Question

1. What is the difference between 1-mode and 2-mode graph? Give an example for each.

2. List various graph data structures to store social network information.

3. What is “six degrees of separation” in the context of social networks? What is the average degree of separation for Facebook and Twitter (you can cite other studies that have reported these statistics)?

4. What is “strength of weak ties”? Explain the rationale behind this phenomenon.

5. List and describe the various centrality measures. Also include their mathematical formulae.

6. What is triadic closure? How can you measure triadic closure property of a network? Explain why we observe a strong triadic closure in social networks.

7. Are co-citation measure and bibliographic coupling measure symmetric or asymmetric? Prove

Answer 1

BIPARTITE GRAPATH:

The bipartite graph, also called a bigraph, is a set of graph vertices decomposed into two disjoint sets such that no two graph vertices within the same set are adjacent. A bipartite graph is a special case of a k-partite graph with . The illustration above shows some bipartite graphs, with vertices in each graph colored based on to which of the two disjoint sets they belong.

Bipartite graphs are equivalent to two-colorable graphs. All acyclic graphs are bipartite. A cyclic graph is bipartite iff all its cycles are of even length

Another interesting concept in graph theory is a matching of a graph. This concept is especially useful in various applications of bipartite graphs. Let's discuss what a matching of a graph is, and how we can use it in our quest to find soulmates mathematically.

3)

A complete graph has an edge between every pair of vertices. For a given number of vertices, there's a unique complete graph, which is often written as KnKn, where n is the number of vertices.

A connected graph is any graph where there's a path between every pair of vertices in the graph.

Note that every complete graph is necessarily connected (one path between any pair of vertices is just to follow the edge between those vertices), but connected graphs are not necessarily complete (for instance, every tree is a connected graph, but KnKn can't be a tree for n≥3n≥3, since it must contain a cycle).

For example, this is the complete graph on 7 vertices, K7K7. It's also a connected graph:

The connecting graph has been given below has per the best path shpwing.