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Yukio Hayashi

Publications and source records attributed to Yukio Hayashi.

At least 19 recordsLinked to original sources
arXiv2026

Limited Improvement of Connectivity in Scale-Free Networks by Increasing the Power-Law Exponent

It has been well-known that many real networks are scale-free (SF) but extremely vulnerable against attacks. We investigate the robustness of connectivity and the lengths of the shortest loops in randomized SF networks with realistic exponents $2.0 < γ\leq 4.0$. We show that smaller variance of degree distributions leads to stronger robustness and longer average length of the shortest loops, which means the existing of large holes. These results will provide important insights toward enhancing the robustness by changing degree distributions.

cs.SI↗
arXiv2025

Larger holes as narrower degree distributions in complex networks

Although the analysis of loops is not so much because of the complications, it has already been found that heuristically enhancing loops decreases the variance of degree distributions for improving the robustness of connectivity. While many real scale-free networks are known to contain shorter loops such as triangles, it remains to investigate the distributions of longer loops in more wide class of networks. We find a relation between narrower degree distributions and longer loops in investigating the lengths of the shortest loops in various networks with continuously changing degree distributions, including three typical types of realistic scale-free networks, classical Erdös-Rényi random graphs, and regular networks. In particular, we show that narrower degree distributions contain longer shortest loops, as a universal property in a wide class of random networks. We suggest that the robustness of connectivity is enhanced by constructing long loops of O(log N).

physics.soc-ph↗
arXiv2025

Universal vulnerability in strong modular networks with various degree distributions between inequality and equality

Generally, networks are classified into two sides of inequality and equality with respect to the number of links at nodes by the types of degree distributions. One side includes many social, technological, and biological networks which consist of a few nodes with many links, and many nodes with a few links, whereas the other side consists of all nodes with an equal number of links. In comprehensive investigations between them, we have found that, as a more equal network, the tolerance of whole connectivity is stronger without fragmentation against the malfunction of nodes in a wide class of randomized networks. However, we newly find that all networks which include typical well-known network structures between them become extremely vulnerable, if a strong modular (or community) structure is added with commonalities of areas, interests, religions, purpose, and so on. These results will encourage avoiding too dense unions by connecting nodes and taking into account the balanced resource allocation between intra- and inter-links of weak communities. We must reconsider not only efficiency but also tolerance against attacks or disasters, unless no community that is really impossible.

physics.soc-ph↗
arXiv2025

Vulnerable Connectivity Caused by Local Communities in Spatial Networks

Local communities by concentration of nodes connected with short links are widely observed in spatial networks. However, how such structure affects robustness of connectivity against malicious attacks remains unclear. This study investigates the impact of local communities on the robustness by modeling planar infrastructure reveals that the robustness is weakened by strong local communities in spatial networks. These results highlight the potential of long-distance links in mitigating the negative effects of local community on the robustness.

cs.SI↗
arXiv2024

Fast convergence to an approximate solution by message-passing for complex optimizations

Message-passing (MP) is a powerful tool for finding an approximate solution in optimization. We generalize it to nonlinear product-sum form, and numerically show the fast convergence for the minimum feedback vertex set and the minimum vertex cover known as NP-hard problems. From the linearity of MP in a logarithmic space, it is derived that an equilibrium solution exists in a neighborhood of random initial values. These results will give one of the reason why the convergence is very fast in collective computation based on a common mathematical background.

physics.soc-ph↗
arXiv2023

Optimal Network Robustness Against Attacks in Varying Degree Distributions

In varying degree distributions, we investigate the optimally robust networks against targeted attacks to nodes with higher degrees. In considering that a network tends to have more robustness with a smaller variance of degree distributions, we clarify the optimal robustness at random regular graphs in their comprehensive discrete or random perturbations. By comparing robustness measurements on them, we find that random regular graphs have the optimal robustness against attacks in varying degree distributions.

physics.soc-ph↗
arXiv2022

More Tolerant Reconstructed Networks by Self-Healing against Attacks in Saving Resource

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.

physics.soc-ph↗
arXiv2022

Emergence of Robust and Efficient Networks in a Family of Attachment Models

Self-organization of robust and efficient networks is important for a future design of communication or transportation systems, because both characteristics are not coexisting in many real networks. As one of the candidates for the coexisting, the optimal robustness of onion-like structure with positive degree-degree correlations has recently been found, and it can be generated by incrementally growing methods based on a pair of random and intermediation attachments with the minimum degree selection. In this paper, we introduce a continuous interpolation by a parameter $β\geq 0$ between random and the minimum degree attachments to investigate the reason why the minimum degree selection is important. However, we find that the special case of the minimum degree attachment can generate highly robust networks but with low efficiency as a chain structure. Furthermore, we consider two intermediation models modified with the inverse preferential attachment for investigating the effect of distance on the emergence of robust onion-like structure. The inverse preferential attachments in a class of mixed attachment and two intermediation models are effective for the emergence of robust onion-like structure, however, when $β$ is large enough, a small amount of random attachment is necessary for the network efficiency. Such attachment models indicate a prospective direction to the future growth of our network infrastructures.

