Detecting the Influencer on Social Networks Using Passion Point and Measures of Information Propagation ^† †

Abstract

Influencer marketing is a modern method that uses influential users to approach goal customers easily and quickly. An online social network is a useful platform to detect the most effective influencer for a brand. Thus, we have an issue: how can we extract user data to determine an influencer? In this paper, a model for representing a social network based on users, tags, and the relationships among them, called the SNet model, is presented. A graph-based approach for computing the impact of users and the speed of information propagation, and measuring the favorite brand of a user and sharing the similar brand characteristics, called a passion point, is proposed. Therefore, we consider two main influential measures, including the extent of the influence on other people by the relationships between users and the concern to user’s tags, and the tag propagation through social pulse on the social network. Based on these, the problem of determining the influencer of a specific brand on a social network is solved. The results of this method are used to run the influencer marketing strategy in practice and have obtained positive results.

1. Introduction

Online social networks are an efficient tool for spreading information. They have been proven to be very powerful in many situations—e.g., Facebook and Twitter during the 2008 U.S. presidential elections [1]—and in digital marketing. Researchers have recently focused on modeling, visualizing, tracking, and predicting information diffusion to better understand the dynamics of social networks [2,3,4]. Using this understanding, other issues—such as analyzing revolutionary waves, optimizing social marketing campaigns, and anticipating and handling the information diffusion in the future—can be resolved better.

Twitter is a social networking site where people communicate in short messages called tweets. Anyone who follows you on Twitter can see any short message posted by you [5]. The determining of influencers on Twitter has many applications; for example, it can be used for political sciences, human mobility, and transportation [6].

The identification of the influencer for a brand plays a vital role in influencer marketing. There are many understandings of what an influencer is. The definition of an influential user involves proposed criteria of influence. Influential users may be leaders [7], authoritative actors [8], or prestigious [9] or topical experts on specific domains [10]. All of these can affect other people. They can even create trends. On social networks, an influential user is similar, but it is in the virtual world, such as a leader of a country, CEO, singer, artist, actor, actress, director, journalist, and so on. They can attract other people and receive many interactions from users via several systems. Information from him/her obtains fast propagation on the social network. Hence, the influencer makes a brand, approaching goal customers easily and quickly.

Detecting the influencer on social networks benefits the brand. Some critical psychological factors affect attitudes towards purchasing online [11]. These factors are elements in overall studies of online behavior. The influencer is a factor that impacts the behavior of shopping online.

In this paper, a model for representing a social network is presented, called the SNet model. It includes two main objects: users and tags. This model can represent the relationship between these objects. The method for the computing of the passion point is proposed by combining the number of positive posts created about the specific brand, the average number of interactions per post, and the number of active days of the user. The passion point is used to determine the community that interests the brand/product/news.

Some measures of influence on the social network are proposed based on the structure of the SNet model. They represent the ability to impact other people by the relationships between users and the concern to the user’s tags. The measure of information propagation through social pulse has been studied. The problem of determining the influencer of a specific brand/product/news on an online social network is solved by using these measures. Firstly, from the global network to a brand, a product, or a piece of news, we create a sub-graph that presents the community that loves the brand and the information diffusion among users in that community. After that, based on the influence measures proposed, we determine the user, leading to an effect on people in the community structure.

The next section presents related works for detecting the influencer on the social network. Section 3 constructs a model for representing relations on a social network. Section 4 proposes some measures of influence for a user, based on information propagation. Section 5 presents a formula to evaluate the user’s passion point with a brand or product. The structure of a community loving a brand is established based on the passion point. The process and algorithms to determine the influencer on a social network are also presented in this section. Section 6 shows the experimental results in reality based on the proposed method. The last section concludes the paper and presents some future works.

2. Related Work

Chen et al. [12] described the properties of diffusion models, as well as numerous extensions to them, introducing aspects such as competition, budget, and time-criticality. They also studied the problem of influence maximization, which selects key individuals to influence a large fraction of a network. The problem can be applied to detect the influencer on a social network. However, these properties are general; they have not yet delved deep into the real-world problem.

Laroche et al. [13] built a nomological network of relationships between brand community markers, value creation practices, brand trust, and brand loyalty. They measured community-related constructs that were useful in conducting future survey-based brand community studies. Based on these results, they studied to explore the brand’s loyal communities, which had positive effects on the goal customers of that brand.

