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Mining Community-Level Influence in Microblogging Network: A Case Study on Sina Weibo.

1. Introduction

Community-level influence analysis is an emerging problem, which can be used in many filed, for example, recommendation system [1, 2], public opinion prediction [3], and cybersecurity analysis [4]. There are many researchers who are interested in analyzing the social influence in social networks [5], but rarely assessing the influence in community level. With the rapid spread of online social networks, such as Twitter, Facebook, and Sina Weibo, large amounts of data with the real world are produced, which provide support for the social influence analysis.

How to establish an effective model for analyzing community-level influence has become an important research for online social network. Community-level influence is greater than individual-level influence, but few researchers have studied community influence. The existing studies establish various social influence analysis models [6, 7], but they just study the influence in the individual level and mostly ignore the existence of a common influence pattern from a community that includes multiple nodes. A large number of achievements have been obtained on individual-level influence, but most of the studies are based on static statistics method [8-11], link analysis algorithms [12-14], or probabilistic models [15-17]. These studies do not consider whether the user is willing to receive or diffuse information or what the role of social trust between users is or do not remove zombie fans. However, these factors are very important for analyzing the social influence. Meanwhile, the existing works about community-level influence focus on the influence strength between communities and ignore the problem of analyzing the community-level influence. For example, Belak et al. [18] calculated the community-level influence by only averaging influence of all users in a community.

An important observation is that zombie fans have no contribution to the social influence, and the willingness of users to diffuse information has a certain effect on the accuracy of calculating social influence, and social trust plays an important role in social influence. The trust degree of user A to user B determines the influence of user B on user A. The more the user A trusts user B, the more influence the user B has on the user A. Because user influence is the basis of the community influence, a little carelessness on the former will lead to errors on the later.

Aiming to assess the community-level influence effectively and accurately, we construct a community-level influence analysis model that can assess community influence. Based on our model, a community-level influence analysis algorithm (short for CIAA) is proposed, which can assess the community influence more effectively and accurately. The main idea of our model is as follows. First, we eliminate the interference of zombie fans on the social influence to make the results more accurate. Then, in the process of calculating user influence, we consider the social trust and use the random walk method to calculate the user influence. In evaluating the user's theme information, the user mean willingness is calculated by exploring the content related to the user's theme information. We combine these two factors (the user influence and the user willingness to diffuse theme information) to calculate the user final influence. Finally, the community-level influence is calculated by comprehensively studying the user final influence, the social trust, and relationship tightness between intrausers of communities. Experiments are conducted on a real-world dataset crawled from Sina Weibo. Comparing with the state-of-the-art algorithm (the averaging user influence algorithm [18]), the results show that our model is more effective and accurate to evaluate the community-level influence.

The contributions of this paper can be summarized as follows. (1) We formulate the problem of analyzing the community-level influence and design a community-level influence analysis model. (2) CIAA, a community-level influence analysis algorithm based on our model, is proposed, which is effective and reliable to evaluate the community influence of microbloggers from Sina Weibo. (3) We conduct extensive experiments to assess the performance of the proposed model. Experimental results on the real-world dataset demonstrate the superiority of the proposed CIAA.

The rest of the paper is organized as follows. In Section 2, we summarize the related works. In Section 3, we propose the community-level influence analysis model and give an example to illustrate its working principle, and the CIAA is proposed. In Section 4, we conduct experiments on the realworld dataset crawled from Sina Weibo and then analyze the performance of the proposed approach. Finally, we state the conclusion and future work in Section 5.

2. Related Works

Since Katz and Lazarsfeld [19] found that social influence plays an important role in social life and decision-making in the 1950s, researchers in computer field have spare no effort to study the relevant problems. It is found that the popular users play an important role in adopting innovation, social public opinion propagation and guidance, group behavior formation and development [5], and so on.

There are a great deal of research efforts to measure individual-level influence [20, 21], typically, the "opinion leaders." Existing methods can be categorized into three types: the network structure based methods, the user behavior based methods, and the mutual information based methods. The network structure based methods are degree centrality [22], closeness centrality [23], betweenness centrality [24], eigenvector centrality [25], Katz centrality [26], PageRank [27], and clustering coefficient [28]. We know that node degree essentially means the connection between a node and its neighbors. The method based on node degree can intuitively express this meaning, and its computational cost is smaller than other methods [29]. These methods are widely used in measuring the users' influence in the social network. However, the methods based on node degree only reflect the connection between the users and their neighbors and cannot measure the users' influence in the entire social network for the local influence of users. For example, based on the community scale-sensitive maxdegree, Hao et al. [30] proposed an influential users discovering approach called CSSM when placing advertisements. CSSM uses the degree centrality and neighbor's degree to evaluate node's (microbloggers) influence. However, the algorithm does not consider the contribution of microblogs to user influence. Comparing with the methods based on the degree, the method based on the shortest path (closeness centrality and betweenness centrality) can measure the individual-level influence in the entire social network. Nevertheless, its computational complexity is higher than the degree centrality method. For example, based on text mining and social network analysis, Bodendorf and Kaiser [31] proposed an approach to detect opinion leaders in directed graph of user communication relationship. It can predict tendency of network opinion leaders via closeness centrality and betweenness centrality. Moreover, measuring the individual-level influence by the shortest path is an ideal status, and it is difficult to achieve in the real-world application scenarios. Besides, the methods based on random walk only consider the structure characteristics of the node while ignoring the behavior characteristics. For example, Xiang et al. [32] provided an understanding of PageRank and authority from an influence propagation perspective by performing random walks. However, they did not consider the personal attributes to understanding of PageRank as well as the relationship between PageRank and social influence analysis. Zhu et al. [33] proposed a novel information diffusion model called CTMC-ICM, which introduces the continuous-time Markov Chain theory into the Independent Cascade Model. Based on the model, they proposed a new ranking metric called SpreadRank. Based on continuous-time Markov process, Li et al. [34] proposed a dynamic information propagation model called IDM-CTMP to predict the influence dynamics of social network users. IDM-CTMP defined two other dynamic influence metrics and could predict the spreading coverage of a user within a given time period. Zhou et al. [35] established new upper bounds to significantly reduce the number of Monte-Carlo simulations in greedy-based algorithms, especially at the initial step. Based on the bound, they proposed a new upper bound based lazy forward algorithm for discovering the top-k influential nodes in social networks.

