Network is one of the best data models to represent human behavior and their interactions. For instance, social network users can share their interests and news on social network platforms, traffic users can express their common interests and daily activities by trajectory networks, telephone network users show their society interactions at periodic levels. In the area of network science, lots of research have been developed to investigate the information flow and influence diffusion models in such complex networks. However, the frangibility of the network haven’t been fully exploited. The frangibility of a network may be affected by multiple factors in the network, e.g., the removal of users may result in the disconnection of the network, or the high communication cost of the network; the addition of users may enrich the network so that the communication cost can be largely reduced; the changed paths of consuming network content may also vary the communication of the information flow in the network. It is highly challenging to diagnose the frangibility of the complex networks. Traditional works have paid great efforts to discovery the influential users or seed users at different situations using the metrics like centrality, betweenness, and ego network, or using the linear threshold model, independent cascade model, and the weighted user-defined path models. However, these works still focused on the influence diffusion, rather than the frangibility of the networks in the dynamic environment. In addition, it is desirable for researchers to investigate the non-human defined metrics to uncover the frangibility of networks, with which the correlated key players can be retrieved. To solve the challenging issue, in machine learning, concept learning has become one of the primary research in the small sample learning research. Concept learning strategy aims to perform recognition or form new concepts from few observations though fast processing. Conceptually, concept learning employs matching rules to associate the concepts in the concept system with small samples input. It is very helpful to perform cognition or complete a recognition task in data analytics. With the capability of small samples and the learnt knowledge, it can help to advance the realistic key player discovery models and efficiently find the key players for different target criteria. Therefore, through this special issue, we would like to invite authors to submit their valuable research papers on all aspects of these areas with the above issues. This Special Issue of Complexity invites researchers working in the field cross-cutting information and knowledge-based systems, data science and artificial intelligence to submit original papers discussing and promoting ideas and practices about advanced complex network management and analytics technologies for the frangibility driven key user discovery. The list of possible topics includes, but is not limited to: • Key User Detection Model with Dynamic Network Change • Concept Learning from Small Samples to User Profiling in Networks • Concept Learning from Small Samples to Attribute Filling in Networks • Concept Learning for Event Type Disambiguation in Networks • New Knowledge driven Concept Learning across Multiple Networks • Root Cause Diagnoses based Concept Learning for Network Flow Change • Novel Feature Detection Model for Identifying Frangibility of Network • Efficient Structural Hole Computation in Complex Networks • Top-k Influential Users Detection in Attributed Networks • Anchor Vertex Exploration to Enrich the Networks • Dynamic Network Metric Evaluation • Community-level Information Diffusion with Concept Learning Authors can submit their manuscripts via the Manuscript Tracking System at https://mts.hindawi.com/login/. Reviewing will be double-blind, meaning the authors' identities will be hidden from the reviewers. We will follow policies for plagiarism, submission confidentiality, reviewer anonymity, and prior and concurrent paper submission based on the Publisher of Hindawi.