arXiv subjects

Shogo Mizutaka

Publications and source records attributed to Shogo Mizutaka.

13 recordsLinked to original sources

arXiv2024

Properties of the connected components in projections of random bipartite networks: Effects of clique size fluctuations

We examined the structure of projections of random bipartite networks characterized by the degree distribution of individual and group nodes through the generating function method. We decomposed a projection into two subgraphs, the giant component, and finite components and analyzed their degree correlation. The projections never exhibit a negative degree correlation. Positive degree correlations in the networks originating from the clique size fluctuation remain after the decomposition at the set of finite components although the values of their clustering coefficient are still finite. The giant component can exhibit either positive or negative degree correlations based on the structure of the projection. However, they are positively correlated in most cases. In addition, we determined the relation between the finite components in a supercritical phase possessing the giant component and the projection in a subcritical phase when the degree distributions for group and individual are Poisson.

physics.soc-ph↗

arXiv2022

Synergistic epidemic spreading in correlated networks

We investigate the effect of degree correlation on a susceptible-infected-susceptible (SIS) model with a nonlinear cooperative effect (synergy) in infectious transmissions. In a mean-field treatment of the synergistic SIS model on a bimodal network with tunable degree correlation, we identify a discontinuous transition that is independent of the degree correlation strength unless the synergy is absent or extremely weak. Regardless of synergy (absent or present), a positive and negative degree correlation in the model reduces and raises the epidemic threshold, respectively. For networks with a strongly positive degree correlation, the mean-field treatment predicts the emergence of two discontinuous jumps in the steady-state infected density. To test the mean-field treatment, we provide approximate master equations of the present model. We quantitatively confirm that the approximate master equations agree with not only all qualitative predictions of the mean-field treatment but also corresponding Monte-Carlo simulations.

physics.soc-ph↗

arXiv2021

Revisiting finite size effect of percolation in degree correlated networks

In this study, we investigate bond percolation in networks that have the Poisson degree distribution and a nearest-neighbor degree-degree correlation. Previous numerical studies on percolation critical behaviors of degree-correlated networks remain controversial. We perform finite-size scaling for the peak values of the second-largest cluster size and the mean cluster size and find a large finite-size effect when a network has a strong degree-degree correlation. Evaluating the size dependence of estimated critical exponents carefully, we demonstrate that the bond percolation in the networks exhibits the mean-field critical behavior, independent of the strength of their nearest-neighbor degree correlations.

physics.soc-ph↗

arXiv2020

Structure of percolating clusters in random clustered networks

We examine the structure of the percolating cluster (PC) formed by site percolation on a random clustered network (RCN) model. Using the generating functions, we formulate the clustering coefficient and assortative coefficient of the PC. We analytically and numerically show that the PC in the highly clustered networks is clustered even at the percolation threshold. The assortativity of the PC depends on the details of the RCN. The PC at the percolation threshold is disassortative when the numbers of edges and triangles of each node are assigned by Poisson distributions, but assortative when each node in an RCN has the same small number of edges, most of which form triangles. This result seemingly contradicts the disassortativity of fractal networks, although the renormalization scheme unveils the disassortative nature of a fractal PC.

physics.soc-ph↗

arXiv2020

Emergence of Long-Range Correlations in Random Networks

We perform an analytical analysis of the long-range degree correlation of the giant component in an uncorrelated random network by employing generating functions. By introducing a characteristic length, we find that a pair of nodes in the giant component is negatively degree-correlated within the characteristic length and uncorrelated otherwise. At the critical point, where the giant component becomes fractal, the characteristic length diverges and the negative long-range degree correlation emerges. We further propose a correlation function for degrees of the $l$-distant node pairs, which behaves as an exponentially decreasing function of distance in the off-critical region. The correlation function obeys a power-law with an exponential cutoff near the critical point. The Erdős-Rényi random graph is employed to confirm this critical behavior.

physics.soc-ph↗

arXiv2020

Percolation on a maximally disassortative network

We propose a maximally disassortative (MD) network model which realizes a maximally negative degree-degree correlation, and study its percolation transition to discuss the effect of a strong degree-degree correlation on the percolation critical behaviors. Using the generating function method for bipartite networks, we analytically derive the percolation threshold and the order parameter critical exponent, $β$. For the MD scale-free networks, whose degree distribution is $P(k) \sim k^{-γ}$, we show that the exponent, $β$, for the MD networks and corresponding uncorrelated networks are same for $γ>3$ but are different for $2<γ<3$. A strong degree-degree correlation significantly affects the percolation critical behavior in heavy-tailed scale-free networks. Our analytical results for the critical exponents are numerically confirmed by a finite-size scaling argument.

physics.soc-ph↗

arXiv2018

Disassortativity of percolating clusters in random networks

We provide arguments for the property of the degree-degree correlations of giant components formed by the percolation process on uncorrelated random networks. Using the generating functions, we derive a general expression for the assortativity of a giant component, $r$, which is defined as Pearson's correlation coefficient for degrees of directly connected nodes. For uncorrelated random networks in which the third moment for the degree distribution is finite, we prove the following two points. (1) Assortativity $r$ satisfies the relation $r\le 0$ for $p\ge p_{\rm c}$. (2) The average degree of nodes adjacent to degree-$k$ nodes at the percolation threshold is proportional to $k^{-1}$ independently of the degree distribution function. These results claim that disassortativity emerges in giant components near the percolation threshold. The accuracy of the analytical treatment is confirmed by extensive Monte Carlo simulations.

