We will propose several dynamic network models based on a simple AR(1) network

framework. The setting depicts the dynamic changes for network edges explicitly, and facilitates simple and efficient inference (such as maximum likelihood estimation, model diagnostic checking and change-point detection) with theoretical underpinning. It serves as a building block to accommodate various network structures such as dynamic stochastic block structures, dot-product networks and dynamic graphon models. We aim to explore more complex structures based on this AR(1) setting,

resembling some well-documented stylized features observed in real network data, and providing more realistic depiction of the changes over time and more reliable future prediction.

Our research agenda will start with the in-depth research in the two areas.

• Dynamic networks with transitivity and homophily
• Sparse dynamic networks with node-degree heterogeneity

Upon the successes of the investigations above, we will explore the cross-project collaborations to tackle more challenging and practically more relevant topics, including, for example, dynamic network models with weighted edges exhibiting transitivity and/or homophily (jointly with P2), dynamic graph embeddings for AR(1) networks based on transition probabilities instead of static connection

probabilities (jointly with P4), and identifying dynamic network structure and forecasting future changes using the information from the count processes defined on nodes