The aforementioned models focus only on assessing the social influence of single individuals. However, a small number of works attempt to build models on the community influence analysis. Qi et al. [36] applied degree centrality, closeness centrality, and betweenness centrality to groups and classes as well as individuals. Latora and Marchiori [37] put forward a group information centrality to measure the importance of node sets. Mehmood et al. [38] exploited information diffusion records to calculate the influence strength between different communities. Although these works preliminarily study the community-level influence, none of them focuses on how to measure a community's influence. Belak et al. [18] assessed the community-level influence according to the average of the all users' influence in the same community. Because the distribution of the users' influence is uneven in different communities, average based method is inequitable to bigger communities, while summation based method is inequitable to smaller ones. At present, community-level influence analysis is still a challenging problem.

3. Proposed Methodology

We construct our model and implement the corresponding algorithm in this section. First, we give the related definitions in Section 3.1. Then, we propose the community-level influence analysis model for microbloggers. Next, we describe the working principle of our model via an example in Section 3.2. Finally, the community-level influence analysis algorithm is proposed in Section 3.3.

3.1. Related Definitions and Community-Level Influence

Analysis Model

3.1.1. Related Definitions. Social networks and communities are described as follows: a typical social network can be represented as a bipartite graph G = [V,E], V is a set of nodes (users) in a social network, and E is a set of edges used to describe the relationships between nodes. A community can be represented as a subgraph of a social network: that is, C = {CV, CE}; CV c V is a set of users in a community. CE [equivalent to] E is a set of relationships between users within a community. A node is defined as a user within the community if he/she belongs to the community; otherwise, he/she is defined as a user outside the community. The set of users outside the community is written as UOC. Modeling and calculating the community influence of C; are the basis of our work, and the objective function of our model is as follows:

CI ([C.sub.i]) = f(G, [C.sub.i]). (1)

CI([C.sub.i]) denotes the community influence of the community [C.sub.i], and the function f(G, [C.sub.i]) indicates that the assessment method is based on G and [C.sub.i]. There are two entities (i.e., users and communities) which can produce influence. To study the community-level influence, we give the related definitions as follows.

Definition 1.

Trust. A node in a social network has a certain trust degree in other nodes according to its past contact with other nodes or the reputation of other nodes [39, 40]. According to the different sources of trust, we divide the trust into direct trust and indirect trust.

(1) Direct Trust (DT). Assume that the node v is the entry node of the node u, indicating that there is contact between u and v. According to the previous contacts and the reputation of u, v will have direct trust on u.

(2) Indirect Trust (IT). Assume that the node u is the reachable node of the node v; v will have indirect trust on u because the reputation of u can be transmitted to v.

Users not only have mutual trust, but also mutually influence each other. According to the different sources of influence, this paper divides the influence into direct influence and indirect influence.

Definition 2.

(1) Direct Influence (DI). Assume that the node v is the entry node of the node u; u will have an influence on v: that is, u produces direct influence on v.

(2) Indirect Influence (II). Assume that the node u is a reachable node of the node v; u will have an influence on v through transmission layer by layer: that is, u produces indirect influence on v.

In order to assess the overall influence of u on v, we define the user combined influence.

Definition 3.

User Combined Influence (UCI). Because v has direct trust or indirect trust to u, and u has direct influence or indirect influence on v, we comprehensively combine the four factors to calculate the combined influence of u on v.

Definition 4.

(1) User Influence (UI). User influence refers to the influence of individual on other users.

(2) Community Influence (CI). Community influence is the overall influence of the community, which is formed by the UI of all the users in the community and the community's self-factors.

Definition 5.

Mean Willingness to Diffuse Theme Information (MW). In communities, some users receiving the theme information may not diffuse it, some users prefer to post their own blog, and some users prefer to forward others' blog. We assess the community influence by taking into account the diffusion of information between users. MW represents a user' willingness to diffuse the information of a blog. The theme information of the user u is stored in the set T(u) = {[t.sub.ui], [t.sub.u2], ..., [t.sub.uj], ...}, where tuj represents the user's jth theme information. If [t.sub.uj] is diffused in a social network, a path map [g.sub.uj] is formed to describe the propagation path. We store the path graphs formed by T(u) in the set g(u) = {[g.sub.u1], [g.sub.u2], ..., [g.sub.uj]}.

3.1.2. Model Framework. Our model consists of four modules: data preprocessing module, data source module, the user final influence module, and the community influence module. Figure 1 shows our model framework.

Data preprocessing module is used to eliminate zombie fans. We judge the zombie fans from the behavior dimension and time dimension. Behavior dimension is based on the amount of theme information posted by the user and the fans' influence of the user. Time dimension is based on the user login frequency and the frequency of diffusing theme information. Finally, the data preprocessing results are stored to the data source.

Data source module is responsible for providing the relevant data needed for influence analysis. We establish the user information table, the microblog table, the user fans information table, and the user attention table to access the user's relevant information efficiently.

The user final influence module first calculates the mean willingness to diffuse theme information for each user in a community and then calculates the user's influence. Next, it combines these two results to get the user final influence.