There are some methods to represent the knowledge of relations, such as the computational network for computational relations between objects [14] and the Rela-model for the knowledge of relations [15]. However, the computational network is only active for reasoning on computational relations, and it cannot be used to represent the relations between objects on a social network. The Rela-model is applied to construct the knowledge bases of expert systems. Although this model is general for representing relations of a social network, it is unable to represent some characteristics of users on the social network. Hence, these methods cannot be used to solve the problem of determining the influencer on a social network.

Another feature for detecting the influencer is the favorite with a brand or product. If the user loves the brand, he/she uses positive posts to review it regularly. The passion point quantifies how much the passion, dedication, and contribution of each user promotes the brand to a specific community that cares for the brand. This point is useful to classify brand lovers.

The positive rate of a post can be used to determine the user’s love for a brand. The binomial proportion is defined as the number of successes divided by the number of trials. This method was used to classify schema for irony detection in Greek political tweets on Twitter [16]. Our hypothesis states that the positive rate of a post is observed as the binomial proportion [17]; we can compute that rate. Based on the positive rate, the passion point to measure the favorite of a user with a brand is established. This point is also the foundation to build a loyal brand community. This community is used to detect the influencer on a social network.

Valdiviezo et al. [18] presented a scheme for visualizing sentiment changes in real-time in social networks, called SCWorld. Besides getting a large-granularity view of relationships among dynamic clusters of topics on the social network, users can observe the graph representing the sentiment changes. This graph reflects the aggregated polarity of postings on social networks. Nonetheless, SCWorld does not have the measures for detecting the influencers.

The biometric eye tracking is applied to determine how attention is paid to fashion promotion by curvy influencers in comparison with communications by fashion brands on a social network [19]. However, this method does not mention the characteristics of an influencer on a social network.

The speed of information propagation was studied in [20]. It was determined based on the social pulse. However, this study did not mention the measurement of the influence of one tag to another. In [6], the authors presented measures of influence for a user on Twitter. These measures have many values impacting the cover of a user on Twitter. However, it has not yet mentioned the tweet propagation. The study in [21] presented an influent measure based on the speed of tag propagation; however, this measure has not yet reflected the information impact of a user on a social network.

Morente-Molinera et al. [22] presented a method to determine how debate on the social network is progressing based on the consensus among the participants. Sentiment analysis was also used to measure the preference level that social media users have regarding a specific set of alternatives. Nonetheless, these methods cannot recognize trends on a social network to detect an influencer.

3. Model for Representing Relations on Social Networks

There are two main kinds of objects on a social network: users and the tags posted by users. A tag may be a post, image, or clip. Some conditions of research relations on a social network are as follows:

• Tags in this paper are text-based posts only.
• All users on the social network understand the meaning of a tag.

In this paper, some symbols are used:

• TIME is the data type as the timestamp.
• #(A) is the number of elements in set A.

Definition 1.

The model for representing relations on a social network, called SNet, includes three components:

(U, T, R)

where U is a set of users on a social network and T is a set of tags on a social network. A user can have many tags, and a tag can be related to many users. R is a set of relations on a social network.

3.1. U–Set of Users on a Social Network

U is a set of users on a social network. Each user is a tube of five elements:

(Profile, ListTags, ListFriends, ListFollowers)

• Profile: includes the personal information of a user, such as ID, name, DOB, and phone number.
• ListTags = [t₁,…,t_n]: list of tags t_i in T-set, which are related to the corresponding user (i = 1…n).
• ListFriends = [f₁,…,f_m]: list of other users f_j in U-set, which are friends with the corresponding user (j = 1…m).
• ListFollowers = [l₁,…,l_p]: list of other users l_k in U-set, which are followers of the corresponding user (k = 1…p).

(Relations friends and followers are defined in Section 3.3).

3.2. T–Set of Tags on a Social Network

T is a set of tags on a social network. Each tag is a tube of seven elements:

(Content, Owner, Mention, τ, Interaction, Sh, Com)

• Content: describes the content of the tag.
• Owner ∈ U: this is the user as the seeder of the corresponding tag.
• Mention: list of users mentioned in the tag.
• τ ∈ Time: a timestamp of the corresponding tag.
• Interaction: is a set of users who interacted with the corresponding tag.
  • Interaction: = {(u, π_u) ∈ U × Time | interact(u, *this), *this is the corresponding tag,
  • π_u ∈ Time is the timestamp of the interaction corresponding tag of user u}
• Sh is a set of users who shared the corresponding tag.
  • Sh: = {(u, π_u) ∈ U × Time | share(u, *this), *this is the corresponding tag,
  • π_u ∈ Time is the timestamp of the corresponding sharing tag of user u}
• Com is a set of users who have comments on the corresponding tag.
  • Com: = {(u, π_u) ∈ U × Time | comment(u, *this), *this is the corresponding tag,
  •    π_u ∈ Time is the timestamp of the comment of user u}

(Relations interact, share, and comment are defined in Section 3.3).

