Precise influence evaluation in complex networks

Evaluating node influence is fundamental for identifying key nodes in complex networks. Existing methods typically rely on generic indicators to rank node influence across diverse networks, thereby ignoring the individualized features of each network itself. Actually, node influence stems not only from general features but the multi-scale individualized information encompassing specific network structure and task. Here we design an active learning architecture to predict node influence quantitively and precisely, which samples representative nodes based on graph entropy correlation matrix integrating multi-scale individualized information. This brings two intuitive advantages: (1) discovering potential high-influence but weak-connected nodes that are usually ignored in existing methods, (2) improving the influence maximization strategy by deducing influence interference. Significantly, our architecture demonstrates exceptional transfer learning capabilities across multiple types of networks, which can identify those key nodes with large disputation across different existing methods. Additionally, our approach, combined with a simple greedy algorithm, exhibits dominant performance in solving the influence maximization problem. This architecture holds great potential for applications in graph mining and prediction tasks

Reconstructing networks

Complex networks datasets often come with the problem of missing information: interactions data that have not been measured or discovered, may be affected by errors, or are simply hidden because of privacy issues. This Element provides an overview of the ideas, methods and techniques to deal with this problem and that together define the field of network reconstruction. Given the extent of the subject, we shall focus on the inference methods rooted in statistical physics and information theory. The discussion will be organized according to the different scales of the reconstruction task, that is, whether the goal is to reconstruct the macroscopic structure of the network, to infer its mesoscale properties, or to predict the individual microscopic connections.Comment: 107 pages, 25 figure

Topology Reconstruction of Dynamical Networks via Constrained Lyapunov Equations

The network structure (or topology) of a dynamical network is often unavailable or uncertain. Hence, we consider the problem of network reconstruction. Network reconstruction aims at inferring the topology of a dynamical network using measurements obtained from the network. In this technical note we define the notion of solvability of the network reconstruction problem. Subsequently, we provide necessary and sufficient conditions under which the network reconstruction problem is solvable. Finally, using constrained Lyapunov equations, we establish novel network reconstruction algorithms, applicable to general dynamical networks. We also provide specialized algorithms for specific network dynamics, such as the well-known consensus and adjacency dynamics.Comment: 8 page