A Scalable Approach for Strengthening Social Media Ties Using Multi-Dimensional Analysis

The degree of connection or proximity between persons or entities inside a social network is referred to as relationship strength in social media. It can range from weak and superficial connections to strong and profound bonds. Measuring social media tie strength is significant for various reasons, including providing valuable insights to people, organizations, researchers, and the platforms themselves [1]. Understanding the strength of social media relationships between users may lead to more successful communication, marketing initiatives, and user experience improvements.  Measuring the strength of connections in social networks is a difficult issue. This is due to the fact that the strength of a connection may be impacted by a variety of factors, including the frequency of interaction, emotional intimacy, and amount of trust between the two people. It is critical to accurately measure the strength of ties inside social networks for tasks such as identifying important users, forecasting information dissemination patterns, and enhancing recommendation systems. Quantitative evaluation enables more exact decision-making. That is why we have adopted a multi-dimensional approach to calculate tie strength in this paper. 

So far in the real world of networks, only direct or mutual connections have been made among the users. Thus, conventional methods were used to ascertain the strong connections among users in social networking sites which are linked to one another. Methods for building networks and their associated tie structures have also been discussed so far. Full network methods [2], Snowball methods [3], and Ego-centric networks [4] are popular among them. In the context of measuring tie strength in social networks, these methods offer different approaches to data collection and analysis. While ego-centric networks and snowball approaches concentrate on certain subsets or individual views inside the network, full network methods offer a comprehensive picture of the whole network. Researchers may consider these techniques to learn more about tie strength and the importance of it in social networks, depending on the study aims and the resources at their disposal. In most cases, the information we collect comes from real-world networks where individuals have a variety of connections with one another due to their social activities. In addition, the acquired information must be pertinent to the connections between users. In a university, for instance, it makes no difference if student registration numbers are entered into the database instead of the number of student publications (the original requirement). Like one-way connections between individuals on social media, state-of-the-art algorithms to find strengths in different linkages do not work well with social media. Numerous efforts have been made for various user connections based on various metrics such as correlation, classification, clustered community, etc. In addition, our paper emphasizes the importance of strengthening the robustness of existing network connections through the utilization of many, diverse connections.

The idea that the strength of ties between two networks can vary depending on how much they overlap was initially proposed by Granovetter [5]. Relationship strength, he mentioned, is the sum of many characteristics such as length of association, psychological impact, degree of user closeness, etc. Granovetter argues that strong ties are formed when social circles meet, while weak ties serve as a conduit for information between groups of friends who might not otherwise interact. For information to spread throughout a whole network, weak ties are therefore more important than strong ones.

One of the most debated areas of study currently is how to measure the quality of a network’s connections. Finding a good way to measure relationship strength is a major obstacle to research in this area. Before tackling more complex issues in social networks, like Friend Recommendations in a Social Bookmarking System [6], diffusion-based similarity on tripartite graphs [7], etc., this fundamental problem must be solved. Having access to someone’s connection strength with another user is helpful in many contexts, such as predictions, module recommendations, news items, and more [8]. The quality of certain public webwork aids may be raised based on the evaluation of correlation robustness by the public webwork contributor.

Recent studies have focused specifically on developing methods for gauging the intensity of connections within social networks [9]. Predictions of a relationship’s stability have been made using interaction data. However, the majority of the currently available methods only consider the strength of users’ direct ties inside public internet networks. Alice and Bob may not be friends, but they do have a mutual friend. A similar challenge arises in social networks when trying to ascertain the quality of the connections between such individuals. As a result, we took an unconventional approach to determine the quality of connections mediated by third parties. In light of changing social network dynamics, it is necessary and potentially very advantageous to take an innovative approach to evaluating the quality of connections facilitated by third parties. It offers a more sophisticated view of connection strength and its implications for different sectors, including marketing, social science, and the architecture of online platforms. It also emphasizes the growing complexity of contemporary networks and the effect of intermediaries.