3.3. R–Set of Relations on a Social Network

R is a set of binary relations on a social network. There are two kinds of relations:

R = R_U ∪ R_T

• R_U: a set of relations between two users.
• R_T: a set of relations between a user and a tag.

The detailed relations are shown in Table 1:

Table 1. Relations on a social network.

Kind	Relation	Meaning
Relations between two users (RU)	friend ⊆ U × U	friend(u, v): the user u is a friend of the user v.
	follower ⊆ U × U	follower(u, v): the user u is a follower of the user v.
Relations between a user and a tag (RT)	interact ⊆ U × T	interact(u, t): the user u interacts with a tag t, such as u likes/views/searches the tag t.
	comment ⊆ U × T	comment(u, t): the user u has a comment on a tag t.
	share ⊆ U × T	share(u, t): the user u shares a tag t.

4. Measures of Influence for a User

In this section, the measures of influence for a user on a social network as the SNet model are proposed. They include the vector representing the ability of the influence on other people by the relationships between users and the concern to the user’s tags. Besides this, they also include the speed of the user’s tag propagation on the social network.

4.1. Influential Vector of a User

Given a user u ∈ U, there are some metrics on the user u:

• SI(u): sharing the impact of the user u. It measures the impact of the user’s post in terms of the shared tags.

$$SI(u)=\frac{{\alpha }_1.\#(S{U}_1(u))+{\alpha }_2.\#(S{U}_2(u))+{\alpha }_3.\#(S{U}_3(u))}{\#(u.ListFriends)+\#(u.ListFollowers)}$$

(1)

where $SU(u):={\displaystyle \underset{t\in u.Listags}{\cup }t.Sh}$: a set of users sharing u’s tags.

SU₁(u):={v | v ∈ SU(u) and friend(u, v) }: set of users sharing u’s tags and those users are friends of user u.

SU₂(u):={v | v ∈ SU(u) and follower(v, u) }: set of users sharing u’s tags and those users are followers of user u.

SU₃(u):= SU(u) \ (SU₁(u) ∪ SU₂(u)): set of users sharing u’s tags, and those users are not related to user u.

α₁, α₂, α₃: are weighted numbers, 0 < α₁ ≤ α₂ ≤ α₃ < 1.

When a user shares a tag, it means he/she was interested in this tag. A friend is more interested in the post than a follower, and an unrelated user is only interested in the post if this post is very exciting [23]. Therefore, the weight for the sharing of followers is higher than the weight for the sharing of friends, and the weight for the sharing of unrelated users is higher than the weights for the sharing of friends and followers. Thus, we have α₁ ≤ α₂ ≤ α₃. These weighted numbers can be determined based on the characteristic of a social network.

• CI(u): comment impact of the user u. It measures the impact of comments on u’s tags.

$$CI(u)=\frac{{\beta }_1.\#(C{U}_1(u))+{\beta }_2.\#(C{U}_2(u))+{\beta }_3.\#(C{U}_3(u))}{\#(u.ListFriends)+\#(u.ListFollowers)}$$

(2)

where $CU(u):={\displaystyle \underset{t\in u.Listags}{\cup }t.Com}$: a set of users having comments on u’s tags.

CU₁(u):={v | v ∈ SU(u) and friend(u, v) }: set of users having comments on u’s tags and those users are friends of user u.

CU₂(u):={v | v ∈ SU(u) and follower(v, u) }: set of users having comments on u’s tags and those users are followers of user u.

CU₃(u):= CU(u) \ (CU₁(u) ∪ CU₂(u)): set of users having comments on u’s tags and those users are not related to user u.

β₁, β₂, β₃: are weighted numbers, 0 < β₁ ≤ β₂ ≤ β₃ < 1. These weighted numbers can be determined based on the characteristic of a social network.