The community influence module first calculates the community size, the tightness of user relationship, and the user-integrated influence in the community and then evaluates the community influence by integrating the three factors.

3.2. Working Principle. In this subsection, we introduce the working principle of each module in the model framework in detail. We assume that u and v are two users in community C. After performing data preprocessing, Figure 2 shows the working principle, where the mathematical notations will be described in the following subsections in detail.

The working principle can be described as the following steps.

Step 1. Calculate the DiffuV and SV of v. Then calculate the MW(v) of v. Finally, calculate UI(v) of v.

Step 2. According to Step 1, calculate the MW(v) and UI(v) of u.

Step 3. Integrate MW and UI to calculate the UII(C). Then calculate CS and RT(C). Finally, combine the three factors to calculate the community influence.

3.2.1. Data Preprocessing. In microblogging networks, some users of ulterior motives or business purpose lead to producing the zombie fans. According to the definition in [41], zombie fans are the users who are fake fans generated and maintained mostly for economic purpose. Zombie fans certainly interfere in analyzing the social influence. A small number of empirical researches have been conducted on recognizing zombie fans [41-43]. The existing studies were mostly subject to the Twitter platform.

Presently, researchers generally detect the zombie fans based on the amount of attention, the number of fans, original and forward information frequencies, and other basic attributes. With the ever-changing escalation of zombie fans, zombie fans will produce more features [44]. The existing feature-based methods to eliminate zombies may gradually fail. We observe that because zombie fans are occasionally managed via software program or a few people behind, zombie fans often rarely speak, even seldom log in, or no longer are used; and their behaviors can be vastly different with ordinary users in profile information and contents. Moreover, no matter how the features of zombie fans change, they can be split into time dimension and behavior dimension. Thus, it is reasonable to recognize zombie fans from the time dimension and behavior dimension, and it is more able to adapt to the needs of detecting zombie fans in microblogging networks.

Algorithm 1: Eliminating zombie fans.

(1) Input: V, E, LF, DAF, NUI, NAU, NUF
(2) Output: G = (V, E)
(3) Select the users who are the last 10% of the login frequency
    and whose login time interval is greater than 7 days, into the
    set LF
(4) Put the users with the top 10% of the diffusing advertisement
    frequency into the set DAF
(5) Select the users who are the last 10% of the number of user'
    theme information into the set NUI
(6) Put the users with the top 10% of the attention users into the
    set NAU
(7) Put the users with the number of fans between 10-200 into
    the set NUF
(8) ZF = LF n DAF n NUI n NAU n NUF
(9) Update V = V - ZF and E = E-EZF
(10) return V, E


According to expert knowledge criteria [45], in the time dimension, we assess zombie fans from the user login frequency and the diffusing advertisement frequency. Thus, time dimension includes login frequency (LF) and diffusing advertisement frequency (DAF). Login frequency refers to the number of logins in a period. The lower the frequency of login is, the higher the probability of the user becoming zombie fans is. The login frequency is calculated as follows:

LF = [DELTA]tLoginNumber/[DELTA]t (2)

where LoginNumber indicates the number of logins. The higher the diffusing advertisement frequency is, the higher the probability of the user becoming zombie fans is. The diffusing advertisement frequency is calculated as follows:

DAF = [DELTA]TNumberOfDiffusingAdvertisement/[DELTA]t (3)

where NumberOfDiffusingAdertisement indicates the number of diffusing advertisement frequencies.

For the same reason, in the behavior dimension, we assess zombie fans from the amount of user theme information and the individual influence of the user s fans. Thus, we take into account the number of user theme information (NUI), the number of attention users (NAU), and the number of user's fans (NUF).

To ensure that the criteria of the parameters are reliable, the corresponding criteria are obtained by prior knowledge, expert knowledge, or experimental trial. For example, we select the users who are the last 10% of the login frequency and whose login time interval is greater than 7 days into the set LF. To reduce the amount of calculation, we filter all users in a microblogging network. If a user has a certified user in his/her fans, the user is not considered a zombie fan. If a user does not have a certified user in his/her fans, the details to eliminate zombie fans can be described in Algorithm 1.

As we can see that, unlike the classification and pattern recognition, the proposed method to eliminating zombie fans does not require labeled data and training model. It is effective and easy to use in practice.

3.2.2. The User Final Influence. The traditional models are simple, not taking into account the degree of social trust between users and the user's willingness to diffuse theme information. However, the two factors are important to the user final influence. In this paper, the user final influence is calculated by integrating the MW and UI. Because the influence of a user on other users is related to the user's willingness to exert his/her influence, the bigger the value of MW, the greater the probability of the user diffusing a theme information. UFI is calculated as follows:

UFI (u) = MW (w)x UI (u). (4)

Mean Willingness to Diffuse Theme Information. The higher frequency of diffusing theme information means a higher user influence, because more users will know the user. Therefore, MW reflects the probability that a user has high-impact in a microblogging network. The parameter [mathematical expression not reproducible] indicates the state of receiving theme information for the user V as follows:

[mathematical expression not reproducible] (5)

The initial value of [mathematical expression not reproducible] is set to 0. Meanwhile, to know the result of v diffusing the theme information [t.sub.uj], we observe [g.sub.uj]. The parameter [mathematical expression not reproducible] indicates whether v diffuses the theme information that he/she received.

[mathematical expression not reproducible] (6)

When the outdegree of v is greater than 0, it indicates that v has already diffused the theme information; otherwise, v has never diffused the theme information. The number of users receiving theme information is written as NRTI and the number of users diffusing theme information is written as NDTI.