This paper mainly contributes to compute the tie strength based three different factors, namely Analogy Profile, Analogy Friendship and Analogy Reaction among social media users. While we combine the individual profile information, number of established connections with that particular individual and the frequency of sharing information or comments to its own network give the best possible way to find the tie strength among the users in that social media network. The novelty of the computation of tie strength in this manuscript provides the application of the three unique formula, like Pearson Correlation as AP, Jaccard’s coefficient as AF, and User Interconnection Potency Level as AR together to fit on the three factors mentioned above. Finally, we compute the proposed formula for tie strength and implemented in different real time social media datasets to check the accuracy. Three influential factors α, β, and γ increase the significance of the outcome of our experiments. As all the three parameters are assigned almost equal weightages, it leads to a good score in precision, recall and DSC. In this way the probability of losing efficient connections will also be reduced and performs better to enhance relationship strength. After the execution of the experiments, our proposed method has achieved better results compared with the existing methods and it is well elaborated in the Results & Discussion section later.

The paper is structured as follows: the second section provides context for the topic by discussing relevant background information and previous research. In the third section, we discussed the enumerative structure of our suggested method in detail. Our suggested model’s workflow, the methods used to calculate relationship strength, the assessment matrices, and the dataset are all discussed in detail here. The fourth section contains a summary and analysis of the experimental data. This paper concludes with a discussion of our evaluation results and directions for further research.

Figure 1 depicts the workflow of our proposed approach. In our model, we have considered mainly three factors to compute the tie strength. We have considered ten numbers of different real time social media networks for our experiment. All the dataset consists of the profile values, strongly and weakly connected component and the structure of the network. We must first gather profile information, circles, and ego networks from all networks. One circle represents the real-time network's interconnectivity ('friend list').

1.png

Figure 1. Work flow of the proposed model

3.1 Computation of tie strength

In our work, we used three parameters to calculate relationship strength among Facebook users: Analogy Profile, Analogy Friendship, and Analogy Reaction. Pearson Correlation was chosen as the Analogy Profile, Jaccard's coefficient as the Analogy Friendship, and User Interconnection Potency Level as the Analogy Reaction. Finally, we compute our relationship strength for Facebook users. Let's go through all three elements briefly in order to calculate the tie strength:

(1) Analogy Profile:

In our innovative method, we employed modified Pearson Correlation [34] as an Analogy Profile. In order to evaluate the chance of knot formation between the vertices v_i & v_j, the unification neighbourhood set, Uni_ij is defined as:

$\mathrm{Uni}_{\mathrm{ij}}=\left\{\mathrm{p} \mid\left(\mathrm{A}_{\mathrm{i}}[\mathrm{p}]>\right.\right.$ null $)$ otherwise $\left(\mathrm{A}_{\mathrm{j}}[\mathrm{p}]>\right.$ null $\left.)\right\}$                   (1)

An appreciable association connecting the unification neighborhood set, Uni_ij, A_i and A_j specifies the greater constructional analogy between vertices i and j. To determine the association in the midst of two vertices, the association coefficient in the midst of the unification neighborhood set of vectors is determined. In our paper, the Pearson correlation coefficient is used as an analogy profile to calculate the correlation strength of two users on the social media network. The association in the midst of the unification neighborhood vectors set A_i and A_j is estimated as:

$\mathrm{CR}_{i j}=\frac{\sum_{\mathrm{p} \in \mathrm{Uni_{ij}}}\,\,\left(A_i[\mathrm{p}]-\overline{A_l}\right)\left(A_j[\mathrm{p}]-\overline{A_J}\right)}{\sqrt{\sum_{\mathrm{p} \in \mathrm{U}_{\mathrm{ij}}}}\,\,\,\,\,\left(A_i[\mathrm{p}]-\bar{A}_l\right)^2 \sqrt{\sum_{\mathrm{p} \in \mathrm{U}_{\mathrm{ij}}}}\,\,\left(A_j[\mathrm{p}]-\overline{A_j}\right)^2}$       (2)

$\overline{A_l}$ is the mean standards in the unification neighbourhood vector set A_i and it can be estimated as: $\bar{A}_l=\frac{\sum \mathrm{p} \in \operatorname{Uni}_{\mathrm{ij}}\,\left(A_i[\mathrm{p}]\right)}{U n i_{i j}}$. Even if two nodes have no shared neighbours in our approach, they may have considerable structural similarities. As a result, a link may be identified by comparing their neighbours.