physics.soc-ph↗

arXiv2018

Simple model of fractal networks formed by self-organized critical dynamics

In this paper, a simple dynamical model in which fractal networks are formed by self-organized critical (SOC) dynamics is proposed; the proposed model consists of growth and collapse processes. It has been shown that SOC dynamics are realized by the combined processes in the model. Thus, the distributions of the cluster size and collapse size follow a power-law function in the stationary state. Moreover, through SOC dynamics, the networks become fractal in nature. The criticality of SOC dynamics is the same as the universality class of mean-field theory. The model explains the possibility that the fractal nature in complex networks emerges by SOC dynamics in a manner similar to the case with fractal objects embedded in a Euclidean space.

physics.soc-ph↗

arXiv2017

Fractality and degree correlations in scale-free networks

Fractal scale-free networks are empirically known to exhibit disassortative degree mixing. It is, however, not obvious whether a negative degree correlation between nearest neighbor nodes makes a scale-free network fractal. Here we examine the possibility that disassortativity in complex networks is the origin of fractality. To this end, maximally disassortative (MD) networks are prepared by rewiring edges while keeping the degree sequence of an initial uncorrelated scale-free network that is guaranteed to become fractal by rewiring edges. Our results show that most of MD networks with different topologies are not fractal, which demonstrates that disassortativity does not cause the fractal property of networks. In addition, we suggest that fractality of scale-free networks requires a long-range repulsive correlation in similar degrees.

physics.soc-ph↗

arXiv2017

Structural instability of large-scale functional networks

We study how large functional networks can grow stably under possible cascading overload failures and evaluated the maximum stable network size above which even a small-scale failure would cause a fatal breakdown of the network. Employing a model of cascading failures induced by temporally fluctuating loads, the maximum stable size $n_{\text{max}}$ has been calculated as a function of the load reduction parameter $r$ that characterizes how quickly the total load is reduced during the cascade. If we reduce the total load sufficiently fast ($r\ge r_{\text{c}}$), the network can grow infinitely. Otherwise, $n_{\text{max}}$ is finite and increases with $r$. For a fixed $r\,(<r_{\text{c}})$, $n_{\text{max}}$ for a scale-free network is larger than that for an exponential network with the same average degree. We also discuss how one detects and avoids the crisis of a fatal breakdown of the network from the relation between the sizes of the initial network and the largest component after an ordinarily occurring cascading failure.

physics.soc-ph↗

arXiv2016

Robustness analysis of bimodal networks in the whole range of degree correlation

We present exact analysis of the physical properties of bimodal networks specified by the two peak degree distribution fully incorporating the degree-degree correlation between node connection. The structure of the correlated bimodal network is uniquely determined by the Pearson coefficient of the degree correlation, keeping its degree distribution fixed. The percolation threshold and the giant component fraction of the correlated bimodal network are analytically calculated in the whole range of the Pearson coefficient from $-1$ to $1$ against two major types of node removal, which are the random failure and the degree-based targeted attack. The Pearson coefficient for next-nearest-neighbor pairs is also calculated, which always takes a positive value even when the correlation between nearest-neighbor pairs is negative. From the results, it is confirmed that the percolation threshold is a monotonically decreasing function of the Pearson coefficient for the degrees of nearest-neighbor pairs increasing from $-1$ and $1$ regardless of the types of node removal. In contrast, the node fraction of the giant component for bimodal networks with positive degree correlation rapidly decreases in the early stage of random failure, while that for bimodal networks with negative degree correlation remains relatively large until the removed node fraction reaches the threshold. In this sense, bimodal networks with negative degree correlation are more robust against random failure than those with positive degree correlation.

physics.soc-ph↗

arXiv2015

Fractal and Small-World Networks Formed by Self-Organized Critical Dynamics

We propose a dynamical model in which a network structure evolves in a self-organized critical (SOC) manner and explain a possible origin of the emergence of fractal and small-world networks. Our model combines a network growth and its decay by failures of nodes. The decay mechanism reflects the instability of large functional networks against cascading overload failures. It is demonstrated that the dynamical system surely exhibits SOC characteristics, such as power-law forms of the avalanche size distribution, the cluster size distribution, and the distribution of the time interval between intermittent avalanches. During the network evolution, fractal networks are spontaneously generated when networks experience critical cascades of failures that lead to a percolation transition. In contrast, networks far from criticality have small-world structures. We also observe the crossover behavior from fractal to small-world structure in the network evolution.

physics.soc-ph↗

arXiv2015

Robustness of scale-free networks to cascading failures induced by fluctuating loads

Taking into account the fact that overload failures in real-world functional networks are usually caused by extreme values of temporally fluctuating loads that exceed the allowable range, we study the robustness of scale-free networks against cascading overload failures induced by fluctuating loads. In our model, loads are described by random walkers moving on a network and a node fails when the number of walkers on the node is beyond the node capacity. Our results obtained by using the generating function method shows that scale-free networks are more robust against cascading overload failures than Erdős-Rényi random graphs with homogeneous degree distributions. This conclusion is contrary to that predicted by previous works which neglect the effect of fluctuations of loads.

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