• Ir(u): interactor ratio for the tag of the user u.

$$Ir(u)=\frac{{\gamma }_1.\#(I_1(u))+{\gamma }_2.\#(I_2(u))+{\gamma }_3.\#(I_3(u))}{\#(u.ListFriends)+\#(u.ListFollowers)}$$

(3)

where $I(u):={\displaystyle \underset{t\in u.Listags}{\cup }t.Interaction}$: a set of users interacting on u’s tags.

I₁(u):= {v | v ∈ I(u) and friend(u, v) }: a set of users interacting on u’s tags, and those users are friends of user u.

I₂(u):= {v | v ∈ I(u) and follower(v, u) }: a set of users interacting on u’s tags, and those users are followers of user u.

I₃(u):= I(u) \ (I₁(u) ∪ I₂(u)): a set of users interacting on u’s tags, and those users are not related to user u.

γ₁, γ₂, γ₃: are weighted numbers, 0 < γ₁ ≤ γ₂ ≤ γ₃ < 1. These weighted numbers can be determined based on the characteristic of a social network.

• Popularity (u):

Most social networks are scale-free networks [24]. A scale-free network is a network whose degree distribution follows a power law, so the number of nodes in the network that have k connections, denoted P(k), goes for large values of k as P(k) = k ^−γ, where γ is a constant number (2 < γ < 3) [25]. Hence, in the social network, a popularity measure of a user can be calculated based on the number of in-links of the users as follows [25]:

$$Popularity(u)=1-e^{-\lambda .\#(F)}$$

(4)

where F:= u.ListFriends, ∪ u.ListFollowers, and λ: is a constant.

Definition 2. (Influence of user).

Given a user u∈ U, the measure of influence for the user u is represented by the vector:

IU(u) = (Impress(u), Popularity(u))

(5)

where impress

$$(u)=\frac{\alpha .SI(u)+\beta .CI(u)+\gamma Ir(u)}{\alpha +\beta +\gamma }$$

(6)

SI(u), CI(u), Ir(u) are computed by Formulas (1), (2), and (3), respectively.

α,β, and γ: are weighted numbers.

Impress(u) is the average of the impact of sharing, commenting, and interacting of user u. In this paper, we assume that: when a user shares a post, he/she thought this post was useful to others; when a user comments on a post, he/she thought about it; when a user likes a post, it may be a habit of the user [23]. Thus, we have 0 <γ≤β≤α < 1.

4.2. Information Propagation

Definition 3. 

(Social pulse [20]). Given a tag t ∈ T, the time window δ.

(a) A set of users who are engaging in the corresponding tag t of user u in the time window δ.

$$\begin{array}{l}{I}_t^u(\delta )=\{v\in \mathrm{U}|(v,{\pi }_v)\in \mathrm{U}\times \mathrm{TIME},\\ v\in (t.Interaction\cup t.Sh\cup t.Com),\\ v\ne u,{\pi }_v\in [t.\tau ,t.\tau +\delta ]\\ \}\end{array}$$

(7)

where π_v is the timestamp for the interacting, sharing, or commenting of user v to the corresponding tag t.

(b) The social pulse for the tag t in the time window δ is the value:

$$P_t(\delta )={\displaystyle \sum _{v\in t.Sh}\#(I_t^v(\delta ))}$$

(8)

Definition 4. (Average of Interactions).

Let u ∈ U be a user; the average of interactions for each tag of user u in the time window δ is computed by:

$$A{I}_u(\delta )=\frac{{\displaystyle \sum _{t\in u.ListTags}{P}_t(\delta )}}{\#(u.ListTags)}$$

(9)

Each user has two main influent measures: IU(u) = (Impress(u), and Popularity(u)) (Definition 2). The value of Impress(u) represents the average of the impact of the interacting of the user u. This value shows the impact of the user u to other users. Thus, when making the comparison of the influence between two users, this value is the priority. For detecting an influencer in the time window δ, the average value of interactions needs to be used in the ordering. In Definition 5, we remind the lexical order between two 2D-vectors, and this order is used to compare the influence between two users in Definition 6.

Definition 5. (The lexical order between two 2D-vectors).

Let ∘ be a set of real value, and vectors a = (a₁, a₂) ∈ ∘², and b = (b₁, b₂) ∈ ∘². Define:

$$\mathrm{a}\le \mathrm{b}\iff [\begin{array}{l}{a}_1<b_1\\ a_1=b_1\mathrm{and}{a}_2\le b_2\end{array}$$

Definition 6. (influential user/influencer).

