Implicit Social Network is a connected social structure among a group of persons, where two of them are linked if they have some common interest. One real-life example of such networks is the implicit social network among the customers of an online commercial house, where there exists an edge between two customers if they like similar items. Such networks are often useful for different commercial applications such as target advertisement, viral marketing, etc. In this article, we study two fundamental problems in this direction. The first one is that, given the user-item rating data of an E-Commerce house, how we can design implicit social networks among its users and the second one is at the time of designing itself can we obtain the connectivity information among the users. Formally, we call the first problem as the Implicit User Network Design Problem and the second one as Implicit User Network Design with Connectivity Checking Problem. For the first problem, we propose three different algorithms, namely ‘Exhaustive Search Approach’, ‘Clique Addition Approach’, and ‘Matrix Multiplication-Based Approach’. For the second problem, we propose two different approaches. The first one is the sequential approach: designing and then connectivity checking, and the other one is a concurrent approach, which is basically an incremental algorithm that performs designing and connectivity checking simultaneously. Proposed methodologies have experimented with three publicly available rating network datasets such as Flixter, Movielens, and Epinions. Reported computational time shows that the ‘Clique Addition Approach’ is the fastest one for designing the implicit social network. For designing and connectivity checking problem the concurrent approach is faster than the other one. We have also investigated the scalability issues of the algorithms by increasing the data size.

隐性社交网络是一群人之间相互联系的社会结构，如果他们有共同的兴趣，则其中的两个人会相互联系。此类网络的一个现实示例是在线商业商店客户之间的隐式社交网络，如果两个客户喜欢相似的商品，则在两个客户之间存在优势。这样的网络通常可用于不同的商业应用，例如目标广告，病毒式营销等等。在本文中，我们研究了这个方向上的两个基本问题。第一个是，鉴于电子商务商店的用户项目评分数据，我们如何在其用户之间设计隐式社交网络，第二个是在设计自身时可以获取用户之间的连通性信息。正式地，我们将第一个问题称为隐式用户网络设计问题，将第二个问题称为具有连接性检查的隐式用户网络设计问题。对于第一个问题，我们提出了三种不同的算法，分别是“穷举搜索法”，“群体加法法”和“基于矩阵乘法的法”。。对于第二个问题，我们提出了两种不同的方法。第一种是顺序方法：设计然后进行连通性检查，另一种是并发方法，基本上是一种同时执行设计和连通性检查的增量算法。提议的方法已经尝试了三个公开的评级网络数据集，如Flixter，Movielens和Epinions。报告的计算时间表明，“群体加法”是设计隐式社交网络的最快方法。对于设计和连接检查问题，并发方法比另一种方法要快。我们还通过增加数据大小来研究了算法的可伸缩性问题。