Identifying Multiple Influential Spreaders in Complex Networks by Considering the Dispersion of Nodes

Identifying multiple influential spreaders, which relates to finding k (k > 1) nodes with the most significant influence, is of great importance both in theoretical and practical applications. It is usually formulated as a node-ranking problem and addressed by sorting spreaders’ influence as measured based on the topological structure of interactions or propagation process of spreaders. However, ranking-based algorithms may not guarantee that the selected spreaders have the maximum influence, as these nodes may be adjacent, and thus play redundant roles in the propagation process. We propose three new algorithms to select multiple spreaders by taking into account the dispersion of nodes in the following ways: (1) improving a well-performed local index rank (LIR) algorithm by extending its key concept of the local index (an index measures how many of a node’s neighbors have a higher degree) from first-to second-order neighbors; (2) combining the LIR and independent set (IS) methods, which is a generalization of the coloring problem for complex networks and can ensure the selected nodes are non-adjacent if they have the same color; (3) combining the improved second-order LIR method and IS method so as to make the selected spreaders more disperse. We evaluate the proposed methods against six baseline methods on 10 synthetic networks and five real networks based on the classic susceptible-infected-recovered (SIR) model. The experimental results show that our proposed methods can identify nodes that are more influential. This suggests that taking into account the distances between nodes may aid in the identification of multiple influential spreaders.

Graph Neural Networks for Fast Node Ranking Approximation

Graphs arise naturally in numerous situations, including social graphs, transportation graphs, web graphs, protein graphs, etc. One of the important problems in these settings is to identify which nodes are important in the graph and how they affect the graph structure as a whole. Betweenness centrality and closeness centrality are two commonly used node ranking measures to find out influential nodes in the graphs in terms of information spread and connectivity. Both of these are considered as shortest path based measures as the calculations require the assumption that the information flows between the nodes via the shortest paths. However, exact calculations of these centrality measures are computationally expensive and prohibitive, especially for large graphs. Although researchers have proposed approximation methods, they are either less efficient or suboptimal or both. We propose the first graph neural network (GNN) based model to approximate betweenness and closeness centrality. In GNN, each node aggregates features of the nodes in multihop neighborhood. We use this feature aggregation scheme to model paths and learn how many nodes are reachable to a specific node. We demonstrate that our approach significantly outperforms current techniques while taking less amount of time through extensive experiments on a series of synthetic and real-world datasets. A benefit of our approach is that the model is inductive, which means it can be trained on one set of graphs and evaluated on another set of graphs with varying structures. Thus, the model is useful for both static graphs and dynamic graphs. Source code is available at https://github.com/sunilkmaurya/GNN_Ranking

On analyzing graphs with motif-paths

Path-based solutions have been shown to be useful for various graph analysis tasks, such as link prediction and graph clustering. However, they are no longer adequate for handling complex and gigantic graphs. Recently, motif-based analysis has attracted a lot of attention. A motif, or a small graph with a few nodes, is often considered as a fundamental unit of a graph. Motif-based analysis captures high-order structure between nodes, and performs better than traditional "edge-based" solutions. In this paper, we study motif-path , which is conceptually a concatenation of one or more motif instances. We examine how motif-paths can be used in three path-based mining tasks, namely link prediction, local graph clustering and node ranking. We further address the situation when two graph nodes are not connected through a motif-path, and develop a novel defragmentation method to enhance it. Experimental results on real graph datasets demonstrate the use of motif-paths and defragmentation techniques improves graph analysis effectiveness.

MANET Performance Optimization Using Network-Based Criteria and Unmanned Aerial Vehicles

In this contribution we consider the problem of optimal drone positioning for improving the operation of a mobile ad hoc network. We build upon our previous results devoted to the application of game-theoretic methods for computing optimal strategies. One specific problem that arises in this context is that the optimal solution cannot be uniquely determined. In this case, one has to use some other criteria to choose the best (in some sense) of all optimal solutions. It is argued that centrality measures as well as node ranking can provide a good criterion for the selection of a unique solution. We showed that for two specific networks most criteria yielded the same solution, thus demonstrating good coherence in their predictions.