[mathematical expression not reproducible]

MW is calculated as

MW (v)

[mathematical expression not reproducible] (8)

where w(u) = 1 /outdegree(w). MW(v) is the MW of v. [theta] [member of] [0, 1] is the weight. NP(v) represents the total number of theme information posts by v. In(v) is the set of indegree nodes of v. u>(m) represents the weight of the user w, which is determined by his/her outdegree. nums is the total number of [g.sub.uj]. The initial value of MW(v) is set as 1. We give an example for calculating MW in Figure 3.

Assume that the MW of all users initially are 1, [theta] = 0.6, and then calculate the MW as follows.

(1) MW([u.sub.l]). From Figures 3(b)-3(d), we have [num.sub.s] = 3. For [u.sub.1], he/she posts two-theme information, which forms two theme information graphs in Figures 3(b) and 3(c). Thus, we get the set T([u.sub.1]) ([absolute value of T([u.sub.1])]= = 2). From Figure 3(d), [mathematical expression not reproducible], because the outdegree of node [u.sub.1] is 0, and [u.sub.1] forms its one theme information graph. The MW([u.sub.1]) is calculated as follows:

[mathematical expression not reproducible] (9)

(2) MW([u.sub.2]). Similar to the calculation of MW([u.sub.2]), we have the set T([u.sub.2]), [absolute value of T([u.sub.2])] = 1. From Figures 3(b) and 3(c), we have [mathematical expression not reproducible]. MW([u.sub.2]) is calculated as follows:

[mathematical expression not reproducible] (10) Similarly, for [u.sub.3], [u.sub.4], and [u.sub.5], we have

[mathematical expression not reproducible] (11)

The User Influence. There are mutual impact and mutual trust between users. Social trust plays an important role in calculating the user influence. She/he is impacted by others including users inside and outside the community.

(1) Calculating Direct Trust and Direct Influence. If v is an entry node of m, then v will have direct trust on m.

[mathematical expression not reproducible] (12)

where [DT.sub.vu] is the direct trust of v on u. RU(u) is the reputation of user u. In(u) is the set of entry nodes of u, and RU(u [left arrow] w) is the reputation of the entry neighbor w of u. The value of RU(u) depends on the average reputation of all us entry neighbors. For each node, we give the initial direct trust value 0.1. In Figure 3(a), we calculate the direct trust on u1 from other nodes as follows:

[mathematical expression not reproducible] (13)

u has a direct influence on v as follows:

[mathematical expression not reproducible] (14)

where [DI.sub.uv] is the direct influence of u on v. I(u [left arrow] v) is the degree of interest of v to m. |theme(v, m)| is the amount of the theme information from u in the receiving theme information of v.

In Figure 3, we calculate the direct influence on m, produced by other users as follows:

[mathematical expression not reproducible] (15)

In Figure 3(a), we have

[mathematical expression not reproducible] (16)

(2) Indirect Trust and Indirect Influence. If u is the reachable node of v, then v will have indirect trust on u as follows:

[IT.sub.vu] = RU (u)/[min.sub.vu] (17)

[IT.sub.vu] is vs indirect trust on u. [min.sub.vu] is the length of the shortest path from v to u.

In Figure 3(a), we calculate the indirect trust on [u.sub.1] gained from other nodes as follows:

[mathematical expression not reproducible] (18)

u has an indirect influence on v as follows:

[mathematical expression not reproducible] (19)

In Figure 3(a), we calculate the indirect influence of other nodes on [u.sub.1] as follows. The calculation of I is the same as the above formula.

[mathematical expression not reproducible] (20)

(3) User Combined Influence. Assuming that v can reach u through a path, we introduce the factor [lambda] ([lambda] [member of] [0,1]).

If v is the entry node of u, the combined influence of u on v is

[UCI.sub.uv] = [lambda][DI.sub.uv] + (1- [lambda]) [DT.sub.vu]. (21)

If v is not an entry node of node w, but u is a reachable node of v, the combined influence is

[UCI.sub.uv] = [lambda][II.sub.uv] + (1- [lambda]) [IT.sub.vu]. (22)

Assume [lambda] = 0.3. In Figure 3, we calculate the combined influence of other nodes on [u.sub.1] as follows.

[mathematical expression not reproducible]

(4) User Influence. User influence is got by combining all users' influence:

[mathematical expression not reproducible] (23)

where SUCP represents a set of users that can reach u through a certain path. For example, in Figure 3, the user influence of [u.sub.1] is calculated as follows:

[mathematical expression not reproducible] (24)

When we get MW([u.sub.1]) and UI([u.sub.1]), the user final influence can be calculated according to (4).

3.2.3. Community Influence. The community influence is composed of the users' interaction inside and outside the community. In this paper, we consider it from three factors, that is, the user-integrated influence, the community size, and the degree of relationship tightness among users inside the community.

User-integrated influence (UII) is integrated from the final influence of all users within the community.

UII ([C.sub.i]) = [[summation].sub.u[member of]CV(u)] UFI (u), (25)

where UII([C.sub.i]) is UII of the community [C.sub.i]. CV(m) is the set of users inside community [C.sub.i].

The community size (CS) is important to the calculation of the community-level influence. The larger the number of users in a community is, the greater the influence of the community becomes. The formula is as follows:

CS ([C.sub.i]) = [absolute value of CV ([C.sub.i])]/max (V), (26)

where [absolute value of CV ([C.sub.i])] represents the number of users in a community and max(V) represents the total number of users in the social network.

Algorithm 2: Community-level influence analysis algorithm (CIAA).

