![]() ![]() While numerous studies have investigated whether centrality measures convey redundant information, how centrality and hierarchy measures are related is still an open issue. Several measures based on various aspects of network topology have been proposed in order to quantify these concepts. Indeed, many complex systems exhibit a natural hierarchical structure, and centrality is a fundamental characteristic allowing to identify key constituents. Hierarchy and centrality are two popular notions used to characterize the importance of entities in complex systems. Results show that network density and transitivity play a key role in shaping the pattern of relations between centrality and hierarchy measures. #Second extinction network connection error series#A series of experiments is performed in order to evaluate the combinations of 6 centrality measures with 4 hierarchy measures across 28 diverse real-world networks with varying topological characteristics. In this paper, we investigate the interaction between centrality and hierarchy using several correlation and similarity evaluation measures. Such a phenomenon indicates that the k-core structure could be extremely vulnerable under adversarial attacks, and its robustness thus should be carefully addressed to ensure the security of many graph algorithms. More impressively, for certain real-world networks, only deleting one edge from the k-core may lead to the collapse of the innermost core, even if this core contains dozens of nodes. The experiments on a variety of real-world networks demonstrate that our methods behave much better than a series of baselines, in terms of much smaller Edge Change Rate (ECR) and False Attack Rate (FAR), achieving state-of-the-art attack performance. Then, we propose $Q$ index theoretically as the probability that the terminal node of an edge does not belong to the innermost core, which is further used to guide the design of our heuristic attack methods, namely COREATTACK and GreedåOREATTACK. Firstly, we give the general definition of targeted k-core attack, map it to the set cover problem which is NP-hard, and further introduce a series of evaluation metrics to measure the performance of attack methods. In this paper, we investigate the robustness of the k-core structure under adversarial attacks by deleting edges, for the first time. ![]() A malicious attacker with jamming ability can exploit the vulnerability of the k-core structure to attack the network and invalidate the network analysis methods, e.g., reducing the k-shell values of nodes can deceive graph algorithms, leading to the wrong decisions. The concept of k-core in complex networks plays a key role in many applications, e.g., understanding the global structure, or identifying central/critical nodes, of a network. For 1 million edge batches, on many graphs we run over $100\times$ faster than processing edge-by-edge while remaining under re-computing from scratch. We implement our algorithm and experimentally show that with it core queries can be returned on rapidly changing graphs quickly enough for interactive applications. We develop a novel dynamic batch algorithm to maintain it that improves efficiency over processing edge-by-edge. To address this, we bring an efficient index from community search into the core domain, the Shell Tree Index. This finds vertices that are dense, but not regions it misses connectivity. ![]() Prior batch core algorithms have only addressed half the problem of maintaining cores, the problem of maintaining a core decomposition. We focus on the important problem of maintaining cores on rapidly changing dynamic graphs, where batches of edge changes need to be processed quickly. Finding $k$-cores in graphs is a valuable and effective strategy for extracting dense regions of otherwise sparse graphs. ![]()
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