Lecture 7/8 Flashcards
(20 cards)
What is a Network? Or Graph?
Is a set of NODES connected by LINKS
There are Two types of Links
Directed - with direction
Undirected - no direction
What is the total number of connections o a node “I” to its nearest neighbouring node
What is the motivation behind Network Theory?
As systems become come complex and interconnected it is important to understand how failure of a single component might effect other systems/subsystems down the line
What is the clustering coefficient C?
Is the measure of local connectivity,
C=1 - Fully connected Graph
C = 0 - fully sequential Graph
Discuss the strengths and limitations of applying network theory for
quantifying the reliability of infrastructures and assess the vulnerability
to large-area breakdowns
Strengths:
1. allows to simulate complex networks
2. allows to idetify critical components
3. better understand how failure can propagate
Weakness:
1. Neglet dynamic change
2. Challenges in accurately modeling cross-sector interdependencies (eg. Switzerland electricity network also has European connections, in class the model we looked at did not consider this)
What are the different connectivity properties of Poisson, Exponential
and Power-law networks? Discuss the degree distribution of real-world
networks. Focus on both technical and non-technical networks.
Poisson Networks:
Connectivity: Most nodes have a similar number of connections, leading to uniform connectivity.
Advantages: Simple structure, robust to random failures.
Limitations: Vulnerable to targeted attacks on the few highly connected nodes.
Exponential Networks:
Connectivity: More structured than Poisson networks, with slightly varied connectivity.
Advantages: More predictable and organized than Poisson networks.
Limitations: Sensitive to attacks on more connected nodes, less robust than power-law networks.
Power-law Networks:
Connectivity: Highly varied connectivity with a few nodes having many connections (hubs).
Advantages: Robust to random failures due to the low probability of hub failure.
Limitations: Vulnerable to targeted attacks on hubs, which can disrupt the network significantly.
Discuss the tolerance of exponential and scale-free networks against
random failures and targeted attacks.
How does the global connectivity varies with respect to random failures and targeted attacks of increasing
magnitude?
Exponential Networks:
Good global and local connectivity (local robustness due to clusters and global accessibility due to shortcuts among clusters)
Less vulnerable to malicious attacks (no preferential nodes), tolerant to random faults
Power-Law Networks - Scale-Free Networks
Few highly connected nodes
Robustness to random faults but vulnerability to targeted malicious attacks (due to the highly-connected hubs)
If you look at the pictures it makes sense
What is the The degree distribution P(k) ?
The degree distribution P(k) gives the probability that any randomly chosen
vertex has degree k.
k = The total number of connections of a node i to its nearest neighboring
nodes is called its degree ki
What is the underlying assumption in using the shortest path for
characterizing the service of a network system?
the communication/service between two nodes is routed along the shortest path
Different algoriths can be used the find the shortest path
What is the caractheristic path lenght?
Characteristic path length: average of all shortest paths in the network
Definition on the average clustering coefficient C?
The average clustering coefficient C of a network is a measure of local connectivity.
C = 1 for a fully-connected graph
C =0 for a complete sequential graph, i.e., a ring
What is a weighted network? What additional information do weights add to connectivity? How are weights included in the indicators of connectivity of networks?
L and C are applicable only to unweighted networks in which only the topological information on the existence
or absence of a link, with no reference to the physical length and capacity of the link, is retained
The model of a realistic network could be weighed to account also for the physical properties of the systems
(Time or Distance)
Difference between Failure and Attack?
Failure: nodes are removed randomly
Attack: most connected nodes are removed
How do you compute the efficiency matrix ε of a given network? Which indication about the path from node i to node j does the matrix element ε provide?
its simply 1/d –> if there is a non zero value
if d = 0 then ε=0
Given any network, detail the steps of the procedure to quantify the vulnerability of the network to the removal of its links and nodes. Which indicators would you use to quantify this vulnerability?
Degradation of the global efficiency of the network due to the disconnection of a set of its links
Topological degree centrality
Highest importance to the node with the largest number of first neighbors
Topological closeness centrality
Identify the nodes that on average need fewer steps to communicate with the other nodes
Betweenness centrality
A node is central if it is traversed by many of the shortest paths connecting pairs of nodes
Topological information centrality
Relates a node’s importance to the ability of the network to respond to the deactivation of the node we re studying