Given a social network F = (U, T, R) as SNet model, the time windowδ.

(a) 

Let u, v∈ U be users on F. The user u is more influent than the user v in the time windowδ, denoted v << u, if:

ii 

IU(v) ≤ IU(u) and$A{I}_v(\delta )\le A{I}_u(\delta )$

iii 

or$(Popularity(v),A{I}_v(\delta ))\le (Popularity(u),A{I}_u(\delta ))$

(b) 

Let G ⊆ U, a user w ∈ G is an influencer on F in the time window δ if:

#({v ∈ G | v << w}) ≥μ × #(G)

(10)

where μ is a constant, 0 <μ < 1.

5. Determine the Influencer on a Social Network

Community structure has been shown to affect information diffusion [3]. There are two main phenomena of community structure, including homophily and social reinforcement. Homophily denotes a group of users that share similar characteristics. Social reinforcement means that the behavior of one person p can lead to effects on other people who have close relationships with p. In this section, based on a given brand, product, or news, we determine a user that can lead to effects on other people who have close relationships with the user.

5.1. The Graph for Connections between Users

Based on the SNet model, a graph representing the connections between users is a tube (V, E); in which, V is a set of vertexes, and E is a set of edges. A vertex v_i ∈ V in the graph denotes user i, and an edge e_ij ∈ E from node i to node j denotes that there is a relationship between users i and j. Each edge has a weight that is computed as the following definition:

Definition 7.

Given a social network F = (U, T, R) as the SNet model, and a graph (V, E) represents the connections between users on network F, the weight of each edge e ∈ E, denoted w(e), is computed as followed:

• If follower (v_i, v_j), then w(e_ij) = 1.
• If friends (v_i, v_j), then w(e_ij) = w(e_ij) = 2.
• If interacted (v_i, t), then w(e_ik) += 1 with v_k = t.Owner
• For each relation comment (v_i, t), w(e_ik) += 2 with v_k = t.Owner
• If shared (v_i, t), then w(e_ik) += 1 with v_k = t.Owner.

Figure 1 shows an example of the graph representing the connections between users on the network F.

Figure 1. The graph for representation connections between users.

5.2. Creating Graphs for Specific Brands/Products/News

For a given brand, product, or news, we extracted a corresponding sub-graph based on the graph representing connections between users. This sub-graph helped us to detect homophily, which is a group of users loving the brand and sharing similar characteristics about brands/products/news.

5.2.1. Passion Point

The passion point measures the favorite of a user with a brand/product/news (called brand in short). It is computed based on the following inputs: total number of the user’s tags, the total number of positive tags about the specific brand that were created by the user, the number of the user’s active days, and the average of interactions with the users per post. The passion point is the foundation to build the homophily that loves the brand.

With given observation, the confidence interval for the actual probability of posting a positive post from an influencer is a range of possible proportions, which may or may not contain the exact proportion. There are many methods to analyze the sentiment of a tag, such as using an ensemble of classifiers. In [26], the ensemble schema is based on three classifiers: Naïve Bayes, Maximum Entropy learner, and a knowledge-based tool performing an in-depth analysis of the natural language sentences.

The model of a binomial distribution is B(n, p), where n is the number of successes, and p is the success probability for each trial. The value of p is unknown, but the range of p can be calculated, in which it is also called the binomial proportion confidence interval. There are several methods to calculate the confidence interval for binomial proportion; however, Wilson score interval methods are the most accurate and the most robust [27]. When the actual coverage probability is closer to the nominal value, the Wilson score interval improves the regular approximation interval.

Definition 8.

([28]). Formula of Wilson confidence interval:

$$\frac{\rho +\frac{z^2}{2n}}{1+\frac{z^2}{n}}\pm \frac{z}{1+\frac{z^2}{n}}\sqrt{\frac{\rho (1-\rho )}{n}+\frac{z^2}{4n^2}}$$

(11)

where n: the number of experiments,

n_S: the number of successes,

$\rho =\frac{n_S}{n}:\mathrm{the}\mathrm{binomial}\mathrm{proportion}$

and z is the quantile of a standard normal distribution.

