An OSN is assumed to be a closed world where the information spreads because of informational cascades, i.e., the path followed by a portion of information in the network (diffusion graph). In the information spreading process each node is designated as activated or inactivated. The process of propagation, which is observed as a continuous activation of nodes throughout the networks, is called the activation sequence.

Influence Probability p_uv denotes the probability with which an initial user u influences another user v. The diffusion begins at time step 0, in each time step the user is influenced by the previous time step while attempting to influence their neighbors and succeeds or fails based on the influence probabilities associated with the edges. Subsequently, the influenced neighbors successfully become recently activated users and stay activated for the rest of the diffusion. On activation at a particular time step, a user u has exactly one attempt to activate each of its inactive neighbors with a probability p_uv for each neighbor v. The diffusion ends when no further users are activated.

Social influence and user similarity are the features that represent the user’s interest and can be used to predict user behavior in the future. Thus, identifying the contagion in the individual user attitudes that affects social attitudes toward the intervention, can help to identify the social influence [38]. Furthermore, the influencing node is assumed to be the node that can adopt the cascade, which spreads to inactive nodes and activates them. The contagions are those groups of nodes that are not activated and are also closer to the epidemic of the influential nodes [39].

In addition, social contagion identifies inactive users in the network who become activated by re-sharing information and spreads the information within the community structure. This increase in information sharing leads to stronger interaction within a larger group. In other words, social contagion is higher when similar interests are shared in the intra-communities, and lower when dissimilar interests are shared in the inter-communities. Let us assume a complex network with N nodes (users), where each node i represents the activity x_i(t) following the rate equation as(2) dxidt=W(xi(t))+∑j=1N⁡AijQ(xi(t),xj(t))

Eq. (2) represents the dynamical model and gives a general deterministic description for pair-wise interactions. W(x_i(t)) represents the node i self-dynamics. ∑j=1N⁡AijQ(xi(t),xj(t)) is the interaction between node i along with its neighbor node. A_ij is the adjacency matrix and Q (x_i(t), x_j(t)) represents the dynamic mechanism of the pair-wise interactions, when x_i provides the corresponding actual meaning. In epidemic processes, x_i represents the contagion probability.

In the case of misinformation diffusion, information does not spread properly across the network and results in the propagation of misinformation, which plays an important role in the diffusion process. Consequently, the absolute quantity of interactions with misinformation remains significant and may not fully capture the trending communities. Therefore, the least square method is used to fit the distribution of misinformation in the communities. It is a statistical procedure to determine the best fit for the set of users who belong to the intra-communities and inter-communities and predict user behavior depending on user activity [40]. To be precise, similar interests will fit in the intra-community, whereas dissimilar interests will fit in the inter-community.

The capability of nodes to spread information across the network is ranked based on the neighbor nodes that perform in the diffusion process [41]. The collected misinformation is used to rank them within the communities. Community ranking in the information cascade model is performed to identify the influential information spreader, which also helps to classify influential spreaders in the intervention process.

In multilayer networks, distinct entities are connected via different social interactions. Community detection identifies structurally similar pairs in multilayer networks by grouping them together. It is based on the interaction between distinct entities, which groups the Facebook and Twitter data using a multilayer network model that optimally captures the overlapping community structure in the network. Furthermore, considering that the users adopting information shared in the multilayer network play a significant role in activating the users in the network, the interactions and mutual impact of these unique connections must be faithfully captured. Finally, the Fraction of Intra/Inter-Layer diffusion score is used to evaluate the IID model for a multilayer network, which is discussed with the results in Section 4.3.1.

Social influence is wielded by users through social interactions with other participants by sharing information, opinion, or decisions in the network [42]. The social distance value is less for a higher level of social influence and vice-versa. Accordingly, the social distance value will be lower in the intra-community structure, whereas it will be greater in the inter-community structure, which can be attributed to the presence of more influential users with less social distance value in the network. In this situation, a multilayer network is optimal for handling the dynamic network model.

