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We introduce the concept of self-healing in the field of complex networks. Obvious applications range from infrastructural to technological networks. By exploiting the presence of redundant links in recovering the connectivity of the system, we introduce self-healing capabilities through the application of distributed communication protocols granting the smartness of the system. We analyze the interplay between redundancies and smart reconfiguration protocols in improving the resilience of networked infrastructures to multiple failures; in particular, we measure the fraction of nodes still served for increasing levels of network damages. We study the effects of different connectivity patterns (planar square-grids, small-world, scale-free networks) on the healing performances. The study of small-world topologies shows us that the introduction of some long-range connections in the planar grids greatly enhances the resilience to multiple failures giving results comparable to the most resilient (but less realistic) scale-free structures.
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With increasing threats by large attacks or disasters, the time has come to reconstruct network infrastructures such as communication or transportation systems rather than to recover them as before in case of accidents, because many real networks are extremely vulnerable. Thus, we consider self-healing mechanisms by rewirings (reuse or addition of links) to be sustainable and resilient networks even against malicious attacks. In distributed local process for healing, the key strategies are the extension of candidates of linked nodes and enhancing loops by applying a message-passing algorithm inspired from statistical physics. Simulation results show that our proposed combination of ring formation and enhancing loops is particularly effective in comparison with the conventional methods, when more than half damaged links alive or are compensated from reserved ones.
Complex network infrastructure systems for power-supply, communication, and transportation support our economical and social activities, however they are extremely vulnerable against the frequently increasing large disasters or attacks. Thus, a reconstructing from damaged network is rather advisable than empirically performed recovering to the original vulnerable one. In order to reconstruct a sustainable network, we focus on enhancing loops so as not to be trees as possible by node removals. Although this optimization is corresponded to an intractable combinatorial problem, we propose self-healing methods based on enhancing loops in applying an approximate calculation inspired from a statistical physics approach. We show that both higher robustness and efficiency are obtained in our proposed methods with saving the resource of links and ports than ones in the conventional healing methods. Moreover, the reconstructed network by healing can become more tolerant than the original one before attacks, when some extent of damaged links are reusable or compensated as investment of resource. These results will be open up the potential of network reconstruction by self-healing with adaptive capacity in the meaning of resilience.
A self-organization of efficient and robust networks is important for a future design of communication or transportation systems, however both characteristics are incompatible in many real networks. Recently, it has been found that the robustness of onion-like structure with positive degree-degree correlations is optimal against intentional attacks. We show that, by biologically inspired copying, an onion-like network emerges in the incremental growth with functions of proxy access and reinforced connectivity on a space. The proposed network consists of the backbone of tree-like structure by copyings and the periphery by adding shortcut links between low degree nodes to enhance the connectivity. It has the fine properties of the statistically self-averaging unlike the conventional duplication-divergence model, exponential-like degree distribution without overloaded hubs, strong robustness against both malicious attacks and random failures, and the efficiency with short paths counted by the number of hops as mediators and by the Euclidean distances. The adaptivity to heal over and to recover the performance of networking is also discussed for a change of environment in such disasters or battlefields on a geographical map. These properties will be useful for a resilient and scalable infrastructure of network systems even in emergent situations or poor environments.
Core-periphery structure and community structure are two typical meso-scale structures in complex networks. Though the community detection has been extensively investigated from different perspectives, the definition and the detection of core-periphery structure have not received much attention. Furthermore, the detection problems of the core-periphery and community structure were separately investigated. In this paper, we develop a unified framework to simultaneously detect core-periphery structure and community structure in complex networks. Moreover, there are several extra advantages of our algorithm: our method can detect not only single but also multiple pairs of core-periphery structures; the overlapping nodes belonging to different communities can be identified; different scales of core-periphery structures can be detected by adjusting the size of core. The good performance of the method has been validated on synthetic and real complex networks. So we provide a basic framework to detect the two typical meso-scale structures: core-periphery structure and community structure.
The organisation of a network in a maximal set of nodes having at least $k$ neighbours within the set, known as $k$-core decomposition, has been used for studying various phenomena. It has been shown that nodes in the innermost $k$-shells play a crucial role in contagion processes, emergence of consensus, and resilience of the system. It is known that the $k$-core decomposition of many empirical networks cannot be explained by the degree of each node alone, or equivalently, random graph models that preserve the degree of each node (i.e., configuration model). Here we study the $k$-core decomposition of some empirical networks as well as that of some randomised counterparts, and examine the extent to which the $k$-shell structure of the networks can be accounted for by the community structure. We find that preserving the community structure in the randomisation process is crucial for generating networks whose $k$-core decomposition is close to the empirical one. We also highlight the existence, in some networks, of a concentration of the nodes in the innermost $k$-shells into a small number of communities.
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