The confidence interval is a range of possible proportions (positive rate). The range is broad if the sample size is small, and vice versa. Besides ranking the score of a specific person based on the positive rate, the model helps to capture the effect of lacking evidence at the time of ranking; therefore, the lower bound of the confidence interval is chosen as a ranking score of the passion point.

When the number of tags increases, the positive rate also increases. This is a result of the choices of influencers by the brand. The influencer was paid more by trending brands to post more positive posts about them. The average number of likes per post is also an indicator of the latent variables that represent how well that person polishes his/her image in social media to attract their fan-based community. To take the effects of this phenomenon into account, we modeled the ranking score based on linear regression.

Definition 9. (Passion point).

Given a user u∈ U, and the brand X.

(a) The ranking score for the user u with the brand X:

$${\mathrm{ranking}\_\mathrm{score}}_u(X):=\frac{\rho +\frac{z^2}{2n_u}}{1+\frac{z^2}{n_u}}-\frac{z}{1+\frac{z^2}{n_u}}\sqrt{\frac{\rho (1-\rho )}{n_u}+\frac{z^2}{4n_u^2}}$$

(12)

where n_u = #(u.ListTags),

$n_X=\#(\{t_X\in u.ListTags\left|t_X\mathrm{is}\mathrm{a}\mathrm{positive}\mathrm{tag}\mathrm{with}\mathrm{the}\mathrm{brand}X\right\})$

$\rho =\frac{n_X}{n_u}:\mathrm{the}\mathrm{binomial}\mathrm{proportion}$

z: the quantile of a standard normal distribution.

(b) The passion point of user u with brand X is computed by:

PP_u(X):= ranking_score_u(X) + log(#(u.ListTags)) + log(Impress(u))

(13)

where Impress(u) is computed by Formula (6).

5.2.2. Graphs for Specific Brands/Products/News

In this section, the Algorithm 1 for creating a sub-graph representing the connection between brand-loving users is presented.

Algorithm 1: Creating a sub-graph representing the connection between brand-loving users.

Input: A social network F = (U, T, R) as the SNet model.

Graph G is represents the connections between users.

A specific brand/product/news X.

Output: Extract a sub-graph of users engaging with brand X.

The process of creating sub-graphs is as follows:

Step 1: Traverse each node v in Graph G.

Let ω > 0 be a constant, showing the minimum passion point of a user with brand X.

Check v.ListTags to see whether the corresponding user mentioned brand X in the tags.

If PPv(X) ≥ ω, with PPv(X) is computed by Formula (13).

Insert the node v into the sub-graph and go to Step 2;

Otherwise, go to Step 3.

Step 2: Expand the search space to the node’s neighbors.

Insert edges between the current node and its neighbors into the sub-graph if:

(1) the neighbors also mentioned brand/product/news X, or

(2) the neighbors interact or have comments on the tags of the current node related to X.

In Case (1): if the current user posts the tag t related to the product/brand/news, which is shared from another user y = t.Owner, create an edge between the current user and the user y.

Update the edge’s weight, as shown Definition 7.

Step 3: If there are untraversed nodes in the network, go back to Step 1.

5.3. Determine the Influencer on a Social Network

For a given brand, product, or news, we determined that the influencer on the social network can propagate this specific brand/product/news in the determined time to the most goal audiences as a seeder. The process for determining the influencer is as follows:

Given a social network F = (U, T, R) as SNet model, a specific brand/product/news is X. The Algorithm 2 determines the most influential user to other people on F with the brand X in the time window δ.

Algorithm 2: Determine the most influential user

∙ Stage 1: Determine a group of users who are interested in brand X.

Step 1: Create Graph G, as shown in Definition 7, representing connections between users on the social network.

Step 2: Create a sub-graph of G by the algorithm in Section 5.3 to determine a group of users who are interested in brand X.

This group is denoted GX.

∙ Stage 2: Determine the most influential user to other people in the time window δ.

Step 3: With each u ∈ GX, compute the influence measures of the user u.

• Influence vector IU(u):= (Impress(u), Popularity(u)) as Formula (5) in Definition 2.

• The average of the interaction of u’s tags AIu(δ) is computed by Formula (9).

Step 4: Determine the set of influencers in GX as Definition 6.

S:= { };

for w in GX do

{

Sw(δ):= {v ∈ GX | v << u}, with the relation “<<” is defined in Definition 6.

If #(Sw(δ)) ≥ μ × #(G) then

S: = S ∪ {w};

}

ReturnS is a set of influencers in GX.

