Lecture 03 - Network models Flashcards
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What is another name for a network?
A graph
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What does a network consist of?
Nodes/vertices and edges
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What is a neighbour?
If nodes A and B are connected with an edge, they are neighbours.
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What are the two most common ways to represent networks in a computer?
- Adjacency matrix
- Adjacency list
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What is an adjacency matrix?
A matrix of m * m elements which shows how each node is connected to all other nodes.
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What is an adjacency list?
A dictionary mapping nodes to a list of which other nodes they’re connected to. Python annotation: dict[str, list[str]]
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What is this?
An adjacency matrix
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What is this?
An adjacency list
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What is the degree of a node?
The number of edges connected to it.
For directed nodes, there’s a difference between “indegree” and “outdegree” as well
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What’s the typical way of writing the node’s degree?
deg(i), with i being the i-th node.
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What is a walk?
A list of edges that are sequentially connected to form a continuous route in a network.
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What is a trail?
A walk that doesn’t go through any edge more than once.
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What is a path?
A walk that doesn’t go through any node more than once.
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What is a cycle?
A walk that starts and ends at the same node, without going through any node more than once.
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What is this a description of?
“A list of edges that are sequentially connected to form a continuous route in a network.”
A walk
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What is this a description of?
“A walk that doesn’t go through any edge more than once.”
A trail
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What is this a description of?
“A walk that doesn’t go through any node more than once.”
A path
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What is this a description of?
“A walk that starts and ends at the same node, without going through any node more than once.”
A cycle
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What is a subgraph?
A part of the graph.
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What is a connected graph?
A graph in which a path exists between any pair of nodes.
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What is a connected component?
A subgraph of a graph that is connected within itself, but not to the rest of the graph.
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What is this a description of?
“A graph in which a path exists between any pair of nodes.”
A connected graph
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What is the name of a subgraph that is connected within itself, but not to the rest of the graph.
A connected component
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What is this a description of?
“A part of the graph.”
A subgraph
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What is a complete graph?
A graph in which any pair of nodes are connected
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What is a Regular graph?
A graph in which all nodes have the same degree. Every complete graph is regular.
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What is a Bipartite (n-partite) graph ?
A graph whose nodes can be divided into two (or n) groups so that no edge connects nodes between the groups. The groups can be connected within themselves.
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What is a Tree graph?
A graph in which there is no cycle. A graph made of multiple trees is called a forest graph. Every tree or forest graph is bipartite.
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What is a Planar graph?
A graph that can be graphically drawn in a two-dimensional plane with no edge crossings. Every tree or forest graph is planar.
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What is this an example of?
“A graph in which any pair of nodes are connected”
Complete graph
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What is this an example of?
“A graph in which all nodes have the same degree.”
Regular graph
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What is this an example of?
“A graph whose nodes can be divided into two (or n) groups so that no edge connects nodes within each group”
Bipartite (n-partite) graph
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What is this an example of?
“A graph in which there is no cycle.”
Tree graph
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What is this an example of?
“A graph that can be graphically drawn in a two-dimensional plane with no edge crossings.”
Planar graph
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What is this an example of?
Complete graphs
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What is this an example of?
Regular graphs
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What is this an example of?
Bipartite (n-partite) graphs
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What is this an example of?
Tree graphs
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What is this an example of?
Planar graphs
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What is an undirected edge?
An edge that is connected in both ways to the node, like a pavement.
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What is a directed edge?
An edge that is only connected in one direction, like a one-way street.
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What’s an unweighted edge?
An edge that has no attached weight/cost. Adjacency matrices have just 0 or 1 as elements.
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What is a weighted edge?
An edge with an attached weight/cost, usually positive values, like connection strength or distance.
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What is node strength?
The sum of the weights of the edges attached to the node.
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What’s special about the adjacency matrix of an undirected graph?
It’s symmetric.
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Can two nodes share multiple edges?
Yes, nodes can have multiple edge, directed or undirected, with different weights.
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What is a simple loop?
An edge that starts and ends at the same node.
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What’s an edge called when it has no direction.
An undirected edge.
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What’s an edge called when it has a direction?
A directed edge.
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What’s an edge called when it has a cost/weight?
A weighted edge.
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What’s an edge called when it doesn’t have a cost/weight?
An unweighted edge.
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What is the sum of all edge weights for a node called?
The node strength.
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If you have an adjacency matrix that’s symmetric, what’s that type of network called?
An undirected network.
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What do you call an edge that starts and ends at the same node?
A simple loop.
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What is a simple graph? (4)
A graph that doesn’t contain directed, weighted or multiple edges, and has no self-loops.
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What do you call a graph that doesn’t contain directed, weighted or multiple edges, and has no self-loops.
A simple graph
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What is a multigraph?
A graph that may contain multiple edges and both (un)directed edges. Some definitions include self-loops.
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What do you call a graph that may contain multiple edges and both (un)directed edges. Some definitions include self-loops.
A multigraph.
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What is a hyperedge?
An edge that can connect more than two nodes.
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What do you call an edge that can connect more than two nodes?
A hyperedge
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What are models for “dynamics ON networks”?
Models that deal with how nodes in a network change over time. The network topology is fixed/unchanging.
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What are models that deal with nodes changing, but fixed network topologies?
Models for “dynamics ON networks”
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What are models for “dynamics OF networks”?
Models that deal with changes to the network topology only.
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What are models that deal with changes to the network topology only called?
Models for “dynamics OF networks”
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What are models for “adaptive networks”?
Models that describe the co-evolution of both “dynamics on” and “dynamics of” networks.
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What are models that describe the co-evolution both “dynamics on” and “dynamics of” networks called?
Models for “Adaptive networks”.
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How does the “majority rule model” work?
- Initialize a population with random states (e.g. 0 or 1)
- During the update step, each individual changes to the majority of its neighbours.
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How is the “voter model” different from the “majority rule model”?
In the voter model, a single node pair of connected nodes is chosen at a time. Between them, a vote is transferred.
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What are some variations of the “voter model”? (ORE)
- Original
- Reversed
- Edge-based
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In the voter model, how does the “original variation” work?
A listener is chosen, and then a speaker is chosen from the listener’s neighbourhood.
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In the voter model, how does the “reversed variation” work?
A speaker is chosen, then a random listener is chosen fro the speaker’s neighbourhood.
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What is a different name for the voter model “original variation”?
Push
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What is a different name for the voter model “reversed variation”?
Pull
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In the voter model, how does the “edge-based variation” work?
Edges are chosen at random, then the connected nodes are selected as speaker and listener, respectively.
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How does the “Epidemic model” work? (SIR model)
- Initialize nodes as either susceptible (S) or infected (I).
- I can infect S with some prob.
- I can recover with some prob to either state recovered (R) or S.
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How does the “Diffusion model” work?
During updates, nodes are affected by all their neighbours. Think heat transfer.
N_i.state += C*sum(N_i.neighbors.state) / deg(N_i)
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What are small-world network?
Networks with short paths among all nodes, despite not being a complete graph.
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What are networks with short paths among all nodes called?
Small-world networks.
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What are scale-free networks?
Networks where the distribution of edges between networks follow a power law distribution; that is, most nodes have few neighbors, but some nodes are very central and have many neighbors.
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What do you call a network where most nodes have few neighbors, but a few number of nodes have many neighbors?
A scale-free network.
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What is homophily?
An empirically observed sociological fact that people tend to connect those who are similar to themselves
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Can walks have loops?
Yes
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Can trails have loops?
No
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Can paths have loops?
No
