Figure 5

Detailed illustration and interpretation of all 13 possible three-node connected motifs in directed networks, highlighting six significant motifs and their contextual relevance in Online Social Networks (OSNs). 1. Motif id6 (“Diverging” or “Fan-out” motif): Characterized by a source node (A) diverging to two other target nodes (B and C), this motif can indicate broadcasting or information spreading scenarios in OSNs, with a single user disseminating content to two recipients. 2. Motif id12 (“Chain” motif): Displays a sequential pattern of connectivity, forming a directed “chain” or “path” (\(B->A->C\)). This motif is indicative of sequential information exchange, typically observed in instances like information cascades. 3. Motif id14: Comprises a chain-like structure between two nodes (A and B), with node A also connecting directly to a third node (C). 4. Motif id36 (“Converging” or “Fan-in” motif): Inverts the diverging motif structure, featuring two source nodes (A and B) converging into a single target node (C), representing shared support or common targets within a network. 5. Motif id98 (“Circular” motif): Constitutes a cyclical, unidirectional pattern where each node is linked to one other node (\(A->B\), \(B->C\), and \(C->A\)), enabling a path returning to the origin node. 6. Motif id108 (“Feed-forward Loop” variant): Diverges from the traditional “Feed-forward Loop,” with one node (B) reaching out to two other nodes (A and C), with nodes A and C sharing a reciprocal connection. 7. Motif id238 (“Fully connected motif”): This motif signifies a network condition where all nodes have mutual connections. 8. Motif id38 (“Feed-forward Loop”): Presents a motif where node A connects to nodes B and C, while node B also connects to node C, illustrating instances of information cascading via a direct and intermediary path. 9. Motif id46 (“Feed-forward Loop” variant): Contains two mutually connected nodes (A and B), both independently connecting to a third node (C), indicative of either independent information sharing or non-reciprocal friendship situations within a network. 10. Motif id74: Mimics Motif id14’s configuration, but with nodes A and B sharing mutual connection, and node C also connecting to the first node (A). 11. Motif id78 (“Star” or “Hub” motif): Demonstrates a node A maintaining mutual connections with nodes B and C, but without a direct link between nodes B and C. 12. Motif id102 (“Feed-forward Loop” variant): Incorporates an additional mutual connection between nodes A and C, compared to the typical “Feed-forward Loop” motif that forms a directed chain between nodes A, B and C. 13. Motif id110 (“Feed-forward Loop” variant): This motif exhibits nodes A and B with a mutual connection, a directed edge from node B to node C, and a mutual connection between nodes A and C