A group of researchers has created a model they say can identify and predict how multiple relationships form in social networks. The nuance, they say, is that multiple, distinct types of relationships often occur among users of the same network and existing models that explain how relationships form in a network don't account for these variations.

As an example, they note that when people connect with each other through networks, they connect via multiple relationships. Two Facebook users may be "friends" but may not regularly communicate with each other directly and a user commenting on another's profile or otherwise actively communicating represents a different type of relationship in the network.

Offline, multiple relationships also exist, like when employees in different departments in an organization perform different types of work but still interact with each other. The researchers wanted to know whether the formation of one type of relationship in a network could predict connections via other types of relationships.

The professors developed an integrated statistical framework for simultaneously modeling the connectivity structure of multiple relationships of different types on a common set of actors. They used hierarchical Bayesian methods for estimation and illustrate their model with two applications: the first application used a sequential network of communications among managers involved in new product development activities, and the second used an online collaborative social network of musicians. 

They modeled both direct - a relationship with a clear sender and receiver - and undirected relationships, such as a collaboration relationship, to prove how disparate relationships can be jointly modeled within a common framework. In terms of multiple relationships, the statistical framework created by the researchers can also captured weighted and unweighted relationships. 

In terms of social networking online, the researchers focused on a Swiss social networking site for music artists, where three types of relationships were studied: individual friendships between artists; relationships based on communication or the exchange of information, such as direct messages or comments about upcoming concerts; and artists' downloads of other artists' music. They found that common factors determined the likelihood that each of these relationships would form, including geographical proximity of users; the online, as opposed to offline, popularity of artists; and whether the users shared an identity as an individual artist or as part of a band.

These factors were related with the existence of a relationship and its strength; for instance, the more messages two users sent each other, the stronger the connection between them.

In terms of networking in the workplace, the researchers measured the impact of interventions in a network by focusing on an organization's small network of different groups of managers — such as research and development, marketing, and operations — involved in the development of a new product.

These managers were moved into one shared facility, with researchers examining the types and strength of relationships between managers from different departments before and after the intervention. The model accurately predicted what relationships would form based on common characteristics and predicted the effects of intervention on relationships in the network.

They hope their method can help identify and target influential users in a network, predict network relationships, and improve understanding of the network structure - for the collaboration aspects of Science 2.0, this remains a key obstacle.

The study's applications involved small networks, recent research has shown that while online networks can have millions of members, communities within such networks are relatively small, with sizes in the vicinity of 100 members. This implies that very large networks can be broken down into clusters of tightly knit communities, and when such communities are identified, their methodological framework can then be used on such communities to further understand the nature of linkages within these sub-communities.

Citation: Asim Ansari, Oded Koenigsberg, and Florian Stahl, 'Modeling Multiple Relationships in Social Networks',  Journal of Marketing Research Volume 48, Number 4, August 2011