arXiv subjects

K. -I. Goh

Publications and source records attributed to K. -I. Goh.

59 records · Page 4Linked to original sources

arXiv2002

Betweenness centrality correlation in social networks

Scale-free (SF) networks exhibiting a power-law degree distribution can be grouped into the assortative, dissortative and neutral networks according to the behavior of the degree-degree correlation coefficient. Here we investigate the betweenness centrality (BC) correlation for each type of SF networks. While the BC-BC correlation coefficients behave similarly to the degree-degree correlation coefficients for the dissortative and neutral networks, the BC correlation is nontrivial for the assortative ones found mainly in social networks. The mean BC of neighbors of a vertex with BC $g_i$ is almost independent of $g_i$, implying that each person is surrounded by almost the same influential environments of people no matter how influential the person is.

cond-mat.stat-mech↗

arXiv2002

Fluctuation-driven dynamics of the Internet topology

We study the dynamics of the Internet topology based on the empirical data on the level of the autonomous systems. It is found that the fluctuations occurring in the stochastic process of connecting and disconnecting edges are important features of the Internet dynamics. The network's overall growth can be described approximately by a single characteristic degree growth rate $g_{\rm eff} \approx 0.016$ and the fluctuation strength $σ_{\rm eff} \approx 0.14$, together with the vertex growth rate $α\approx 0.029$. A stochastic model which incorporate these values and an adaptation rule newly introduced reproduces several features of the real Internet topology such as the correlations between the degrees of different vertices.

cond-mat.stat-mech↗

arXiv2001

Universal Behavior of Load Distribution in Scale-free Networks

We study a problem of data packet transport in scale-free networks whose degree distribution follows a power-law with the exponent $γ$. We define load at each vertex as the accumulated total number of data packets passing through that vertex when every pair of vertices send and receive a data packet along the shortest path connecting the pair. It is found that the load distribution follows a power-law with the exponent $δ\approx 2.2(1)$, insensitive to different values of $γ$ in the range, $2 < γ\le 3$, and different mean degrees, which is valid for both undirected and directed cases. Thus, we conjecture that the load exponent is a universal quantity to characterize scale-free networks.

cond-mat.stat-mech↗

arXiv2001

Spectra and eigenvectors of scale-free networks

We study the spectra and eigenvectors of the adjacency matrices of scale-free networks when bi-directional interaction is allowed, so that the adjacency matrix is real and symmetric. The spectral density shows an exponential decay around the center, followed by power-law long tails at both spectrum edges. The largest eigenvalue λ_1 depends on system size N as λ_1 \sim N^{1/4} for large N, and the corresponding eigenfunction is strongly localized at the hub, the vertex with largest degree. The component of the normalized eigenfunction at the hub is of order unity. We also find that the mass gap scales as N^{-0.68}.

cond-mat.stat-mech↗

arXiv2000

Depinning of an anisotropic interface in random media: The tilt effect

We study the tilt dependence of the pinning-depinning transition for an interface described by the anisotropic quenched Kardar-Parisi-Zhang equation in 2+1 dimensions, where the two signs of the nonlinear terms are different from each other. When the substrate is tilted by m along the positive sign direction, the critical force F_c(m) depends on m as F_c(m)-F_c(0) \sim -|m|^{1.9(1)}. The interface velocity v near the critical force follows the scaling form v \sim |f|^θΨ_{\pm}(m^2 /|f|^{θ+ϕ}) with θ= 0.9(1) and ϕ= 0.2(1), where f \equiv F-F_c(0) and F is the driving force.

cond-mat.stat-mech↗