Complex Networks can depict a clear image of real-world systems. A real-world scenario can be represented a graph with interconnected layers - called a multi-layer network. Finding motifs can give an idea of the topology of complex systems and helps to understand the dynamics in the graphs. Looking at motifs as atoms of the network is helpful to analyze the relationship between nodes, and between layers. In this work, we suggest a sub-graph enumeration approach to find and count the motifs in multi-layer network. The proposed work has many application in graph mining, particularly to structure and dynamics of complex networks.

The rumor spreading and influence maximization are two important forms of social network communication. Many social network applications utilize influence maximization for finding the seed node. The most common approach for influence maximization is greedy, which delivers an optimal solution. However, the greedy approach has high computational overhead and offers a limited spreading capability. We address this problem by proposing a novel framework, SpreadMax, for maximizing the spreading process with reduced computational overhead. Our model consists of two phases. In the first phase, we identify seed nodes using hierarchical reachability approach and these designated seed nodes spread infection during the second phase. The proposed model is validated through experiments using real-world data, in comparison with existing methods. We observed that the SpreadMax technique performs better in maximizing the influence.

Diffusion dynamics is the transfer of information from one node to another. Information diffusion has two goals: maximize or minimize information spread over the network. Attractive information such as innovations, awareness campaigns, branding, and advertising help people positively. However, awful information such as rumors, malicious viruses, pornography, and revenge disturb people. The negative information contributes to chaos; therefore, it must be blocked and inhibited from further diffusion. We are motivated to study the problem, namely Influence Minimization . The new information alters the energy level or entropy associated with a node. Entropy quantifies the influence propagation rate across the network. This article proposes two reduction policies that reduce repulsive information’s influence through entropy. We validate the proposed system by considering the user response and surveillance on real-time networks.