As deep learning gains popularity in modelling dynamical systems, we expose an underappreciated misunderstanding relevant to modelling dynamics on networks. Strongly influenced by graph neural networks, latent vertex embeddings are naturally adopted in many neural dynamical network models. However, we show that embeddings tend to induce a model that fits observations well but simultaneously has incorrect dynamical behaviours. Recognising that previous studies narrowly focus on short-term predictions during the transient phase of a flow, we propose three tests for correct long-term behaviour, and illustrate how an embedding-based dynamical model fails these tests, and analyse the causes, particularly through the lens of topological conjugacy. In doing so, we show that the difficulties can be avoided by not using embedding. We propose a simple embedding-free alternative based on parametrising two additive vector-field components. Through extensive experiments, we verify that the proposed model can reliably recover a broad class of dynamics on different network topologies from time series data.

The ability to discover community structures from explorative networks is useful for many applications. Most of the existing methods with regard to community mining are specifically designed for assortative networks, and some of them could be applied to address disassortative networks by means of intentionally modifying the objectives to be optimized. However, the types of the explorative networks are unknown beforehand. Consequently, it is difficult to determine what specific algorithms should be used to mine appropriate structures from exploratory networks. To address this issue, a novel concept, generalized community structure, has been proposed with the attempt to unify the two distinct counterparts in both types of networks. Furthermore, based on the proposed random network ensemble model, a generalized community mining algorithm, so called G-NCMA, has been proposed, which is promisingly suitable for both types of networks. Its performance has been rigorously tested, validated and compared with other related algorithms against real-world networks as well as synthetic networks. Experimental results show the G-NCMA algorithm is able to detect communities, without any prior, from explorative networks with a good accuracy.

Research has shown that many social networks come into being hierarchically based on some basic building blocks called communities, within which the social interactions are very intensive, but between which they are very weak. Network community mining algorithms aim at efficiently and effectively discovering all such communities from a given network. Many related methods have been proposed and applied to different areas including social network analysis, gene network analysis and web clustering engine. Most of the existing methods for mining communities are centralized. In this paper, we present a multi-agent based decentralized algorithm, in which a group of autonomous agents work together to mine a network through a proposed self-aggregation and self-organization mechanism. Thanks to its decentralized feature, our method is potentially suitable for dealing with distributed networks, whose global structures are hard to obtain due to their geographical distributions, decentralized controls or huge sizes. The effectiveness of our method has been tested against different benchmark networks.