(2) Analogy Friendship:

Analogy Friendship is calculated using Jaccard's coefficient [35] in this paper. In general, two individuals in online social networks are more likely to be connected if they have the greatest number of common buddies. Relationship strength may therefore be measured based on mutual connections in a network. It is a typical similarity metric in data recovery that assesses whether or not both p and q create a feature f (arbitrarily picked feature). This approach yields the following measurement:

$\operatorname{value}(p ; q):=\frac{|\gamma(p) \cap \gamma(q)|}{|\gamma(p) \cup \gamma(q)|}$               (3)

(3) Analogy Reaction:

Here, we have used the User Interconnection Potency Level [36] as Analogy Reaction (AR) in our paper. Mostly two users on social media have the strongest association if they share useful information most of the time on a priority basis between themselves. Relationship strength may also be computed by measuring the interconnection potency level. Suppose two users x and y have dissimilar interconnection levels as A, B, C and D to constitute ‘communicate’, ‘like’, ‘opinion’, and ‘onward’ respectively. In both ways, communication is established between x and y. Then the analogy reaction (AR) is calculated as:

$\begin{aligned} &  \\ & A R(x, y)=\frac {\min \left(A_{i j}, A_{j i}\right)+\min \left(B_{i j}, B_{j i}\right)+\min \left(C_{i j}, C_{j i}\right)+\min \left(D_{i j}, D_{j i}\right)}{\max \left(A_{i j}, A_{j i}\right)+\max \left(B_{i j}, B_{j i}\right)+\max \left(C_{i j}, C_{j i}\right)+\max \left(D_{i j}, D_{j i}\right)} \\ & \end{aligned}$                (4)

The logical principles span is [0,1] for Analogy Reaction (x, y), where 0 indicates fragile interconnection potency and 1 indicates secure interconnection potency.

(4) Computation of Tie Strength:

All three variables have been measured at this point. By giving more value to connections between people who are otherwise very different, we can determine the relative strength of the relationships in our real-world network. The desired tie strength can be found as shown below:

Tie Strength $=\alpha *$ Analogy_Profile $+\beta$$*$ Analogy_Friendship $+\gamma$* Analogy_Reaction             (5)

Here, α, β, γ are weighted parameters and the logical principles span is [0,1] and the summation of α, β, and γ is 1.

If we consider about the limitations of Pearson Correlation, Jaccard’s coefficient and User Interconnection Potency Level, it can briefly be described as:

• Pearson Correlation suggests that variables have a linear connection. Because links in social networks are frequently complex and nonlinear, Pearson's correlation may not completely convey the intricacies of tie strength.
• With binary data, where connections are either present or missing, Jaccard's coefficient works effectively. It is possible that it may not account for differences in tie strength within binary relationships.
• As a notion, User Interconnection Potency Level can be subjective and context dependent. Different individuals might assess tie strength differently, therefore correctly quantifying user perceptions may be difficult.

3.2 Evaluation matrices

Strong relationships are less prevalent in many social networks than weak ties, resulting in skewed data. When considering tie strength data, it is critical to account for this imbalance. Tie strength may be defined as the degree of overlap between people’s interactions, interests, or behaviors. Our unconventional approach considers this overlap, making it crucial to assess how well it captures the shared characteristics between individuals. In measuring tie strength, we take an innovative technique that takes into account several characteristics such as interaction frequency, reciprocity, and the effect of reciprocal connections. We are looking for a complete review that takes into account the overall quality of tie strength forecasts.

Due to the above-mentioned rationale, Precision (P) [37], Recall (R), and the Dice Similarity Coefficient (DSC) were chosen as our evaluation metrics because of their relevance to tie strength measurement, suitability for dealing with imbalanced data, ability to assess overlap, ability to provide a holistic evaluation, and ease of interpretation. These measures provide a thorough evaluation of the accuracy and comprehensiveness of our novel technique to evaluate tie strength in social networks.

