# Social Networks

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What is a walk? What is a trail? and what is a Path?
Walk: A sequence of nodes that can be visited by following edges. Trail: Is a walk with no repeating lines/edges. Path: Is a walk with no repeating nodes.
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What is a bipartite network? How do you determine if a network is Bipartite?
A bipartite network is one where nodes can be divided into two sets and there is no edge connecting a node in the same set. Can determine if a network is bipartite by colouring in nodes red or blue. Adjacent nodes must be the opposite colour.
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What are the maximum number of edges for a directed and undirected graph?
Directed = N * (N - 1) and Undirected = (N * (N - 1)) / 2
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What is a planar network? How do you determine if a network is planar?
A network is planar if it can be drawn on the plane with no edge-crossings. To check simply redraw edges that are currently crossed and see if you can draw them on the plane without a crossing. Also confirm Kuratowski's principle.
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What is Euler's Magic Formula?
Euler's Magic Formula states that for planar networks, it satisfies the equation n - m + r = 2 (where n = # of nodes, m = # of edges, and r = # of regions).
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What is kuratowski's principle?
The principle that states that a network that contains the subgraph K5 or K3,3 is definitely not planar.
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What is a complete graph?
A graph that has the maximum number of edges possible. (Remember directed it is n * (n-1) and undirected (n * (n-1)) / 2
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What is the degree of a node? Average degree of a network?
The degree of a node is the number of connections it has attached to it. The average degree of a network can be found using 2m / n.
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What is the density of a network? What is a dense network? What is a sparse network?
The density is a comparison of actual number of links to the maximum number of possible networks for that graph. A dense network will have m edges close to or is the maximum. A sparse network will have m number of edges that is low compared to max.
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What is the diameter of a network?
The diameter of a network is the longest path out of all the shortest possible paths between each pair of vertices.
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What is a connected network?
A network where there is a path between every pair of vertices. If there isn't then the graph is split up into connected components.
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Network Exploration - what is DFS and BFS and what are they suitable for?
Depth First Search: Explores the deepest node as possible before backtracking. Suitable for mazes. Breadth First Search: explores first layer of neighbours before proceeding to the next layer. Suitable for exploring the web.
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What is an algorithm for walking at random?
Start at node V0. Select an adjacent node V1 at random and go to that node. Continue the process until satisfied with the Walk.
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What is the Markov Property?
The Markov Property describes situations where past decisions do not influence the future. (Ex. Flipping a coin)
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What is a stochastic process?
It is a process that develops in time in accordance to probabilistic values. IE a process that develops randomly in time.
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What is degree centrality? What is a k-core?
Degree Centrality is a measure of how many connections one node has to other nodes. A k-core is the largest sub-network with no node of degree less than k.
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What is an algorithm to find a k-core of a network?
Remove all vertices whose degree is less than the current max node degree. Continue until all nodes in the graph have degree k.
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What is a clique?
Clique is a complete subgraph where each pair of vertices are connected
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Why is the clustering coefficient important?
The clustering coefficient is a measure of an "all-my-friends-know-each-other" property. This is sometimes described as the friends of my friends are my friends. A high CC is an indication of small world.
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What is the local clustering coefficient?
the clustering coefficient of a node is the ratio of existing links connecting a node's neighbors to each other to the maximum possible number of such links.
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What is the clustering coefficient of a whole network?
The clustering coefficient for the entire network is the average of the clustering coefficients of all the nodes. A high clustering coefficient for a network is another indication of a small world.
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What is closeness centrality? Why is it useful to know?
A vertex may be important if it has a small mean distance to any other vertex in the network. Closeness Centrality is the mean length of all the shortest paths between v and all other nodes.
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What is the bron-kerbosh algorithm?
The bron-kerbosh algorithm finds all maximal cliques within a network. A maximal clique is a clique where you cannot add an edge as it will not remain a clique.
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Assortative mixing can be distinguished by enumerative or scalar characteristics. What are these?
Enumerative: has a finite set of possible values (gender, race, nationality). Scalar: features whose values can be sorted like age or salary.
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What is homphily (assortative mixing)? What is modularity?
Homophily is the tendency that individuals associate themselves with similar people. Modularity is a measure of homophily; Observed % - Expected %
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What is covariance?
Covariance is a measure of assortative mixing according to scalar characteristics.
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What is a component?
A group of nodes that are all connected to each other, directly or indirectly.
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What is a giant component?
The component that connects most of the nodes. Ex. The web has the Internet as the giant.
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What is a weakly connected component? (directed)
Every node can be reached from every other node by following links in either direction.
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What are Strongly connected components? (directed)
Every node within the network can be reached by following the directions of edges.
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What is a strongly connected graph? (directed)
A directed graph is strongly connected if there is a path between all pairs of vertices
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What algorithm finds strongly connected components of a directed network?
The Kosaraju algorithm. It uses two passes of DFS and stores visited nodes in a stack.
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What is the six degree of seperation?
The theory that everyone and everything is 6 or fewer steps away.
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What is a small world network?
A small-world network in which most nodes are not neighbors of one another, but most nodes can be reached from every other node by a small number of hops or steps
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What is the purpose of degree distribution?
It offers another view of the degree of each node within a network. By plotting on a graph we can see the probability distribution of all the nodes in a network.
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What are some common properties of real-life networks?
- Usually have big variations in degree distributions; - Most nodes have a small degree, with a few hubs;
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What is a scale-free network?
A scale-free network is a network that follows a power-law degree distribution.
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What is meant by power-law? Why is it so important?
"20% of the world's population own 80% of the world's wealth". Many things in life follow a power-law. In a network, many nodes have a small degree, then a few nodes have a very high degree.
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## Other cards in this set

### Card 2

#### Front

A bipartite network is one where nodes can be divided into two sets and there is no edge connecting a node in the same set. Can determine if a network is bipartite by colouring in nodes red or blue. Adjacent nodes must be the opposite colour.

#### Back

What is a bipartite network? How do you determine if a network is Bipartite?

### Card 3

#### Front

Directed = N * (N - 1) and Undirected = (N * (N - 1)) / 2

### Card 4

#### Front

A network is planar if it can be drawn on the plane with no edge-crossings. To check simply redraw edges that are currently crossed and see if you can draw them on the plane without a crossing. Also confirm Kuratowski's principle.

### Card 5

#### Front

Euler's Magic Formula states that for planar networks, it satisfies the equation n - m + r = 2 (where n = # of nodes, m = # of edges, and r = # of regions).