Input: G = {V, E}; C; T(u); g(u); UII = 0; [tau]; p;RT = 0
Output: community influence
(1) for i = 0 to [absolute value of V] do
(2)              MW(i)
(3)              UI(i)
(4) end for
(5) for j = 0 to [absolute value of  CV] do
(6)       UII(j) = MW(j) x UI(j) + UII(j)
(7) end for
(8) CS(C)
(9) for i = 0 to [absolute value of CV] do
(10) [mathematical expression not reproducible]
(11) end for
(12) a([C.sub.i]) = [tau] x UII([C.sub.i]) + p x CS +
    (1- [tau] - p) x RT([C.sub.i])
(13) return CI([C.sub.i])


The degree of relationship tightness (RT) represents the degree of closeness between users inside a community. We describe it from the user's outdegree and indegree as follows:

[mathematical expression not reproducible] (27)

Therefore, we calculate the CI as follows:

CI ([C.sub.i]) = [tau] x UII ([C.sub.i]) + p x CS + (1- [tau] - p) x RT ([C.sub.i]), (28)

where [tau] and p ([tau],p [member of] [0,1]) are used to distinguish the importance of different factors.

3.3. The Proposed Algorithm. According to the above description, we propose a community-level influence analysis algorithm, called CIAA, in a pseudo-code format in Algorithm 2. It can be seen from the algorithm that the total time complexity is O(n). This means that our algorithm can be applied on large-scale social dataset.

4. Experiments

We conduct experiments to validate the effectiveness of the proposed approach on a real-world microblogging network. In this section, we describe the experimental setup followed by the discussion of experiment results.

4.1. Dataset. The real-world dataset in this paper is crawled from Sina Weibo by Weibo crawler. Similar to a hybrid of Twitter and Facebook, Sina Weibo is one of the most popular sites in China. It has more than 33% of the Internet users in China, and its market penetration is equivalent to that of Twitter in the United States. As released by the Sina Weibo, as of June 2016, the active users from different social and cultural backgrounds have reached 282 million monthly and 86.8 million daily. Moreover, there are nearly 100 million new microblogs every day. They promote and disseminate views and attitudes on business, culture, education, and so forth. The crawled data includes 20,151,129 microblogs, 932,578,467 comments, and 9,218 users. In this paper, we collected more than 1000 users from the crawled dataset and divided the related information into Tables 1, 2, 3, and 4 for data sources according to our model framework. They are stored in txt-formatted files.

4.2. Experimental Setting. All experiments are conducted on a PC with Intel Core i5 processor, 8 GB RAM. According to prior knowledge, we set the parameters of the experiments as Table 5.

4.3. Results

4.3.1. Community Structure Analysis. In order to mine and study the characteristic of community, we plot the outdegree distribution and degree distribution of users in community. In a directed social network, the indegree of nodes is the number of fans of the user. The outdegree of nodes is the amount of the user's attention. Figure 4 shows the outdegree and degree distribution of data sources.

As shown in Figure 4, the outdegree distribution and the degree distribution of Sina Weibo dataset follow the powerlaw distribution, which indicates that the social network composed of the dataset is a scale-free network.

4.3.2. Eliminating Zombie Fans. In order to improve the accuracy of our model, we remove zombie fans. According to the eliminating zombie fans method in Algorithm 1, we finally remove 12 zombie fans, as shown in Table 6.

As shown in Table 6, the three sets are NUI, NAU, and NUF. The little black boxes in Table 6 represent the shared users of three sets, and they are the same as the shared users from time dimension and behavior dimension. Therefore, the shared users will be removed. We compare the user final influence without the zombie fans with the user final influence with the zombie fans, as shown in Table 7.

From Table 7, the result of the comparison shows that the accuracy of the UFI with zombie fans for the actual user ranking is only 60%. It is concluded that the elimination of zombie fans is very important for the accuracy of the user final influence.

4.3.3. Accuracy Analysis of the User Final Influence. We calculate the user final influence of users in community, but we compare the top ten users for simplicity. The top 10 user final influences and their related information are shown in Table 8.

According to the UFI ranking in Table 8, we find that these users are authenticated user. It is concluded that the authenticated users are more influential in microblogging networks. There are two reasons for this phenomenon. First, the majority of well-known users are authenticated users, and the influence of well-known users is larger than the user average influence. Second, the authenticated user's identity is transparent, which makes the user have higher social trust. Table 8 also shows that the user final influence needs to be considered from the quality of the user fans, the number of user microblogs, and user authentication.

Table 9 and Figure 5 show the comparison between the UFI method and the microblog-fans ranking algorithm. Table 9 shows the UFI method ranking and the corresponding ranking via microblog-fans ranking algorithm. Figure 5 shows the overall ranking order via the microblog-fans ranking algorithm.

It can be seen from Table 9 and Figure 5 that the UFI ranking is almost completely different from the microblogfans ranking. Overall, according to the UFI method, the number of microblogs and fans of the top users must reach a certain quantity to support individual influence. Thus, the number of microblogs and fans is a factor of measuring influence in UFI method. However, social trust between users can help improve individual influence in the UFI method.

The user final influence is an experimental evaluation of the user, and there is no existing dataset with its comparison. We can only refer to the ranking of the user influence from some affiliations. Based on the ranking of user influence provided by Sina Weibo official, we verify the calculation method proposed in this paper. We compare the results of the proposed method with the official ranking to verify the correctness of the user final influence. Because each microblogging platform has its own influence calculation method, we cannot numerically compare the results, but we compare the results from the relative position, that is, ranking. If the influence rankings of the two methods are in the similar order, we consider the results of the influence analysis to be similar. The comparison of the users ranking by Sina Weibo officially and UFI method is shown in Table 10.

In Table 10, the user final influence calculation method and the user actual ranking are mainly the same but having the user pair of 299 * * * *593 and 365 * * * *215. That is because user influence ranking by Sina Weibo emphasizes the number of microblogs and fans, and the number of microblogs and fans of user 299 *** *593 and user 365 * * * *215 is largely different. However, the UFI method considers the factors of influence more reasonably.

Considering the results of Sina Weibo official as the standard, the accuracy of UFI method will change with different [lambda] and [theta], as shown in Figure 6.