The similarity between the two networks is determined using the subgraph of overlapping community structures in Twitter and Facebook. Influential nodes are detected using fixed attributes that belong to user activities in the social network. The top-k influential node is typically the one that spreads the most information in each community [43]. Thus, the IID model visualizes the community structure for multiple networks. The proposed IID model spreads the influential information, which helps to identify the influential communities in a multilayer network. The diffusion degree centrality of a user v is defined as(3) CDD(v)=∑uϵΓ(v)⁡{λu,v+(λu,vx∑iϵΓ(v)⁡λi,v)} where Γ(v) denotes the neighbor set of v and λ_u,v denotes the propagation probability of user v influencing user u. Eq. (3) incorporates the property of information diffusion along with structural information.

The influence of social consensus information can change individual preferences with respect to mingling with minority group members, even beyond the intervention phase [44]. Furthermore, for an innovation to be adopted, it must have certain qualities [45]. Thus, social consensus information influences the individual’s exact opinions through their attitudes [46].

The diffusion of innovation model identifies trending communities, thereby determining the changes in user interest across the networks. The rate depends on the performance of the spread of innovative information and affects the potential user spread that has not yet influenced the spreader. The rate at which the number of adopters changes with time in given in Eq. (4)(4) dA(t)dt=i(t)[P−A(t)] where A(t) is the total number of users that adopted the innovation until time t, i(t) is the coefficient of diffusion innovativeness of information spread, and P denotes the number of potential users.

The challenge in visualizing multilayer graphs is that multiple edges between two nodes may be plotted atop each other, thereby making them impossible to be discerned [47,48]. Initially, a community detection graph is constructed for the two social media sites. Thus, multilayer network visualization can be achieved for both the Facebook and Twitter data. The influential users are used to characterize the behavior of information spread within the network. Furthermore, the influential trending communities are identified from the shared information of the influential users in the multilayer network.

In this section, the proposed system is evaluated and experimental results for the popular social sites are discussed. Social media users typically interact with each other by sharing or exchanging information. Thus, data from Facebook and Twitter are using extracted using graph API Streams. Not only are these API streams valid as common data for pre-processing, they can also be effectively interpreted to achieve graph data. User influence in the social network is analyzed in terms of participation, content sharing, popularity, and activity. The statistical properties of datasets are summarized in Table 1.

The proposed IID model was compared with six existing methods: SI, SVFR, SIR, FACE, Hydro-IDP and UVSR. The descriptions of the implementation details of these methods are summarized below.

IID: The influential communities across the network are identified based on the information spread among the communities. Information diffusion plays the major role in identifying the influential interaction. The fraction of intra/inter layer (FIL) helps in measuring the efficiency of the model.

SI [6]: The interactive and non-interactive activities are identified using the top k-influence ranks based on node selection.

SVFR [7]: The three types of user reactions to a message are view, ignore, or forward. The view or forward probability is determined based on the content. However, this method requires a reduction in the time delay in information diffusion.

SIR [10]: An EM algorithm is used to predict the diffusion probabilities. However, this method requires an improvement of its propagation into the independent cascade model.

FACE [17]: The golden selection search algorithm is applied under moderate temporal constraints. This method requires a reduced time taken to spread influence information.

Hydro-IDP [26]: The characteristics of information diffusion are extracted to describe and predict the spreading process of information in OSN. However, the influence and diffusivity on social platforms should be improved.

UVSR [48]: A continuous-time, stochastic model is used in this method to characterize the information diffusion process and understand the topological features and temporal dynamics of information diffusion. In this method, the delay probability of diffusion and speed in viewing and sharing must be improved.

In a social graph, nodes or vertices are described as users or actors and the association between nodes are represented by the activity links or edges between them. Initially, Facebook and Twitter communities are identified in the social graph, and the overlap between communities is determined to identify the influence of persons or groups of persons. The user interaction reveals a friendly relationship and forms an overlapping community structure between Facebook and Twitter data.

Modularity metrics are used to evaluate the community detection capabilities of multilayer networks. The value of modularity Q is defined as shown in Eq. (5).(5) Q=∑ik⁡(eii−(∑ik⁡eij)2) where k denotes the number of communities, e_ii is the ratio of the number of edges within the community i to the total number of edges in the entire network and e_ij is the ratio of the number of edges between communities i and j to the total number of edges in the entire network [49,50]. The different users identified are potential users, adopted users, and influential users in the information diffusion process for a multilayer network. The modularity Q value is calculated for a multilayer network based on the different users in the communities, which is shown in Fig. 2.

