A brief look at the social relations and aspects of the Online networks

As an individual, each of us got a good amount of presence in the huge internet community and an increasing fraction of today’s social interactions occur using online social media as communication channels. Despite this, there are still open questions regarding the social value of online interactions. For example, the existence of users with millions of online friends sheds doubts on the relevance of these relations. This article is based on the statistical analysis done on twitter, one of the most popular online social networks, and find that the network formed by the basic type of connections is organized in groups. The activity of the users conforms to the landscape determined by such groups. Also, if you've ever wondered, why every researcher in Complex networks depends on twitter is because in contrast to the normal tweets, which are publicly available mentions usually include personal conversations or references while retweets are highly relevant for the viral propagation of information. This particular distinction between different types of interactions qualifies Twitter as a perfect system to analyze the relation between topology, strength of social relation and information diffusion in online social networks.

This whole analysis is based on the theory of Strength of weak ties proposed by Mark Granovetter which can found (here). Have a read if possible, a very interesting publication classifying the different kinds of social relations (can be implicated to both offline/online networks). It basically deals with the relation between structure, intensity of social ties and diffusion of information in offline social networks. Strong ties refer to relations with close friends or relatives, while weak ties represent links with distant acquaintances. On the other hand, a tie can be characterized by its position in the network. Social networks are usually composed of groups of close connected individuals, called communities, connected among them by long range ties known as bridges. A tie can thus be internal to a group or a bridge. Grannoveter’s theory predicts that weak ties act as bridges between groups and are important for the diffusion of new information across the network, while strong ties are usually located at the interior of the groups. In this article which's based on another research paper aims to show that this theory can applied even to the online networks.

In Twitter mentions are typically used for personal communication, which establishes a parallelism between links with mentions and strength of social ties. The more mentions has been exchanged between two users, even more so if reciprocated, the stronger we consider the tie between them. We define intensity of a link as the number of mentions interchanged on it.


(A) Sample of Twitter network: nodes represent users and links, interactions. The follower connections are plotted as gray arrows, mentions in red, and retweets in green. The width of the arrows is proportional to the number of times that the link has been used for mentions. We display three groups (yellow, purple and turquoise) and a user (blue star) belonging to two groups.
(B) Different types of links depending on their position with respect to the groups’ structure: internal, between groups, intermediary links and no-group links.

According to Granovetter’s theory, one could expect the internal connections inside a group to bear closer relations. Mechanisms such as homophily [43], cognitive balance or triadic closure favor this kind of structural configurations. Unfortunately, we have no means to measure the closeness of a user-user relation in a sociological sense in our Twitter dataset. However we can verify whether the link has been used for mentions, whether the interchange has been reciprocated or whether it has happened more than once. We define the fraction F(i,p) of links with interaction i in position p with respect to the groups
of size s as

where ni
p(s) is the number of links with that type of interaction in
position p with respect to the groups of size s and Ni in the total
number of links with interaction i. The analysis gives you :

(A) Size distribution of the group.
(B) Distribution of the number of groups to which each user is assigned.
(C) Percentage of links of different types, e.g. follower links (black bars), links with mentions (red bars) or retweets (green bars), staying in particular topological localizations in respect to detected groups.

We define the similarity between two groups, A and B, in terms of the Jaccard index of their connections:


The results show that the most likely to attract retweets are the links connecting groups that are neither too close nor too far. This can be explained with Aral’s theory about the trade-off between diversity and bandwidth: if the two groups
are too close there is no enough diversity in the information, while if the groups are too far the communication is poor.

A) Fraction f of internal links as a function of the group size in number of users. The curve for the follower network acts as baseline for mentions and retweets. Note that if mentions/retweets were randomly appearing over follower links then the red/green curve should match the black curve.
(B) Distribution of the number of mentions per link.
(C) Fraction of links with mentions as a function of their intensity. The dashed curves are the total for the follower network (black) and for the links with mentions (red). While the other curves correspond (from bottom to top) to fractions of links with: 1 non-reciprocated mention (diamonds), 3 mentions (circles), 6 mentions (triangle up) and more than 6 reciprocated mentions (triangle
down).

Summary :

The activity in the network in terms of the messages called mentions and retweets clearly correlates with the landscape that the presence of the groups introduces in the network. Mentions, which are supposed to be more personal messages, tend to
concentrate inside the groups or on links connecting close groups. This effect is stronger the larger the number of mentions exchanged and if they are reciprocated.
From the sociological point of view, the way that the activity localizes with respect to the groups allow us to establish a parallelism with the organization of offline social networks.In particular, we can see that the theory of the strength of weak
ties proposed by Granovetter to characterize offline social network applies also to an online network.