Question

The following questions refer to the following graph. B D H E (a) (2 marks) Compute the embeddedness of the edge between nodes A and B (b) (2 marks) Compute the neighbourhood overlap between nodes A and B (c) (2 marks) Given that the graph satisfies the strong triadic closure property, ident most likely strength of the edge between A and E (either strong or weak) and explai reasoning (d) (2 marks) Identify a node in the graph that has high social capital and explain w position in the graph gives it high social capital.

Answer 1

(a)

Answer: Embeddedness: Embeddedness of an edge in a network to be the number of common neighbors the two endpoints have.

Here, the embeddedness of the edge between A & B is 2.

Since A & B have 2 common neighbors i.e C & D.

(b)

Answer: Neighbourhood overlap:  Neighborhood overlap of an edge is embeddedness divided by the total number of neighbors of both nodes connected by that edge.

Here, neighborhood overlap between  nodes A & B is 2:3

As, the embeddedness of the edge between A & B is 2, and nodes connected to at least A or B are 3 (C, D & E).

(c)

Answer: Strong triadic closure property can be defined by understanding the following phenomenon  "If two people in a social network have a friend in common, then there is an increased likelihood that they will become friends themselves at some point in the future."

Thus, here in the given figure, nodes E, G, H satisfies the strong triadic closure property, since, EH & EG are the edged between E & H, E & G, thus establishing a strong bond between E, H & E, G, thereby by according to strong triadic closure property, edge HG should exist, which is present n the figure.

Also, there is a possibility to satisfying of strong triadic closure property between A , E & E, H

therefore given graph satisfies strong triadic closure property.

(d)

Answer: Social Capital in a network system can be defined as, First, social capital is sometimes viewed as a property of a group, with some groups functioning more effectively than others because of the favorable properties of their social structures or networks.

Alternately, it has also been considered as a property of an individual; used in this sense, a person can have more or less social capital depending on his or her position in the underlying social structure or network.

Thus in the given figure, Nodes E & H are having the highest Social Capital among all the nodes in the given network system.