Opinion manipulation on Farsi Twitter.

For Iranians and the Iranian diaspora, the Farsi Twittersphere provides an important alternative to state media and an outlet for political discourse. But this understudied online space has become an opinion manipulation battleground, with diverse actors using inauthentic accounts to advance their goals and shape online narratives. Examining trending discussions crossing social cleavages in Iran, we explore how the dynamics of opinion manipulation differ across diverse issue areas. Our analysis suggests that opinion manipulation by inauthentic accounts is more prevalent in divisive political discussions than non-divisive or apolitical discussions. We show how Twitter's network structures help to reinforce the content propagated by clusters of inauthentic accounts in divisive political discussions. Analyzing both the content and structure of online discussions in the Iranian Twittersphere, this work contributes to a growing body of literature exploring the dynamics of online opinion manipulation, while improving our understanding of how information is controlled in the digital age.

Degree difference: a simple measure to characterize structural heterogeneity in complex networks.

Despite the growing interest in characterizing the local geometry leading to the global topology of networks, our understanding of the local structure of complex networks, especially real-world networks, is still incomplete. Here, we analyze a simple, elegant yet underexplored measure, 'degree difference' (DD) between vertices of an edge, to understand the local network geometry. We describe the connection between DD and global assortativity of the network from both formal and conceptual perspective, and show that DD can reveal structural properties that are not obtained from other such measures in network science. Typically, edges with different DD play different structural roles and the DD distribution is an important network signature. Notably, DD is the basic unit of assortativity. We provide an explanation as to why DD can characterize structural heterogeneity in mixing patterns unlike global assortativity and local node assortativity. By analyzing synthetic and real networks, we show that DD distribution can be used to distinguish between different types of networks including those networks that cannot be easily distinguished using degree sequence and global assortativity. Moreover, we show DD to be an indicator for topological robustness of scale-free networks. Overall, DD is a local measure that is simple to define, easy to evaluate, and that reveals structural properties of networks not readily seen from other measures.

Edge-based analysis of networks: curvatures of graphs and hypergraphs.

The relations, rather than the elements, constitute the structure of networks. We therefore develop a systematic approach to the analysis of networks, modelled as graphs or hypergraphs, that is based on structural properties of (hyper)edges, instead of vertices. For that purpose, we utilize so-called network curvatures. These curvatures quantify the local structural properties of (hyper)edges, that is, how, and how well, they are connected to others. In the case of directed networks, they assess the input they receive and the output they produce, and relations between them. With those tools, we can investigate biological networks. As examples, we apply our methods here to protein-protein interaction, transcriptional regulatory and metabolic networks.