From Figure 6, it can be seen that the UFI method accuracy changes with the different [lambda] and [theta]. When [lambda] = 0.3, [theta] = 0.5, UFI method has the highest accuracy. Therefore, the parameter pair (0.3,0.5) is used for other experiments. We also find that the UFI method is more accurate than the microblog-fans ranking algorithm. Moreover, this experiment indicates the importance of the user willingness to diffusing theme information in the accuracy of the user influence.

4.3.4. Accuracy Analysis ofClAA. Because the existing studies of community influence are few, we compare the proposed algorithm CIAA with the averaging user influence algorithm (AI). We set different parameters pair r and p for comparing the two algorithms. Then, we can calculate the corresponding community influence, as shown in Figure 7.

Figure 7 shows that the results of the CIAA are changing with the different parameter values. When [tau] = 0.5 and p = 0.2, the results of the two algorithms are closest. That is because the AI algorithm is mainly the weighted average of the user influence, and the CIAA is the integration of the user-integrated influence, the communitysize, and the degree of relationship tightness among users inside the community. The greater the proportion of the user final influence, the closer the results of the two algorithms. Therefore, the proposed algorithm outperforms the state-of-the-art baseline algorithm.

5. Conclusion

In this paper, we studied the emerging problem on how to model community-level influence. Online social networks, especially microblogging networks, are more and more important in our daily life. Previous works can effectively cope with the individual influence in microblogging network, but they rarely evaluate the social influence in community level, which outweighs the individual influence. We defined the related concepts for the community-level influence and constructed a model that combined the user influence, social trust, and relationship tightness of intrausers in a community to reveal the community-level influence appropriately. We proposed the algorithm CIAA to cope with the real-world applications. We conducted empirical studies on a realworld microblogging crawled from Sina Weibo, where the CIAA outperformed the state-of-the-art baseline algorithm. To the best of our knowledge, the proposed approach has a significant effect on community influence in microblogging network. The highlights of this paper can be summarized as follows: (1) formulating the problem of analyzing community-level influence and designing a communitylevel influence analysis model; (2) proposing communitylevel influence analysis algorithm called CIAA, to cope with real-world microblogging applications; and (3) extensively demonstrating the superiority of the proposed method. In the future work, we plan to extend the proposed method to assess the community influence in dynamic online social network.

https://doi.org/10.1155/2017/4783159

Conflicts of Interest

The authors declare that there are no conflicts of interest regarding the publication of this paper.

Acknowledgments

This work was supported in part by the National Natural Science Foundation of China under Grants U1433116 and 61702355, in part by the Fundamental Research Funds for the Central Universities under Grant NP2017208, and in part by the Funding of Jiangsu Innovation Program for Graduate Education under Grants KYLX15_0324 and KYLX15_0321.

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Yufei Liu, (1) Dechang Pi, (1,2) and Lin Cui (1)

(1) College of Computer Science and Technology, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu 211106, China

(2) Collaborative Innovation Center of Novel Software Technology and Industrialization, Nanjing, Jiangsu 211106, China

Correspondence should be addressed to Dechang Pi; dc.pi@nuaa.edu.cn

Received 7 June 2017; Accepted 12 November 2017; Published 4 December 2017

Caption: Figure 1: The framework of the proposed model.

Caption: Figure 2: The working steps of the community-level influence analysis model.

Caption: Figure 3: An example of calculating MW: there are five users inside a community, that is [u.sub.1], [u.sub.2], [u.sub.3], [u.sub.4], and [u.sub.5]. There are three users outside the community, that is, [v.sub.1], [v.sub.2], and [v.sub.3]. (a) shows the relationship between these users. (b) shows the diffusion of theme information from [u.sub.1]. (c) also shows the diffusion of theme information from [u.sub.1]. (d) shows the diffusion of theme information from [u.sub.2].

Caption: Figure 4: (a) is the outdegree distribution and (b) is the degree distribution.

Caption: Figure 5: The overall ranking via the microblog-fans ranking algorithm.

Caption: Figure 6: Comparison of accuracy of two methods with different A and 0.

Caption: Figure 7: The community-level influence by two measuring algorithms with different (t, p) pairs.

Table 1: Data structure and description of the user information.

Features          Description

UserID            User' ID
IsVIP             Authenticated user
FansNum           Number of fans
AttenNum          Number of attention users
ThemeAmo          Amount of theme information
Tag               User' label
Time              Login time

Table 2: Data structure and description of the user
theme information (microblogs).

Features          Description

ThemeID           Theme information ID
ThemeFromID       Source ID of theme information
ProNum            Number ofprocesses
ThemeClass        Theme information class
PTime             Post time of theme information

Table 3: Data structure and description of the user fans.

Features          Description

UserID            User' ID
FansID            Fans' ID

Table 4: Data structure and description of the user attention.

Features          Description

UserID            User' ID
AttenID           User-attended ID

Table 5: Parameters for experiments.

Symbol            Description                                   Value

V                 The total number of nodes                     1127
cv                The total number of nodes in the community    20
[lambda]          Parameter                                     0.3
[theta]           Parameter                                     0.5
[tau]             Parameter                                     0.5
p                 Parameter                                     0.3

Table 6: Three user sets for eliminating zombie fans.
# Indicated represent zombie fans.

