Probabilistic Relation between Triadic Closure and the Balance of Social Networks in Presence of Influence

Introduction

In the present world of social communication, the data analysis of social networks and identifying the human behaviour is a challenging issue. A number of researchers have done remarkable analysis on such data and have interpreted different social networking features. One of such features tell us about triadic closure. Triadic closure discussed by the authors in Wang et.al (2012) and Huang et.al, 2014), shown in Figure 1, highlights that if there are two nodes (users) having a common friend, there is a possibility that the two nodes will also become friends in the near future, and this often happens in our social lives. Not only social networking sites, triadic closures are also an obvious phenomenon in different social affiliations as discussed in Lattanzi and Sivakumar (2009). The reason behind this triadic closure somehow depends on the user’s behaviour and social influences.

Figure 1.

Triadic closure property

In the structure of social networks, two types of social relations or links, as described by the authors Tang et.al (2012) and Cartwright and Harary (1956), are practically seen: Positive relation (+ve) deals with the connection between two nodes and negative relation (-ve) which includes the nodes with whom we are not having any friendship. In our further studies, we have extended the concept of negative relations as an enemy link or no connection present between two nodes to generalize the facts. Let us consider the scenario of Facebook, Twitter or any other social networking sites. We often categorize the links in our social networking sites as family, colleagues, familiar and so on. These links are positive links and those with whom we are not connected but come as a suggestion for friendship in the social networking sites can be considered as negative links. Apart from triadic closure, the data analysis shows the stability of the network structure depending upon these +ve or –ve relations. The stability of the social network is defined by the Balanced Theorem described by the authors in Heider (1946) and Heider (1958). The stability comes in the network when we can categorize the +ve and –ve links in two distinct global sets. As social network deals with building up connection among two nodes or people socially, the reasons of such connections are dynamic. Often we always talk about the term affiliation. The social affiliation factors shown by Lattanzi & Sivakumar (2009) and Borgatti and Halgin (2011) influence a lot to create a +ve link. Along with that, the users’ dynamic behaviour and different social contextual influences can also remove a link.

Previous Work

The social structural balance depending upon positive and negative relations was introduced by the author in Heider (1946) and Heider (1958). Many researchers (e.g. Yi Qian Sibel Adalı, 2014) have extended this theory to prove different features of social networks. In paper Khanafiah & Situngkir (2004) the authors have shown their analysis of social networks where multiple agents are present in the scenario. One of the most valuable researches along these lines is the classic work by Davis, Holland, and Leinhardt using the sociometric data bank, a collection of sociometric measurements of positive interpersonal sentiments from different settings to investigate the presence of structural balance, clustering, hierarchy, and transitivity as described by the authors Davis (1970), Davis and Leinhardt (1972) and Holland and Leinhardt (1971, 1973). Many researches have projected on the socio metric measurements and micro level structure (local) and macro level (global) structures have been proposed further.