2.0 - Lines and Networks/Graphs Flashcards
What is a Vertex Index to Coordinate Datastructure?
Assigns coordinates to each vertex:
{0: [0,0],
1: [1.5,1],
2: [2.0,0.5]}
Structural Applications for Lines and Networks
- Trusses
- Gridshells
- Frames
- Facade
Public Utilities Applications for Lines and Networks
- Water Pipe Networks
- National Power Grid
- Telecommunication
- Gas Networks
Transport Applications for Lines and Networks
- Railways
- Trams
- Metro
- Roads
- Flight Paths
What are Geometric Keys and why use them?
The inverse operation of Vertex Index to Coordinate Datastructure and allows indices to be identified from known coordinates:
{‘0.0,0.0’: 0,
‘1.5,1.0’: 1,
‘2.0,0.5’: 2}
NB: There is a fixed decimal point precision and points that don’t exist will return errors.
What does a Connectivity Matrix (Branch-node Matrix) represent and how?
It’s a sparse matrix (m x n) with ‘m’ number of lines and ‘n’ number of vertices and shows what line connects each of the nodes.
‘-1’ is the start of the line and 1 is the end:
C = -1 1 0 0
-1 0 1 0
-1 0 0 1
What is a Coordinate Difference and how is it calculated?
A coordinate difference is simply the distance between the start and end of each line:
u = Cx & v = Cy x and y are the coordinates of each of the vertices
What does the Connectivity Matrix Transpose tell us?
What edges are connected to a given node.
How can the Connectivity Matrix Transpose be used to calculate net flow rate at each node if q = flow rate in each pipe (line)?
f = q*C.transpose
What does the Adjacency Matrix show?
Its an (n x n) Matrix showing how each of the vertices are connected to each other.
A = 0 1 1 1
1 0 1 0
1 1 0 1
1 0 1 0
What is the Degree Matrix?
The Degree Matrix (n x n) is the sum of each row (or column) of Adjacency, A, showing how many other vertices are connected to the corresponding vertex:
D = 3 0 0 0
0 2 0 0
0 0 3 0
0 0 0 2
What is the Laplacian Matrix?
Symmetic (n x n) Matrix with rows and columns that sum to 0:
L = D - A
Graph (network) representation does not depend on where nodes are placed nor what else?
Nor the length of the connecting lines.
What is the difference between Directed, Undirected and Mixed graphs?
Directed - All lines have a specific flow direction.
Undirected - All lines have no direction restrictions.
Mixed - Mixture of Directed and Undirected Lines.
Name 3 examples of weights on networks.
- Cost to pass through
- Length / Distance Between
- Forces in a Truss