                     NUI

511 * * * *843       320 * * * *657       226 * * * *535
267 * * * *275       377 * * * *140       506 * * * *228
209 * * * *054       314 * * * *751       551 * * * *783
535 * * * *588 #     260 * * * *165       564 * * * *561 #
569 * * * *524       299 * * * *713       326 * * * *401
519 * * * *908       255 * * * *954       546 * * * *117
174 * * * *367       295 * * * *285       366 * * * *383
176 * * * *904       312 * * * *963       140 * * * *523
381 * * * *512       312 * * * *885       357 * * * *742
522 * * * *989       275 * * * *525       547 * * * *573
180 * * * *713       272 * * * *524       558 * * * *440
508 * * * *496 #     393 * * * *610       520 * * * *974
267 * * * *724       325 * * * *361       564 * * * *326
194 * * * *451       299 * * * *433       291 * * * *885
519 * * * *020       398 * * * * 168 #    564 * * * *548
213 * * * *014       526 * * * *623       564 * * * *703
299 * * * *593       297 * * * *117 #     551 * * * *728
365 * * * *215 #     506 * * * *354       269 * * * *324
263 * * * *023       327 * * * *315       377 * * * *804
505 * * * *471       184 * * * *620       349 * * * *961
281 * * * *650       293 * * * *863       387 * * * *165 #
249 * * * *881       530 * * * *172       202 * * * *075
217 * * * *423 #     206 * * * *147       561 * * * *896
393 * * * *557       227 * * * *201       562 * * * *656
367 * * * *587       324 * * * *272       282 * * * *244
354 * * * *437       246 * * * *555       524 * * * *753
202 * * * *713       107 * * * *161 #     524 * * * *189
140 * * * *971       259 * * * *422       546 * * * *882
206 * * * *863       395 * * * *128       554 * * * *705
240 * * * *727       371 * * * *200       508 * * * *954
292 * * * *683       177 * * * *177       565 * * * *036 #
289 * * * *077       321 * * * *383       548 * * * *304
378 * * * *432       299 * * * *217       376 * * * *382
280 * * * *733       315 * * * *540       557 * * * *957
386 * * * *371       562 * * * *957 #     293 * * * *987
219 * * * *655       346 * * * *220       558 * * * *008 #
166 * * * *754       562 * * * *363       352 * * * * 153
248 * * * *174       521 * * * *857       561 * * * *406
246 * * * *354       257 * * * *813

                                          NAU

511 * * * *843       257 * * * *813       122 * * * *644
267 * * * *275       508 * * * *382       203 * * * *473
209 * * * *054       535 * * * *588 #     540 * * * *732
535 * * * *588 #     540 * * * *495       272 * * * *407
569 * * * *524       541 * * * *396       532 * * * *553
519 * * * *908       236 * * * *681       508 * * * *496 #
174 * * * *367       124 * * * *474       567 * * * *764
176 * * * *904       541 * * * *048       514 * * * *452
381 * * * *512       365 * * * *215 #     561 * * * *240
522 * * * *989       557 * * * * 157      219 * * * *090
180 * * * *713       562 * * * *840       554 * * * *983
508 * * * *496 #     295 * * * *781       519 * * * *173
267 * * * *724       217 * * * *423 #     395 * * * *459
194 * * * *451       155 * * * *451       240 * * * *653
519 * * * *020       535 * * * *748       398 * * * * 168 #
213 * * * *014       563 * * * *796       569 * * * *999
299 * * * *593       523 * * * *767       308 * * * *265
365 * * * *215 #     516 * * * *694       553 * * * *815
263 * * * *023       562 * * * *886       315 * * * *642
505 * * * *471       286 * * * *383       199 * * * *843
281 * * * *650       537 * * * *642       564 * * * *561 #
249 * * * *881       266 * * * *792       531 * * * *022
217 * * * *423 #     564 * * * *344       563 * * * *288
393 * * * *557       554 * * * *847       190 * * * *733
367 * * * *587       181 * * * *912       190 * * * *415
354 * * * *437       550 * * * *247       163 * * * *152
202 * * * *713       558 * * * *343       567 * * * *057
140 * * * *971       562 * * * *957 #     548 * * * *952
206 * * * *863       558 * * * *610       562 * * * *816
240 * * * *727       219 * * * *403       186 * * * *260
292 * * * *683       356 * * * *633       532 * * * *335
289 * * * *077       557 * * * *693       329 * * * *831
378 * * * *432       363 * * * *234       558 * * * *008 #
280 * * * *733       559 * * * *028       327 * * * *271
386 * * * *371       551 * * * *896       554 * * * *403
219 * * * *655       185 * * * *423       362 * * * *913
166 * * * *754       122 * * * *644       292 * * * *807
248 * * * *174       531 * * * *740       558 * * * *488
246 * * * *354       531 * * * *866       557 * * * *762

511 * * * *843       384 * * * *495       348 * * * *495
267 * * * *275       569 * * * *865       569 * * * *865
209 * * * *054       512 * * * *879       512 * * * *879
535 * * * *588 #     345 * * * *320       345 * * * *820
569 * * * *524       553 * * * *237       553 * * * *237
519 * * * *908       241 * * * *385       241 * * * *885
174 * * * *367       538 * * * *374       538 * * * *874
176 * * * *904       237 * * * *312       237 * * * *812
381 * * * *512       267 * * * *275       267 * * * *275
522 * * * *989       516 * * * *282       516 * * * *382
180 * * * *713       216 * * * *527       535 * * * *588 #
508 * * * *496 #     395 * * * *398       395 * * * *898
267 * * * *724       531 * * * *874       531 * * * *874
194 * * * *451       531 * * * *985       531 * * * *885
519 * * * *020       518 * * * *654       518 * * * *554
213 * * * *014       540 * * * *388       540 * * * *888
299 * * * *593       393 * * * *530       393 * * * *530
365 * * * *215 #     107 * * * *161 #     260 * * * *887
263 * * * *023       553 * * * *284       553 * * * *284
505 * * * *471       282 * * * *601       282 * * * *501
281 * * * *650       387 * * * * 165 #    506 * * * *834
249 * * * *881       558 * * * *740       558 * * * *740
217 * * * *423 #     381 * * * *565       381 * * * *565
393 * * * *557       377 * * * *522       377 * * * *522
367 * * * *587       532 * * * *773       532 * * * *773
354 * * * *437       326 * * * *463       326 * * * *463
202 * * * *713       183 * * * *325       183 * * * *825
140 * * * *971       297 * * * *117 #     107 * * * *161 #
206 * * * *863       215 * * * *573       215 * * * *673
240 * * * *727       373 * * * *905       373 * * * *905
292 * * * *683       331 * * * *172       331 * * * *172
289 * * * *077       372 * * * *172       372 * * * *172
378 * * * *432       385 * * * *668       385 * * * *668
280 * * * *733       564 * * * *754       558 * * * *008 #
386 * * * *371       375 * * * *410       375 * * * *410
219 * * * *655       565 * * * *036 #     569 * * * *628
166 * * * *754       387 * * * *841       387 * * * *841
248 * * * *174       538 * * * *261       538 * * * *261
246 * * * *354                            531 * * * *866