physics.soc-ph↗
arXiv2020

A loop enhancement strategy for network robustness

Many real systems are extremely vulnerable against attacks, since they are scale-free networks as commonly existing topological structure in them. Thus, in order to improve the robustness of connectivity, several edge rewiring methods have been so far proposed by enhancing degree-degree correlations. In fact, onion-like structures with positive degree-degree correlations are optimally robust against attacks. On the other hand, recent studies suggest that the robustness and loops are strongly related to each other. Therefore, we focus on enhancing loops as a new approach for improving the robustness. In this work, we propose edge rewiring methods and evaluate the effect on the robustness by applying to real networks. Our proposed methods are two types of rewirings in preserving degrees or not for investigating the effect of the degree modification on the robustness. Numerical results show that our proposed methods improve the robustness to the level as same or more than the state-of-the-art methods. Furthermore, our work shows that the following two points are more important for further improving the robustness. First, the robustness is strongly related to loops more than degree-degree correlations. Second, it significantly improves the robustness by reducing the gap between the maximum and minimum degrees.

physics.soc-ph↗
arXiv2020

Effective Self-Healing Networks against Attacks or Disasters in Resource Allocation Control

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.

physics.soc-ph↗
arXiv2019

Emergence of an Onion-like Network in Surface Growth and Its Strong Robustness

We numerically investigate that optimal robust onion-like networks can emerge even with the constraint of surface growth in supposing a spatially embedded transportation or communication system. To be onion-like, moderately long links are necessary in the attachment through intermediations inspired from a social organization theory.

physics.soc-ph↗
arXiv2017

A new design principle of robust onion-like networks self-organized in growth

Today's economy, production activity, and our life are sustained by social and technological network infrastructures, while new threats of network attacks by destructing loops have been found recently in network science. We inversely take into account the weakness, and propose a new design principle for incrementally growing robust networks. The networks are self-organized by enhancing interwoven long loops. In particular, we consider the range-limited approximation of linking by intermediations in a few hops, and show the strong robustness in the growth without degrading efficiency of paths. Moreover, we demonstrate that the tolerance of connectivity is reformable even from extremely vulnerable real networks according to our proposed growing process with some investment. These results may indicate a prospective direction to the future growth of our network infrastructures.

physics.soc-ph↗
arXiv2016

Spatially self-organized resilient networks by a distributed cooperative mechanism

The robustness of connectivity and the efficiency of paths are incompatible in many real networks. We propose a self-organization mechanism for incrementally generating onion-like networks with positive degree-degree correlations whose robustness is nearly optimal. As a spatial extension of the generation model based on cooperative copying and adding shortcut, we show that the growing networks become more robust and efficient through enhancing the onion-like topological structure on a space. The reasonable constraint for locating nodes on the perimeter in typical surface growth as a self-propagation does not affect these properties of the tolerance and the path length. Moreover, the robustness can be recovered in the random growth damaged by insistent sequential attacks even without any remedial measures.

physics.soc-ph↗
arXiv2015

Asymptotic behavior of the node degrees in the ensemble average of adjacency matrix

Various important and useful quantities or measures that characterize the topological network structure are usually investigated for a network, then they are averaged over the samples. In this paper, we propose an explicit representation by the beforehand averaged adjacency matrix over samples of growing networks as a new general framework for investigating the characteristic quantities. It is applied to some network models, and shows a good approximation of degree distribution asymptotically. In particular, our approach will be applicable through the numerical calculations instead of intractable theoretical analysises, when the time-course of degree is a monotone increasing function like power-law or logarithm.

physics.soc-ph↗
arXiv2015

Recoverable DTN Routing based on a Relay of Cyclic Message-Ferries on a MSQ Network

An interrelation between a topological design of network and efficient algorithm on it is important for its applications to communication or transportation systems. In this paper, we propose a design principle for a reliable routing in a store-carry-forward manner based on autonomously moving message-ferries on a special structure of fractal-like network, which consists of a self-similar tiling of equilateral triangles. As a collective adaptive mechanism, the routing is realized by a relay of cyclic message-ferries corresponded to a concatenation of the triangle cycles and using some good properties of the network structure. It is recoverable for local accidents in the hierarchical network structure. Moreover, the design principle is theoretically supported with a calculation method for the optimal service rates of message-ferries derived from a tandem queue model for stochastic processes on a chain of edges in the network. These results obtained from a combination of complex network science and computer science will be useful for developing a resilient network system.

cs.DC↗
arXiv2015

Growing Self-organized Design of Efficient and Robust Complex Networks

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.

physics.soc-ph↗
arXiv2013

Combinatorial and approximative analyses in a spatially random division process

For a spatial characteristic, there exist commonly fat-tail frequency distributions of fragment-size and -mass of glass, areas enclosed by city roads, and pore size/volume in random packings. In order to give a new analytical approach for the distributions, we consider a simple model which constructs a fractal-like hierarchical network based on random divisions of rectangles. The stochastic process makes a Markov chain and corresponds to directional random walks with splitting into four particles. We derive a combinatorial analytical form and its continuous approximation for the distribution of rectangle areas, and numerically show a good fitting with the actual distribution in the averaging behavior of the divisions.

cond-mat.stat-mech↗