Lecture 03 - Network models Flashcards by Rikard Donnelly

Networks

What is another name for a network?

A graph

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Networks

What does a network consist of?

Nodes/vertices and edges

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Networks

What is a neighbour?

If nodes A and B are connected with an edge, they are neighbours.

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Networks

What are the two most common ways to represent networks in a computer?

Adjacency matrix
Adjacency list

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Networks

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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Networks

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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Networks

What is this?

An adjacency matrix

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Networks

What is this?

An adjacency list

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Networks

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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Networks

What’s the typical way of writing the node’s degree?

deg(i), with i being the i-th node.

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Networks

What is a walk?

A list of edges that are sequentially connected to form a continuous route in a network.

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Networks

What is a trail?

A walk that doesn’t go through any edge more than once.

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Networks

What is a path?

A walk that doesn’t go through any node more than once.

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Networks

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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Networks

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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Networks

What is this a description of?

“A walk that doesn’t go through any edge more than once.”

A trail

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Networks

What is this a description of?

“A walk that doesn’t go through any node more than once.”

A path

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Networks

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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Networks

What is a subgraph?

A part of the graph.

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Networks

What is a connected graph?

A graph in which a path exists between any pair of nodes.

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Networks

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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Networks

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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Networks

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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Networks

What is this a description of?

“A part of the graph.”

A subgraph

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# Networks What is a complete graph?

A graph in which any pair of nodes are connected

# Networks What is a Regular graph?

A graph in which all nodes have the same degree. Every complete graph is regular.

# Networks 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.

# Networks 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.

# Networks 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.

# Networks What is this an example of? "A graph in which any pair of nodes are connected"

Complete graph

# Networks What is this an example of? "A graph in which all nodes have the same degree."

Regular graph

# Networks 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

# Networks What is this an example of? "A graph in which there is no cycle."

Tree graph

# Networks What is this an example of? "A graph that can be graphically drawn in a two-dimensional plane with no edge crossings."

Planar graph

# Networks What is this an example of?

Complete graphs

# Networks What is this an example of?

Regular graphs

# Networks What is this an example of?

Bipartite (n-partite) graphs

# Networks What is this an example of?

Tree graphs

# Networks What is this an example of?

Planar graphs

# Networks What is an undirected edge?

An edge that is connected in both ways to the node, like a pavement.

# Networks What is a directed edge?

An edge that is only connected in one direction, like a one-way street.

# Networks What's an unweighted edge?

An edge that has no attached weight/cost. Adjacency matrices have just 0 or 1 as elements.

# Networks What is a weighted edge?

An edge with an attached weight/cost, usually positive values, like connection strength or distance.

# Networks What is node strength?

The sum of the weights of the edges attached to the node.

# Networks What's special about the adjacency matrix of an undirected graph?

It's symmetric.

# Networks Can two nodes share multiple edges?

Yes, nodes can have multiple edge, directed or undirected, with different weights.

# Networks What is a simple loop?

An edge that starts and ends at the same node.

# Networks What's an edge called when it has no direction.

An undirected edge.

# Networks What's an edge called when it has a direction?

A directed edge.

# Networks What's an edge called when it has a cost/weight?

A weighted edge.

# Networks What's an edge called when it doesn't have a cost/weight?

An unweighted edge.

# Networks What is the sum of all edge weights for a node called?

The node strength.

# Networks If you have an adjacency matrix that's symmetric, what's that type of network called?

An undirected network.

# Networks What do you call an edge that starts and ends at the same node?

A simple loop.

# Networks What is a simple graph? (4)

A graph that doesn't contain directed, weighted or multiple edges, and has no self-loops.

# Networks What do you call a graph that doesn't contain directed, weighted or multiple edges, and has no self-loops.

A simple graph

# Networks What is a multigraph?

A graph that may contain multiple edges and both (un)directed edges. Some definitions include self-loops.

# Networks What do you call a graph that may contain multiple edges and both (un)directed edges. Some definitions include self-loops.

A multigraph.

# Networks What is a hyperedge?

An edge that can connect more than two nodes.

# Networks What do you call an edge that can connect more than two nodes?

A hyperedge

# Networks 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.

# Networks What are models that deal with nodes changing, but fixed network topologies?

Models for "dynamics ON networks"

# Networks What are models for "dynamics OF networks"?

Models that deal with changes to the network topology only.

# Networks What are models that deal with changes to the network topology only called?

Models for "dynamics OF networks"

# Networks What are models for "adaptive networks"?

Models that describe the co-evolution of both "dynamics on" and "dynamics of" networks.

# Networks What are models that describe the co-evolution both "dynamics on" and "dynamics of" networks called?

Models for "Adaptive networks".

# Networks 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.

# Networks 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.

# Networks What are some variations of the "voter model"? (ORE)

- Original - Reversed - Edge-based

# Networks 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.

# Networks 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.

# Networks What is a different name for the voter model "original variation"?

Push

# Networks What is a different name for the voter model "reversed variation"?

Pull

# Networks 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.

# Networks 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.

# Networks 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)

# Networks What are small-world network?

Networks with short paths among all nodes, despite not being a complete graph.

# Networks What are networks with short paths among all nodes called?

Small-world networks.

# Networks 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.

# Networks 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.

# Networks What is homophily?

An empirically observed sociological fact that people tend to connect those who are similar to themselves

# Networks Can walks have loops?

Yes

# Networks Can trails have loops?

# Networks Can paths have loops?