6. Testing and Experimental Results

Our influence measures of a user were applied to detect an influencer for marketing a brand or product. Our method has been applied to 10 brands of three customers in practice. In this section, we present the application to determine influencers of one product. We also present the results about the voice of information related to that product on the social network when our customers ran the influencer marketing strategy based on our determined influential users.

6.1. Testing

In this section, because of the secret of the business, we call the brand X, and the time window δ is seven days. Our program is set up by JSON [29]. In this testing, we only mention Vietnamese users on Facebook. Determining the influencer of product X on Vietnamese users of Facebook is processed through two stages, as shown in Section 5.3.

Stage 1: Based on the information of X, a part of the sub-graph represents a group of users, called G_X, who are interested in X, as shown in Figure 2:

Figure 2. Sub-graph presents a group of users who are interested in product X.

Stage 2: Through this group, we continued to determine whether the user could be the influencer for the brand X in the time window δ = 7 days, as shown in Table 2. In this stage, the values of coefficients in the formulas were chosen as follows:

Table 2. Comparing the number of interactions related to product X in October, 2018, September, 2018, and November, 2018.

Duration	Posts	Comments	Shares	Total	Rate
October, 2018	22,511	638,278	140,782	801,571
September, 2018	15,193	24,2714	86,052	343,959	133%
November, 2018	8883	218,341	83,673	310,897	−61%

• The values of (α₁, α₂, α₃) in Formula (1), (β₁, β₂, β₃) in Formula (2), and (γ₁, γ₂, γ₃) in Formula (3) were chosen by the assumption that: the weight of a follower’s interaction was higher than a friend’s, and the weight of an unrelated user’s interaction was higher than other users. Despite the opinions from the experts and managers in online marketing, the values of parameters in formulas were chosen as follows:

  α₁ = 0.25  α₂ = 0.5  α₃ = 0.75

  β₁ = 0.25  β₂ = 0.5  β₃ = 0.75

  γ₁ = 0.25  γ₂ = 0.5  γ₃ = 0.75
• The values of (α, β, γ) in Formula (6) are α = β = γ = 0.5.
• The value of μ in Formula (12) is 0.8, which means a user is an emerging influencer if he/she is more influential than 80% of users in the group G_X.

The list of emerging users for the influencer is shown in Figure 3. Our customers can select some influencers from this list to make their marketing plan for product X.

Figure 3. List of emerging users for the influencer.

6.2. Experimental Results

Based on the list of emerging users for the influencer in Figure 3, our customer ran an influencer marketing strategy for product X on Facebook users in Vietnam in October, 2018 through two phases:

• Phase 1: Our customer used four users in our list for their influencer marketing strategy from 9–16 October.
• Phase 2: Our customer used other users—who were famous Key Opinion Leaders (KOLs) in Vietnam—for the marketing from 27–31 October 2018.

In the results that followed, the interactions were only counted when they were related to product X. The results of this influencer marketing strategy were as follows:

September and November, 2018 were the months that did not run the influencer marketing strategy. Table 2 shows the number of interactions in October, 2018 increasing compared with the previous month (September) and the following month (November) with the number of posts, comments, and shares. The number of interactions in October, 2018 increased by 133% compared with the previous month, and in the following month, it decreased by 61%.

After running the influencer marketing strategy for the duration time in Phase 1 (9–16 October) and Phase 2 (27–31 October), the number of interactions related to product X on the social network increased, as shown in Figure 4.

Figure 4. Total of interactions related to product X of Vietnamese users on Facebook in 30 days (9 October–8 November).

Table 3 shows the detailed results of the number of interactions related to product X in each phase and seven days after:

Table 3. Number of interactions related to product X in October, 2018.

Phase	Duration	Posts	Comments	Shares
Phase 1	9–16 October	9108	229,158	54,934
	17–24 October	5350	171,701	28,256
	Total	14,458	400,859	83,190
Phase 2	26–31 October	3241	108,519	25,504
	1–8 November	3691	58,427	25,993
	Total	6932	166,946	51,497
	Rate 1	36%	47%	46%

¹ the rate is computed between the number of interactions from 26–31 October and from 9–16 October.

Table 3 shows the effectiveness of the determined influencers by our proposed method. The rate of interactions in the duration time to run the influencer marketing in Phase 1 is more than double that of the duration time in Phase 2. After seven days from the time for running the influencer marketing, the number of interactions in Phase 1 is also higher than in Phase 2.

