Takehisa Hasegawa

Cascade dynamics on clustered network

We investigate information cascades on a clustered network model generated from a projection of bipartite graphs by numerical simulations and compare it with that on a non-clustered network having the same degree distribution. Our result indicates that global cascades occur more easily on clustered networks than on non-clustered ones. Furthermore, we extend a recursive method by Gleeson and Cahalane to estimate the order parameter analytically and find that the result gives an excellent approximation to the observed transition point.

Monte Carlo simulation study of the two-stage percolation transition in enhanced binary trees

We perform Monte Carlo simulations to study the Bernoulli (p) bond percolation on the enhanced binary tree which belongs to the class of nonamenable graphs with one end. Our numerical results show that the system has two distinct percolation thresholds pc1 and pc2. The mean cluster size diverges as p approaches pc1 from below. The system is critical at all the points in the intermediate phase (pc1 < p < pc2) and there exist infinitely many infinite clusters. In this phase, the corresponding fractal exponent continuously increases with p from zero to unity. Above pc2 the system has a unique infinite cluster.

Suppressing epidemics on networks by exploiting observer nodes.

To control infection spreading on networks, we investigate the effect of observer nodes that recognize infection in a neighboring node and make the rest of the neighbor nodes immune. We numerically show that random placement of observer nodes works better on networks with clustering than on locally treelike networks, implying that our model is promising for realistic social networks. The efficiency of several heuristic schemes for observer placement is also examined for synthetic and empirical networks. In parallel with numerical simulations of epidemic dynamics, we also show that the effect of observer placement can be assessed by the size of the largest connected component of networks remaining after removing observer nodes and links between their neighboring nodes.

Observability transitions in correlated networks.

Yang, Wang, and Motter [Phys. Rev. Lett. 109, 258701 (2012)] analyzed a model for network observability transitions in which a sensor placed on a node makes the node and the adjacent nodes observable. The size of the connected components comprising the observable nodes is a major concern of the model. We analyze this model in random heterogeneous networks with degree correlation. With numerical simulations and analytical arguments based on generating functions, we find that negative degree correlation makes networks more observable. This result holds true both when the sensors are placed on nodes one by one in a random order and when hubs preferentially receive the sensors. Finally, we numerically optimize networks with a fixed degree sequence with respect to the size of the largest observable component. Optimized networks have negative degree correlation induced by the resulting hub-repulsive structure; the largest hubs are rarely connected to each other, in contrast to the rich-club phenomenon of networks.

Profile and scaling of the fractal exponent of percolations in complex networks

We propose a novel finite-size scaling analysis for percolation transition observed in complex networks. While it is known that cooperative systems in growing networks often undergo an infinite-order transition with inverted Berezinskii-Kosterlitz-Thouless singularity, it is very hard for numerical simulations to determine the transition point precisely. Since the neighbor of the ordered phase is not a simple disordered phase but a critical phase, conventional finite-size scaling technique does not work. In our finite-size scaling, the forms of the scaling functions for the order parameter and the fractal exponent determine the transition point and critical exponents numerically for an infinite-order transition as well as a standard second-order transition. We confirm the validity of our scaling hypothesis through Monte Carlo simulations for bond percolations in some network models: the decorated (2,2)-flower and the random attachment growing network, where an infinite-order transition occurs, and the configuration model, where a second-order transition occurs.

Generalized scaling theory for critical phenomena including essential singularities and infinite dimensionality.

We propose a generic scaling theory for critical phenomena that includes power-law and essential singularities in finite and infinite dimensional systems. In addition, we clarify its validity by analyzing the Potts model in a simple hierarchical network, where a saddle-node bifurcation of the renormalization-group fixed point governs the essential singularity.

Generating-function approach for bond percolation in hierarchical networks.

We study bond percolations on hierarchical scale-free networks with the open bond probability of the shortcuts p and that of the ordinary bonds p. The system has a critical phase in which the percolating probability P takes an intermediate value 0 < P < 1. Using generating function approach, we calculate the fractal exponent ψ of the root clusters to show that ψ varies continuously with p in the critical phase. We confirm numerically that the distribution n(s) of cluster size s in the critical phase obeys a power law n(s) ∝ s(-τ), where τ satisfies the scaling relation τ=1+ψ(-1). In addition the critical exponent β(p) of the order parameter varies as p, from β ≃ 0.164694 at p=0 to infinity at p=p(c)=5/32.

Robustness of networks against propagating attacks under vaccination strategies

We study the effect of vaccination on the robustness of networks against propagating attacks that obey the susceptible?infected?removed model. By extending the generating function formalism developed by Newman (2005?Phys.?Rev.?Lett.?95?108701), we analytically determine the robustness of networks that depends on the vaccination parameters. We consider the random defense where nodes are vaccinated randomly and the degree-based defense where hubs are preferentially vaccinated. We show that, when vaccines are inefficient, the random graph is more robust against propagating attacks than the scale-free network. When vaccines are relatively efficient, the scale-free network with the degree-based defense is more robust than the random graph with the random defense and the scale-free network with the random defense.

Critical phase of bond percolation on growing networks

The critical phase of bond percolation on the random growing tree is examined. It is shown that the root cluster grows with the system size N as N ψ and the mean number of clusters with size s per node follows a power function n s ∝ s(-τ) in the whole range of open bond probability p . The exponent τ and the fractal exponent ψ are also derived as a function of p and the degree exponent γ and are found to satisfy the scaling relation τ=1+ψ(-1). Numerical results with several network sizes are quite well fitted by a finite-size scaling for a wide range of p and γ, which gives a clear evidence for the existence of a critical phase.

Outbreaks in susceptible-infected-removed epidemics with multiple seeds.

We study a susceptible-infected-removed (SIR) model with multiple seeds on a regular random graph. Many researchers have studied the epidemic threshold of epidemic models above which a global outbreak can occur, starting from an infinitesimal fraction of seeds. However, there have been few studies of epidemic models with finite fractions of seeds. The aim of this paper is to clarify what happens in phase transitions in such cases. The SIR model in networks exhibits two percolation transitions. We derive the percolation transition points for the SIR model with multiple seeds to show that as the infection rate increases epidemic clusters generated from each seed percolate before a single seed can induce a global outbreak.