• Journal of the Korea Society of Computer and Information
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• v.24 no.7
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• pp.61-69
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• 2019

In this paper, a classification method of random graph models is proposed and it is based on centralities of the random graphs. Similarity between two random graphs is measured for the classification of random graph models. The similarity between two random graph models $G^{R_1}$ and $G^{R_2}$ is defined by the distance of $G^{R_1}$ and $G^{R_2}$, where $G^{R_2}$ is a set of random graph $G^{R_2}=\{G_1^{R_2},...,G_p^{R_2}\}$ that have the same number of nodes and edges as random graph $G^{R_1}$. The distance($G^{R_1},G^{R_2}$) is obtained by comparing centralities of $G^{R_1}$ and $G^{R_2}$. Through the computational experiments, we show that it is possible to compare random graph models regardless of the number of vertices or edges of the random graphs. Also, it is possible to identify and classify the properties of the random graph models by measuring and comparing similarities between random graph models.

• Communications of the Korean Mathematical Society
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• v.11 no.4
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• pp.1137-1145
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• 1996

A Steinhaus graph is a labelled graph whose adjacency matrix $A = (a_{i,j})$ has the Steinhaus property : $a_{i,j} + a{i,j+1} \equiv a_{i+1,j+1} (mod 2)$. We consider random Steinhaus graphs with n labelled vertices in which edges are chosen independently and with probability $\frac{1}{2}$. We prove that almost all Steinhaus graphs are Hamiltonian like as in random graph theory.

• Journal of the Korean Institute of Telematics and Electronics C
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• v.34C no.8
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• pp.79-87
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• 1997

For the representation of a complex object, the object is decomposed into several parts, and it is described by these decomposed parts and their relations. In genral, the parts can be the primitive elements that can not be decomposed further, or can be decomposed into their subparts. Therefore, the hierarchical description method is very natural and it si represented by a hierarchical attributed graph whose vertieces represent either primitive elements or graphs. This graphs also have verties which contain primitive elements or graphs. When some uncertainty exists in the hierarchical description of a complex object either due to noise or minor deformation, a probabilistic description of the object ensemble is necessary. For this purpose, in this paper, we formally define the hierarchical attributed random graph which is extention of the hierarchical random graph, and erive the equations for the entropy calculation of the hierarchical attributed random graph, and derive the equations for the entropy calculation of the hierarchical attributed random graph. Finally, we propose the application areas to use these concepts.

• Journal of the Korea Society of Computer and Information
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• v.22 no.3
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• pp.61-67
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• 2017

This paper analyzes the robustness of the network based on the centrality of vertices in the graph. In this paper, a random graph is generated and a modified graph is constructed by adding or removing vertices or edges in the generated random graph. And then we analyze the robustness of the graph by observing changes in the centrality of the random graph and the modified graph. In the process modifying a graph, we changes some parts of the graph, which has high values of centralities, not in the whole. We study how these additional changes affect the robustness of the graph when changes occurring a group that has higher centralities than in the whole.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.18 no.1
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• pp.147-169
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• 2024

In pace with the development of network technology at lightning speed, social networks have been extensively applied in our lives. However, as social networks retain a large number of users' sensitive information, the openness of this information makes social networks vulnerable to attacks by malicious attackers. To preserve the link privacy of individuals in social networks, an uncertain graph method based on node random response is devised, which satisfies differential privacy while maintaining expected data utility. In this method, to achieve privacy preserving, the random response is applied on nodes to achieve edge modification on an original graph and node differential privacy is introduced to inject uncertainty on the edges. Simultaneously, to keep data utility, a divide and conquer strategy is adopted to decompose the original graph into many sub-graphs and each sub-graph is dealt with separately. In particular, only some larger sub-graphs selected by the exponent mechanism are modified, which further reduces the perturbation to the original graph. The presented method is proven to satisfy differential privacy. The performances of experiments demonstrate that this uncertain graph method can effectively provide a strict privacy guarantee and maintain data utility.

• Korean Journal of Mathematics
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• v.11 no.1
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• pp.65-70
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• 2003

We show that every quasi-random graph $G(n)$ with $n$ vertices and minimum degree $(1+o(1))n/2$ has diameter either 2 or 3 and that every quasi-random graph $G(n)$ with n vertices has a clique number of $o(n)$ with wide spread.

• Communications of the Korean Mathematical Society
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• v.14 no.2
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• pp.295-299
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• 1999

Every quasi-random graph G(n) on n vertices consists of a giant component plus o(n) vertices, and every quasi-random graph G(n) with minimum degree (1+o(1))\ulcorner is connected.

• Bulletin of the Korean Mathematical Society
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• v.56 no.5
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• pp.1199-1210
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• 2019

In this paper, we consider a class of inhomogeneous random intersection graphs by assigning random weight to each vertex and two vertices are adjacent if they choose some common elements. In the inhomogeneous random intersection graph model, vertices with larger weights are more likely to acquire many elements. We show the Poisson convergence of the number of induced copies of a fixed subgraph as the number of vertices n and the number of elements m, scaling as $m={\lfloor}{\beta}n^{\alpha}{\rfloor}$ (${\alpha},{\beta}>0$), tend to infinity.

• Communications for Statistical Applications and Methods
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• v.26 no.3
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• pp.261-272
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• 2019

In this paper, we propose a procedure to build a prediction interval of the sum of dependent binary random variables over a graph to account for the dependence among binary variables. Our main interest is to find a prediction interval of the weighted sum of dependent binary random variables indexed by a graph. This problem is motivated by the prediction problem of various elections including Korean National Assembly and US presidential election. Traditional and popular approaches to construct the prediction interval of the seats won by major parties are normal approximation by the CLT and Monte Carlo method by generating many independent Bernoulli random variables assuming that those binary random variables are independent and the success probabilities are known constants. However, in practice, the survey results (also the exit polls) on the election are random and hardly independent to each other. They are more often spatially correlated random variables. To take this into account, we suggest a spatial auto-regressive (AR) model for the surveyed success probabilities, and propose a residual based bootstrap procedure to construct the prediction interval of the sum of the binary outcomes. Finally, we apply the procedure to building the prediction intervals of the number of legislative seats won by each party from the exit poll data in the $19^{th}$ and $20^{th}$ Korea National Assembly elections.

• Korean Journal of Mathematics
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• v.10 no.1
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• pp.29-35
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• 2002

It is well known that a random graph $G_{1/2}(n)$ is Hamiltonian almost surely. In this paper, we show that every quasirandom graph $G(n)$ with minimum degree $(1+o(1))n/2$ is also Hamiltonian.