In the practice, the number of general interactions in Phase 2 was higher than in Phase 1; however, most of them mentioned KOLs and did not mention product X. Thus, with our customers, these interactions did not affect their sales revenue. Table 3 only counted the interactions that were related to product X. Moreover, although the run time in Phase 2 was shorter than the run time in Phase 1, the cost of the run time in Phase 2 was more expensive than the cost in Phase 1 because, in Phase 2, the customer used famous KOLs in Vietnam.

After running the influencer marketing strategy for the duration of one month (9 October–8 November), as shown in Figure 5, product X had a significant voice of information on Vietnamese Facebook users compared with competitor’s products.

Figure 5. Share of voices about the information on Vietnamese users of Facebook between product X and competitor products in 30 days from the time the influencer marketing strategy was run (9 October–8 November).

Based on the above results, our method was effective in determining the influencer for a brand/product/news. The influencer impacted the interactions of users on a social network. Our method also received positive feedback from our customers.

6.3. Discussions

The proposed method for detecting the influencer for marketing a brand or product can be applied in practice. Our measures have been tested on Vietnamese social network sites through the real influencer marketing strategy. The influencers detected by our method were useful in impacting the interactions of users on a social network in this strategy. The number of interactions of our determined influencers related to the brand was higher. They could impact the sales revenue of the brand in the online marketing strategy. In the real word, the proposed method received positive feedback from the customers when it was used to run influencer marketing strategies.

Nonetheless, our method only focused on tags on the social network as text. In the real world, many tags are images (or video clips). A user may write short posts, but he/she usually uses pictures to show their interest in a brand. Our method has not yet detected some cases. Furthermore, our method belongs to the field of the branch. When implementing this method, we must collect data in this field: the community of users in this field and their activities on the social network, corpus of the field.

The formula of passion is computed based on the following inputs: the total number of the user’s posts, the total number of positive posts about the specific brand that were created by the user, the number of the user’s active days, and the average of interactions with the users per post. Thus, these formulas for computing the passion point in our method can be used in other countries. However, the determining of positive posts belongs to the method to analyze the sentiment of the post, and the current methods for sentiment analysis usually use a corpus of a language. This corpus belongs to the language. For determining positive posts on a social network, we also developed a method for sentiment analysis based on the grammatical structure of Vietnamese users [30]. Thus, the method of determining positive posts cannot be used in other languages.

7. Conclusions and Future Works

In this paper, a model for representing a social network, called the SNet model, is proposed. This model represents the kinds of relationships between users and tags on the social network. A graph-based approach was proposed for computing the impact of the users and the speed of information propagation. There are two main influential measures, including the influence on other people by relationships between users and the concern to the user’s tags, and the tag propagation through social pulse on the social network. Based on the structure of the SNet model, the formula for the computing of passion points is also proposed. This point measures the love of users towards the brand. It is used to cluster the community that loves the brand. A method detecting the influencer in the brand-lover’s community is proposed. There are two main influential measures: the extent of the influence on other people by the relationships between users and the concern to user’s tags, and the tag propagation through social pulse on the social network.

The influencer of a specific brand or product on online social networks was determined through two stages: determining a group of users who love the brand, and determining the most influential users in the time window δ. Our method has been applied in the real world to detect the list of emerging influencers for specific brands. Its results received positive feedback from the customers when they used them to run their influencer marketing.

In the future, the content of a tag will be studied more clearly to evaluate the sentiment of the tag’s content. The sentiment analysis of tags is helping to cluster the community that love the brand based on the passion point more precisely [31]. The passion point is also affected by the diligence of the user’s posting. The formula of this point has to be added to the parameter about this diligence. In reality, some tags do not belong to the seeder; they still have a significant impact on the social network. Thus, analyzing the relationships between the tag propagation and the followers helps to measure the influence of a tag. The improved method will be made in comparison with other methods, such as using the opinion propagation-based scenarios [32] and using measures of network structure (outdegree centrality, betweenness centrality, and clustering coefficient) [33].

Moreover, online marketing strategies need to meet the requirements of the consumer behaviors. In further research, some methods used to determine the change in consumer behaviors have been studied. Based on this, we can recognize the changing of the user’s engagement with a commercial brand quickly. This can combine with detecting the influencer to establish an effective online marketing strategy. This strategy can approach the emerging costumers correctly.