Social Network Analysis: Mapping Connections and Influence

Basics of Social Network Analysis

if you pick an unknown person from anywhere in the world, you know him/her on average by 6 connections as per the “theory of six degrees of separation”?

In mathematical terms, this structure is called a graph. The individual participants in the network are referred to as nodes or vertices. The specific node under study is known as the ego, while the nodes directly connected to the ego are called alters. The connections or relationships between these actors are known as edges or ties. These edges can be visualized as lines drawn between two nodes, and they may or may not have arrowheads, depending on the nature of the relationship.

For example, if you (the ego) and your friend (an alter) regularly go out for snacks and share the bill equally, the relationship is reciprocal. In such cases, the edge connecting you and your friend does not have an arrowhead, indicating that the connection works both ways. On the other hand, a directed graph represents relationships that are not necessarily mutual. Here, the edges have arrowheads to indicate the direction of the relationship. For instance, if you frequently call your friend but they never initiate the call, the relationship is asymmetrical. In this scenario, you act as the sender and your friend as the receiver. The edge connecting you to your friend would have an arrow pointing towards your friend, illustrating the one-way nature of the interaction.

1.2 Adjacency Matrix

Figure 1.2: Undirected graph (connection represented by a line segment) Figure 1.3: Directed graph (connection represented by an arrow)

1.3 Centrality Measures

general notion of the ‘importance’

Degree Centrality

It measures the number of connections of a node. Where, is the number of edges incident on vertex v is the maximum number of edges incident on a node u present in the network. Or, is the number of edges incident on a node.