2]));
break;
default:
break;
}
Kernels are used to generate pre-programmed motifs. The above strand passed to a single seed Vertex produces the following matrix and graph:
GEXF - save graph to file
You can view saved graphs which are exported as GEXF (Graph Exchange XML Format) for display in Gephi
Building clusters from the outside:
Operations on sets of Vertices in clumps from the outside tend to produce more geological or crystal shapes.
This is a logarithmic cluster with edges reflecting the repetitive global split
Does it feel kind of like ice, inorganic?
Driving clusters from the inside:
Fibonacci:
look feel has more body, more life?
Other pictures in assets >>>
The big round one has a look and feel of a wrinkly brain given its modular shape scrunched into space.
Additional graphs not pictured in graphs >>>
- go to TESTS
METHODS
| Graph Method | Use | Big O Time | Big O Space | IN | OUT |
|---|---|---|---|---|---|
| PrintMatrix | console output | O(n2) | O(n2) | - | void |
| PrintVertices | console output | O(n) | O(n) | - | void |
| PrintEdges | console output | O(n2) | O(n) | - | void |
| RegisterKey | associates a Vertex ID to a MatrixKey | O(1) | O(1) | Vertex | void |
| MatrixEntry | updates matrix with row and column | O(n) | O(1) | Vertex | void |
| AddStrandVertex | vertex addition | O(1) | O(1) | - | Vertex |
| AddClusterVertex | vertex addition | O(1) | O(1) | - | Vertex |
| DeleteVertex | Removes Vertex from matrix, keys, list, count | O(1) | O(1) | Vertex | - |
| MatrixRemoval | Removes target Vertex from Matrix | O(n) | O(1) | Vertex | - |
| DeleteMatrixKey | Remove Vertex from MatrixKeys, mirror matrix contraction | O(n) | O(1) | Vertex | - |
| JoinVertexPairUndirected | Combines two Vertices on a new one, preserving their degrees | O(n) | O(1) | Vertex | - |
| DoppleSet | Mirrors a set of Vertices and their edges with a new set | O(n2) | O(n) | List Vertex | List Vertex |
| CreateClusterVertex | create and add Vertex; cluster Kernel (inert) | O(1) | O(1) | - | Vertex |
| CreateStrandVertex | create and add Vertex; strand Kernel | O(1) | O(1) | - | Vertex |
| AssimilateVertex | add, register, count, and enter matrix | O(1) | O(1) | Vertex | Vertex |
| AssimilateVertices | List Vertex to be added | O(n) | O(1) | List Vertex | void |
| DirectedEdge | directed edge between two Vertices | O(n) | O(n) | Vertex, Vertex, int | void |
| UndirectedEdge | undirected edge from one Vertex to another | O(1) | O(1) | Vertex, Vertex, int | void |
| OutDegreeCount | count and return edges from a Vertex | O(n) | O(1) | Vertex | int |
| OutDegreeVertices | collect and return vertices pointed to from a vertex | O(n) | O(n) | Vertex | List Vertex |
| InDegreeCount | count and return edges to a Vertex | O(n) | O(1) | Vertex | int |
| InDegreeVertices | collect and return vertices pointing to a vertex | O(n) | O(n) | Vertex | List Vertex |
| DirectedEdgeCount | sum of a Vertex indegree and outdegree | O(1) | O(1) | Vertex | int |
| MutualEdgeCount | for undirected, count mutual connections | O(1) | O(1) | Vertex | int |
| NeighborCount | direction agnostic neighbor count | O(1) | O(1) | Vertex | int |
| NeighborSet | direction agnostic neighbor list | O(1) | O(1) | Vertex | List Vertex |
| IslandCount | nonconnected Vertex count | O(n) | O(1) | - | int |
| IslandSet | nonconnected Vertex list | O(n) | O(n) | - | List Vertex |
| NeighborsWithinK | collect reference to all Vertices within K of a target | O(n3) | O(n) | Vertex, int | List Vertex |
| MaxConnections | calculate the max potential global undirected edges for a given number of Vertices | O(n) | O(1) | int | int |
| IsSelfRefrence | check for edge to self | O(1) | O(1) | Vertex | bool |
| PurgeSelfRefrence | removes edge to self | O(n) | O(n) | Vertex | void |
| PurgeSelfReferences | removes multigraph, returns number removed | O(n2) | O(1) | - | int |
| FullConnectSet | complete undirected weighted connection for a set of Vertices to each other | O(n2) | O(n) | List Vertex, int | LIST |
| ConnectionsBetweenCount | count the number of related Vertices in a set | O(n2) | O(n) | List Vertex | int |
| NondirectionalClusteringCoefficient | measures how connected a Vertex's neighbors are to each other | O(1) | O(1) | Vertex | int |
big O time and space does not include dependent functions, such as NondirectionalClusteringCoefficient simply:
return decimal.Divide(ConnectionsBetweenCount(n), MaxConnections(n.Count()));
both of which have their own runtime complexity.