# Finding Multiplier nodes without graph analysis

This article provides an overview of statistical indicators to find users that have a significant high impact of other users. In the past, this was mostly done by graph analysis. This approach uses indicators that need no graph analysis for their results.

### Introduction

Multiplier nodes are users in social networks that have a significant number of friends and produce a high amount of network traffic. They communicate with other users or their posts were seen by a lot of people. Finding these users can be a profitable task for marketing researchers. The main idea is to feed this Multiplier user with coupons and concessions. The user then responds on the social networks and writes about his experience with the product. The scope of users that read those responses should be at the maximum. For this procedure, some graph analysis approaches exist. In this article a procedure without graph analysis is shown. These considerations are limited by a theoretical level.

### Indicators

The following concepts act as indicators for a specific campaign. In this document, a campaign is denoted as description of the marketing campaign including related:

• Keywords
• Phrases
• Emotions

In contrast to graph analysis, where the Multiplier is found using a graph optimizing algorithm, this analysis uses indicators to find the Multiplier. No single indicator can be seen as a full qualified indicator, which successfully estimates the Multiplier. Therefore a bunch of indicators are needed to verify the others.

User Network Value (UNV)

The UNV represents an index that shows the connection of each user from straight friends up to third degree friends (friends-of-friends-of-friends). The calculation uses a weight for each degree ηi. The number of friends is denoted with fi. Equation below represents the UNV. where i ∈ {allUsers} and j denotes the degree of friendship. The weights should be chosen to be 1 after a summation. A possible allocation is shown can be seen below:

η1 = 0.5, η2 = 0.35, η3 = 0.15

User Activity Index (UAI)

To find out which user represents the perfect Multiplier node, another indicator points out the activity of each user in the history. To realize the UAI the activities in the past time windows must be classified in time clusters ci. For each system component si (message, comment and others) as number of activities exists a weight wi which represents the importance of each component. The idea behind UAI is an increasing length of the time cluster that corresponds with the age of the cluster. Furthermore the weight decreases corresponding to the age.

length(ci) > length(cj)

where i > j and the higher number represent an older time cluster. To define the the borders of a time cluster ci two variables are defined:

hiL < hiH

which denote the lower and higher bound of a time cluster and can be allocated with the number of hours (or minutes) from the current time.
The interpretation of the UAI is shown in equation. The uai of user i is calculated using the number of produced system components s of user i together with the weight w of system component k. This is calculated for each time cluster j.

Neighborhood Trusting Profile and Polarization (NTPP)

The friends of the user are the key of this calculation. A Multiplier user should have a well friend environment and not known as an annoying individual. This calculation tries to estimate this state, but it is not able to find ‘spammers’ successfully.
The system components are denoted with si and the corresponding weights are defined with wi. Responses to this system components are denoted with ri. If the system component has no responses, then this parameter can be used to define the acceptance within the community. A simple proposal to calculate this value is shown below. which defines the NTTP of user i. Additional investigations are necessary and can be covered using text analysis of system components and responses.

System Component Text Matching (SCTM)

Each marketing campaign can be described by a set of keywords K = {relevantWords}. We define a similarity function sim(x,K) which returns a similarity value between a users text xij (ith user and jth text) and the elements of K. This method is able to find hidden potentials. This calculation must be done for each user with all written texts. The SCTM should use a weight w for each individual text type. The sim()-function as well as the calculation for each user can be defined in various ways. Therefore SCTM has no explicit calculation rule. All in all, a similarity index can be a powerful measure to find the correct person and classify as Multiplier.

Text Length Classification (TLC)

This measurement provides an array of information about the text lengths for all system components as well as some special information This contains the longest and shortest as well as the mean value for each system component. The next step is the classification into length clusters (for example 0-5, 6-10, …, 151-200, …). This indicator is able to find spammers and avoids the selection of them as Multiplier user.

Emotional Context Analysis (ECA)

The ECA indicator uses the emotional value of a user to select them for Multiplier calculations. Emotions are denoted with ei from (1-10). The origin emotions are rage, sorrow, fun, surprise, disgust, fear and love. A given set of words that are annotated with the corresponding emotions are defined with W. The idea contains the estimation of an emotional value between the users texts Xi and the resulting emotional value context Zi. With Zi the similarity between user and campaign emotions can be compared. This indicator should be used to refine the selection of potential Multipliers. The solely usage of this indicator is not expressive enough.

### Conclusion

All introduced indicators are described theoretical. Some theoretical experiments with self-constructed social network users point out, that this approach is able to find the desired node. Nonetheless, practical experiments using the users of a real social network can bring more insight into the utility of this approach.
All in all the found indicators can be used to support the traditional graph analysis and used for the refinement of possible Multipliers. Further work on this approach contains the search for new indicators and the test of significance of existing indicators.