We have also compared our obtained P, R and DSC values with the other existing algorithms to check the performance of our proposed approach. The formulas are stated below:

$\begin{aligned} & \text { Precision, } P =\frac{\mid \text { Accurate Pragmatic } \mid}{\mid \text { Accurate Pragmatic }|+| \text { Fake Pragmatic } \mid}\end{aligned}$            (6)

$\begin{aligned} & \text { Recall, } R =\frac{\mid \text { Accurate Pragmatic } \mid}{\mid \text { Accurate Pragmatic }|+| \text { Fake Contradiction } \mid}\end{aligned}$              (7）

Dice Similarity Coefficient, $D S C=2 * \frac{P * R}{P+R}$             （8）

3.3 Dataset

In this paper, the real time social media networks have been collected from SNAP [38] library. SNAP is renowned for its efficiency and scalability in handling large-scale network datasets. As our research involves the analysis of social network data, which can be extensive and complex, SNAP's ability to efficiently process and manipulate such data is invaluable. SNAP has extensive popularity and a thriving user and development community. This guarantees that it receives frequent updates, bug corrections, and access to a multitude of materials, making it a dependable and well-supported tool for our research requirements. The specific functions provided by SNAP are closely aligned with the objectives of our research. Its skills for network visualization, statistical analysis, and tie strength assessment are critical to fulfilling our research objectives. The SNAP library was chosen for data collecting and analysis because of its efficiency, scalability, broad algorithmic support, community support, and compatibility with the study aims. These benefits ensure that we may undertake thorough and extensive network analysis to draw significant insights and successfully contribute to the area.

Table 1. Statistics of the facebook network

Table 2. Statistics of the Twitter network

Table 3. Statistics of the Google+ network

Table 4. Statistics of the epinions network

Table 5. Statistics of the wiki-vote network

Table 6. Statistics of the google web graph

Table 7. Statistics of the astro physics collaboration

Table 8. Statistics of the amazon product network

Table 9. Statistics of the livejournal social network

Table 10. Statistics of the stanford web network

We have considered mainly ten different real time networks, namely Facebook, Twitter, Google+, Epinions, Wikipedia vote network, Google web graph, Astro Physics collaboration network, Amazon product co-purchasing network, LiveJournal social network, and Stanford web graph. The statistics of the nodes as well as edges present in the largest strongly connected components (SCC) and weakly connected components (WCC) are also available. The diversified values of the clustering coefficient can be seen among all the networks. All these real-world social media networks consist of ‘friends list’ that is indicated by circles. Survey participants provided all of the existing data in the networks. Profile information, ‘circles’, and ego networks are used to depict the datasets. By reinstating an individual user’s internal id with the current merit, the existing data in these networks is identifiable. Furthermore, when feature vectors from datasets are provided, their meaning is obscured. The statistics of these networks are shown in Tables 1-10.

A novel approach to identify relationship strength based on three authenticate factors has been presented in this paper. Ten different real time social media networks have been used for the experimental result. We have compared our findings with two popular methods, namely TP-URS and URSMF, in this paper. According to the obtained results, our proposed approach delivers efficient performances in all the datasets. Our proposed strategy, on the other hand, performed efficient accuracy and recall values due to almost equal distribution of weightages in influence factors. This resulted in higher DSC levels. This is how our approach has outperformed the other two methods. However, parameter adjustment is also necessary to balance the intensity of user relationships which is considered as the current limitations in our method. Our method simultaneously evaluates three distinct properties in a compatible manner, resulting in significantly reduced data noises and losses, a more accurate connection strength rating, and improved buddy recommendation system performance. The results showed that the proposed method excelled in practically all real-time social media datasets. The results provided by our proposed approach open a new window to enhance the relationship strength among the users in social media platforms. Although it is very difficult to compute relationship strength in a dynamic network running in real time as the numbers of users are increasing or decreasing in non-linear way. Our findings could be the potential impact on large social media datasets to compute relationship strength for any dynamic network. In this way, the real time connections in social media may be calculated and the monitoring activities of the administrators will also be efficient. However, our proposed approach requires parameter adjustment for improved performance. As a consequence, we wish to make the algorithm adaptive so that we may change the parameters automatically in future work. Applications of machine learning and deep learning algorithms may enhance the better result in case of computing relationship strength among online social media users. In the near future, we will try to apply our strategy on additional real-world networks to see how it compares to existing methods.