In the IID model, active nodes are considered as senders, and the nodes being activated are considered as receivers. On activation, each node has one attempt at activating each of its neighbor nodes in the social graph. A node u has a random threshold θ_u ∼ U [0, 1]. Each Neighbor node v influences node u according to a degree centrality C_(D)u, v as given by Eq. (6)(6) Influencenode=∑vneighborofu⁡C(D)u,v≤1

A node u becomes active when the fraction of its active neighbors is at least θ_u, as given by Eq. (7)(7) Activenode=∑vactiveneighborofu⁡C(D)u,v≥θu

The spread of information begins with a collection of active nodes and continues until no further activation of nodes is possible. When a user u becomes activated at a particular time step, it has exactly one attempt to activate each of its inactive neighbors with the probability p_uv for each neighbor v. The diffusion ends when there are no further users that can be activated. Depending on the number of nodes interacting in the network, the degree centrality and active nodes increase, as shown in Table 2.

In social networks, an active node denotes that the node was selected to spread the behavior, innovation, or decision. Based on the social influence effect, information can spread across the network through the principles of herd behavior and informational cascade [51,52]. Some topics can become quite popular, spread worldwide, and contribute to new trends.

Finally, the components of an information diffusion method practiced in an OSN can be similar to a discussion of information carried by messages that spread along the edges of the network according to a particular mechanism. The interaction based on specific properties depends on the edges and nodes in the social network [53]. For instance, the most relevant recent activity as well as the weaknesses, strengths, and improvements for each feature must be analyzed, as shown in Table 3.

Identifying the numerous influential spreaders in a social network is critical for ensuring the efficient diffusion of information. For instance, a social media campaign can improve efficiency by targeting the influential individuals who can initiate huge information cascades that will result in more adoptions. The output of user interested communities or the trending communities are shown in Table 1. The communities are ranked based on the extraction of misinformation in the communities, as shown in Table 4.

The top five ranked communities are C12, C7, C5, C15, and C1 and the categories they belong to are environment, news, sports, disease, and education respectively. These are the topics on which significant diffusion of information occurs. Based on the information cascade that occurs in each of these communities, the score is calculated and the communities are ranked.

The analysis of community interaction behavior shows that the users who join communities determine the factors that are shared among them. These new influential users form the larger group that was analyzed for influential community structure behavior. The trending communities for the multilayer networks of Facebook and Twitter are shown in Fig. 3.

The FIL is used to measure the spreading of an information cascade within or between the layers of a multilayer network. The FIL score denotes the fraction of user interaction in the diffusion network and the average rate of information cascade over the different layers. Following this, the probability of information diffusion was applied to calculate the FIL diffusion score of information spread from one user to another in the multilayer network. Thus, the trending influential communities are identified using the IID model, and the FIL diffusion score is used to measure the efficiency of the IID model on a different social network. The precision, recall, accuracy, and F-measures evaluated based on the FIL diffusion score are shown in Table 5.

Precision. The ratio of the number of similar users in the same layer to the total number of users. It is also called a positive predictive value. The precision value is calculated using Eq. (8).(8) Precision=∑⁡SLSU(∑⁡SLSU+∑⁡SLDU)

Recall. The ratio of the number of similar users in the same layer to the total number of users in the different layers. It is also called a true positive rate. The recall value is calculated using Eq. (9).(9) Recall=∑⁡SLSU(∑⁡SLSU+∑⁡DLSU)

Accuracy. The ratio of correctly predicted observations referred to as users in a similar layer to the total observation referred to as the total number of users in different layers. The accuracy value is calculated using Eq. (10).(10) Accuracy=∑⁡SLSU+∑⁡DLDU∑⁡SLSU+∑⁡SLDU+∑⁡DLSU+∑⁡DLDU

F measure. The F1 score is used to consolidate precision and recall into one measure; the F1 measure is calculated using Eq. (11).(11) Fmeasure=2×Precision∗RecallPrecision+Recall

The fraction of Intra/Inter-Layer diffusion score is determined using Eqs. (8)–(11) as shown in Fig. 4.

The overall performance in terms of precision, recall, and F-measure for the proposed method compared with the six existing methods was evaluated based on the FIL diffusion score, as shown in Fig. 5.