Group 7 : OrientExpress Blog

In order to add relevant credits with each person on mobile contacts based on every interaction, the contacts priority ranking algorithm can be adopted as the social ranking algorithm in this application.

The proposed algorithm is based on the Social Strength Calculation Approach, and the evaluation criterion mainly is the user’s mobile communication history.

Here, we suppose that the user has seven contacts in his mobile contacts list, and the communication history record is shown as the Table 1 below.

For the reason that each frequency parameter f has three dimensions i, j and k, like the Figure below.

Then, we can get the relevant values for the parameters i, j and k in the following tables:

After that, we can use these values to transform the mobile communication history record table to the frequency logs table below.

Then, the utility function below can be used to formulate the social strength calculation.

What’s more, because different communication methods have different weight and will add different credits to the social strength with each contact, so in this application we set that “Real Meet” > “Video” > “Call” > “SMS”. Accordingly, we set the weight parameters as the table below.

For Communication Service of Mobile Communication (i=1). The strength of the user with each contact is (from a=1 to a=7):

Hence, we get:

S(1,1)=100.7738
S(1,2)=104.2857
S(1,3)=210.4762
S(1,4)=45.5953
S(1,5)=47.8571
S(1,6)=82.7975
S(1,7)=8.2143

For Communication Service of Real Communication (i=2). The strength of the user with each contact is (from a=1 to a=7):

Hence, we get:

S(2,1)=60
S(2,2)=30
S(2,3)=150
S(2,4)=0
S(2,5)=30
S(2,6)=30
S(2,7)=0

After the strength of each communication service of contact a is calculated, the overall strength of that individual contact can be calculated accordingly by the following function:

Hence, we get:

S(1)= 172.7738
S(2)= 140.2857
S(3)= 390.4762
S(4)= 45.5953
S(5)= 83.8571
S(6)= 118.7975
S(7)= 8.2143

Then the application will be able to adopt the calculated results to rank the contacts in a descending order. For example:

Finally, we can get the contacts ranking result as the figure below.

Basic Theory Background
Dunbar’s number is an approximate number of social relationships that humans can maintain with stably over time. This theory is proposed by Robin Dunbar [1], who is an anthropologist in Oxford University of UK. It is derived according to ape’s intelligence and social networks. Dunbar’s number ranges from 100 to 150, defining the size of the group in which every member knows each other. It is determined by human’s mind capability. As the available capital of human’s mind is a constant [2], the number of close relationships is limited. In fact, people will let weaker relationships dissipate and spend efforts to maintain a core group of fewer than 150 or so. [3] In order to maintain a close relationship, considerable investments are required in both emotion and psychology.

Statistics from Facebook
Facebook’s own statistics suggests that the average number of user’s friends is about 130 [4], which is a fact that proves the theory of Dunbar’s number. Although the number of friends of different Facebook’s users is quite different (for example, some Facebook’s users have more than 500 friends), actually, in personal lists of friends, the number of friends that users contact with frequently is quite small and relatively stable. The more actively and closely friends contact with others, the less and more stable the number of such a group is.

Relevance to Our Project
Our social networking application based on mobile contacts aims to strength the interactions and relationships with user’s closest friends by ranking user’s social networks’ information. How to define user’s closest friends? Dunbar’s number tells us that most friends on our social networks are not people that we know and actually interact with most in real life. The closest friends are whom we care about and interact with in our daily lives and they are just in our contacts. Our project’s main idea is to calculate the relationship degrees between user and user’s contacts to quantify the relationships between user and contacts.

References:
[1] R. Dunbar. How Many Friends Does One Person Need? Dunbar’s Number and Other Evo-lutionary Quirks. Faber and Faber, 2010.

[2] Huiji Gao, Xufei Wang, Jiliang Tang and Huan Liu. “Network Denoising in Social Media”, Technical Report, TR-11-002, School of Computing, Informatics, and Decision Systems Engineering, Arizona State University, Tempe, AZ 85287, 2011.

[3] Shyong (Tony) K. Lam and John Riedl, University of Minnesota. Are Our Online “Friends” Really Friends.

[4] See https://www.facebook.com/press/info.php?statistics/

As a social networking application which built based on the mobile contacts, it will be possible to visualize the degree of relationship between you and your friends through our application. In order to add relevant credits with each person on mobile contacts based on every interaction, the contacts priority ranking algorithm can be adopted as the social ranking algorithm in this application.

The proposed algorithm is based on the Markov Chains Theory and Social Strength Calculation Approach, and the evaluation criterion mainly is the user’s mobile communication history.

Firstly, the social strength between the user and all his contacts will be calculated. The social strength is a numerical value which used to define the degree of relationship in the user’s social graph. The communication history log is presented just like the Table 1 below. The interactions mainly contain two categories, which including both mobile interaction and real interaction.

Furthermore, each frequency parameter f has three dimensions i, j and k, which i implies to communication service like mobile interaction or real interaction; j implies to communication tools like call, SMS or video chat; and k implies to the contacts (Figure 1) [1]. The main user is represented as U and the overall social strength of the user U is 1.

Then, the utility function can be used to formulate the social strength calculation. The utility function [1] is:

Where S(i,a) provides the strength of the user U with the contact a especially for the communication service i; q is the total number of communication tools in service i; value f(i,j,a) is the frequency record which has been mentioned in Table 1; parameter thres(i,j) is the threshold value estimated over the usage on communication tool j of the communication service i. After the strength of each communication service of contact a is calculated, the overall strength of that individual contact can be calculated accordingly by the following function [1]:

Where S(a) provides the overall strength of the user U with contact a, parameter thres(i) is the threshold value estimated over the usage of the communication service i.

After the social strength of all interactions between the user and his contacts are calculated, the application then will be able to adopt the calculated results to rank the contacts in a descending order.

References:
[1] Dudarenko, Natalia, Juwel Rana, and Kare Synnes. “Ranking Algorithm by Contacts Priority for Social Communication Systems.” Springer-Verlag Berlin Heidelberg 6249th ser. (2010): 38-49. Print.

[2] Rana, J., Kristiansson, J., Josef, H., Synnes, K.: “Enriching and Simplifying Communication by Social Prioritization”. In: ASONAM 2010: Proceedings of the The 2010 International Conference on Advances in Social Networks Analysis and Mining, Odense, Denmark, August 9-11 (2010).