Consider the social network represented in Figure 4.20. Suppose that this social
ID: 3863797 • Letter: C
Question
Consider the social network represented in Figure 4.20. Suppose that this social network was obtained by observing a group of people at a particular point in time and recording all their friendship relations. Now suppose that we come back at some point in the future and observe it again. According to the theories based on empirical studies of triadic closure in networks, which new edge is most likely to be present? (I.e. which pair of nodes, who do not currently have an edge connecting them, are most likely to be linked by an edge when we return to take the second observation?) Also, give a brief explanation for your answer.
Explanation / Answer
Triadic closure is a concept in social network theory, first suggested by German sociologist Georg Simmel. Triadic closure is the property among three nodes A, B, and C, such that if a strong tie exists between A-B and A-C, there is a weak or strong tie between B-C.This property is too extreme to hold true across very large, complex networks, but it is a useful simplification of reality that can be used to understand and predict networks.
Now to deciede which node is improtant or which node must likely to be present we introduced some network centrality measure techniques which will say that among many nodes in a graph which node is most improtant.
1. Degree Centrality
The first method is degree centrality measures. Perhaps the simplest centrality measure in a network is just the degree of a vertex, the number of edges connected to it. Degree is sometimes called degree centrality in the social networks literature, to emphasize its use as a centrality measure. In directed networks, vertices have both an in-degree and an out-degree, and both may be useful as measures of centrality in the appropriate circumstances. Although degree centrality is a simple centrality measure, it can be very illuminating. In a social network, for instance, it seems reasonable to suppose that individuals who have connections to many others might have more influence, more access to information, or more prestige than those who have fewer connections. Node with the highest degree is most important. The more neighbors a given node has, the greater is its influence. In human society, a person with a large number of friends is believed to be in a favorable position compared to persons with fewer. This leads to the idea of degree centrality, which refers to the degree of a given node in the graph representing a social network.
2. Eigenvector Centrality Measures
A natural extension of the simple degree centrality is eigenvector centrality. We can think of degree centrality as awarding one “centrality point” for every network neighbour a vertex has. But not all neighbours are equivalent. In many circumstances a vertex’s importance in a network is increased by having connections to other vertices that are themselves important. This is the concept behind eigenvector centrality. Instead of awarding vertices just one point for each neighbour, eigenvector centrality gives each vertex a score proportional to the sum of the scores of its neighbours.
Eigenvector centrality is a measure of the influence of a node in a network. It assign relative scores to all the nodes in the network based on the concept that connections to the high scoring nodes contributes more to the score of the node in question than equal connections to the low scoring nodes. Google’s PageRank is a variant of eigenvector centrality measure.