                     NUF

511 * * * *843       214 * * * *635       522 * * * *846
267 * * * *275       514 * * * *515       565 * * * *964
209 * * * *054       314 * * * *302       553 * * * *291
535 * * * *588 #     560 * * * *696       550 * * * *598
569 * * * *524       362 * * * *483       557 * * * *097
519 * * * *908       169 * * * *032       528 * * * *140
174 * * * *367       568 * * * *540       551 * * * *812
176 * * * *904       293 * * * *367       295 * * * *820
381 * * * *512       512 * * * *708       549 * * * *817
522 * * * *989       531 * * * *888       108 * * * *870
180 * * * *713       540 * * * *397       563 * * * *989
508 * * * *496 #     508 * * * *496 #     560 * * * *564
267 * * * *724       514 * * * *924       320 * * * *232
194 * * * *451       503 * * * *355       553 * * * * 123
519 * * * *020       217 * * * *423 #     365 * * * *215 #
213 * * * *014       368 * * * *450       565 * * * * 147
299 * * * *593       241 * * * *965       561 * * * *032
365 * * * *215 #     301 * * * *065       524 * * * *860
263 * * * *023       546 * * * *749       315 * * * *640
505 * * * *471       398 * * * * 168 #    530 * * * *776
281 * * * *650       175 * * * *475       558 * * * *546
249 * * * *881       559 * * * *740       557 * * * *957
217 * * * *423 #     559 * * * *435       565 * * * *036 #
393 * * * *557       521 * * * *073       564 * * * *950
367 * * * *587       564 * * * *561 #     535 * * * *470
354 * * * *437       561 * * * *058       558 * * * *005
202 * * * *713       533 * * * *829       527 * * * *830
140 * * * *971       536 * * * * 141      537 * * * *866
206 * * * *863       384 * * * *830       528 * * * *914
240 * * * *727       207 * * * *025       297 * * * *117 #
292 * * * *683       361 * * * *345       535 * * * *483
289 * * * *077       561 * * * *310       539 * * * *709
378 * * * *432       562 * * * *957 #     562 * * * *106
280 * * * *733       528 * * * *672       558 * * * *843
386 * * * *371       387 * * * * 165 #    316 * * * *442
219 * * * *655       173 * * * *242       560 * * * *121
166 * * * *754       393 * * * *428       288 * * * *500
248 * * * *174       565 * * * *531       549 * * * *206
246 * * * *354       558 * * * *569

Table 7: Comparison of the user final influence.

User ID           UFI without     UFI with      The actual
                  zombie fans    zombie fans      rankings

263 * * * *023         1              3              1
511 * * * *843         2              2              2
519 * * * *020         3              1              3
508 * * * *496         4              4              4
550 * * * *598         5              5              5
267 * * * *724         6              6              6
365 * * * *215         8              8              7
299 * * * *593         7              7              8
522 * * * *989         9              9              9
194 * * * *451         10             10             10

Table 8: Top 10 user information of the UFI.

UFI       User ID         Number     Number     Authenticated
ranking                   of fans    of blogs       or not

1         263 *** *023      128        1515            1
2         511*** *843       282        1282            1
3         519 *** *020       66        101             1
4         508 *** *496      261        5471            1
5         550 *** *598       14         22             1
6         267*** *724       823        1452            1
7         299*** *593       158        109             1
8         365 *** *215      177        945             1
9         522*** *989        13         29             1
10        194 *** *451       69         11             1

Table 9: Comparison of UFI method with microblog-fans ranking
algorithm.

UFI       User ID         Number     Number     Microblog-fans
ranking                   of fans    of blogs       ranking

1         263 *** *023      128        1515            3
2         511*** *843       282        1282            4
3         519 *** *020       66        101             8
4         508 *** *496      261        5471            1
5         550 *** *598       14         22             6
6         267*** *724       823        1452            2
7         299*** *593       158        109             7
8         365 *** *215      177        945             5
9         522*** *989        13         29            10
10        194 *** *451       69         11             9

Table 10: Comparison of user actual ranking with UFI ranking.

User ID           The actual      UFI value     UFI ranking
                    ranking
263 * * * *023         1            1.0000           1
511 * * * *843         2            0.0384           2
519 * * * *020         3            0.0215           3
508 * * * *496         4            0.0107           4
550 * * * *598         5            0.0099           5
267 * * * *724         6           0.00726           6
299 * * * *593         8            0.0028           7
365 * * * *215         7            0.0021           8
522 * * * *989         9            0.0019           9
194 * * * *451         10           0.0016           10
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Title Annotation:Research Article
Author:Liu, Yufei; Pi, Dechang; Cui, Lin
Publication:Complexity
Article Type:Report
Geographic Code:9CHIN
Date:Jan 1, 2017
Words:9439
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