Network Theory and Distributive Infrastructure Systems Flashcards
What is physical dependence (between infrastructure systems)?
Systems share a direct material connection. The physical state of one changes the state of another.
What is informative dependence (between infrastructure systems)?
Systems are connected via information (usually computational) flow. System state depends on signal of another.
What is geographical dependence (between infrastructure systems)?
Systems are connected by geographic proximity. In the same location or close by.
What is logical dependence (between infrastructure systems)?
Any other kind of connection (that isn’t physical, informative, or geographical), that is related to human decisions. Policy, procedural, societal, economic, …
What is an interdependency matrix?
Rows (i) and columns (j) filled with civil/infrastructure systems. Matrix is filled with dependencies between systems (how does j depend on i).
Define Network.
Define Graph.
Network: relational representation of a complex system
Graph: mathematical object that we analyse
What are some network characteristics?
Direction: If links are directed, it is a directed network. If links are not directed, it is an undirected network.
Connection: Fully connected if every node connected by links (cliques). A disconnected network if not (subnetworks)
Planar/non-planar: A planar network is one where all links that cross form a node.
What is the size of a network?
Number of nodes
What is the shortest path of a network?
The shortest distance (usually the lowest number of links) between two nodes.
What is the diameter of a network?
The length of shortest path between the most distanced nodes.
What is the number of cycles of a network?
The number of loops in a network.
mu = L - N + S
higher mu = more complex
What is the beta-index of a network?
A simple measure of network complexity.
Beta = L/N.
(Basically saying more links is more complex)
What is the degree of connectivity
Ratio of actual to potential number of links. Symbol: gamma.
Non-planar: Gamma(np) = L /[1/2 * (N-1) *N]
Planar: Gamma(p) = L / (3N - 6)
How would you represent an undirected network as a matrix?
Aij where:
A = 1 if connected
A = 0 if not connected
How would you represent a directed network as a matrix?
Aij where:
A = 1 if there is a j -> i connection
A = 0 otherwise.
For example if there is a [Node 1] -> [Node 3] connection,
A31 = 1.
What is the node degree?
The number of connections on node i.
For an undirected network:
ki = sum_j(Aij)
For a directed network:
ki(in) = sum_j(Aij)
ki(out) = sum_j(Aji)
In node statistics, what is eigenvalue centrality?
Centrality based on importance of neighbours
In node statistics, what is closeness centrality?
Centrality based on access to all other nodes