사회 관계망에서의 불평등도 측정: 네트워크에 기반한 지니 지수 일반화

학위논문 (석사)-- 서울대학교 대학원 : 경제학부 경제학전공, 2015. 8. 김진우.We construct a novel inequality index that incorporates a social network structure, and name it the network-based Gini index, as it generalizes the Gini index. We also provide a basic axiomatization of our index, following the approach of Sen(1954): Any social welfare function satisfying Weighting Equity, Independent Monotonicity, Zero Weight on Top, and Ordinal Information must rank income distributions of a given mean link income in precisely the same way as the negative of the network-based Gini indexes of the respective distributions. We also show that the network-based Gini index satises Transfer Monotonicity, Scale Invariance, and Comparability. Finally, we construct the weighted network-based Gini index on weighted networks, and verify that the index has a similar axiomatization result and satises almost the same properties with the network-based Gini index.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 Network-based Gini index . . . . . . . . . . . . . . . . . . . . . 4 3 Axiomatization of the network-based Gini index . . . . . . . 7 4 Other properties . . . . . . . . . . . . . . . . . . . . . . . . . . 11 5 Weighted network-based Gini index . . . . . . . . . . . . . . . 16 6 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . 20Maste

Embeddings among Recursive Circulants and Hypercubes

본 논문은 임베딩의 관점에서 재귀원형군과 하이퍼큐브의 관계를 다룬다. 하이퍼큐브는 널리 알려져 있는 연결망 구조이고 재귀원형군은 [14]에서 최근에 제안되었으며 두 연결망 구조 모두 흥미로운 연결망 특성을 가지고 있다. 재귀원형군의 하이퍼큐브에 대한 expansion이 1인 임베딩과 그 역방향 임베딩을 제시하고 각 임베딩의 비용을 분석한다. 본 논문에서 다루고 있는 재귀원형군과 하이퍼큐브의 관계는 다른 연결망 구조의 이들에 대한 임베딩을 연구할 때 유용하다.

Circulant 그래프 및 그의 통신망에 대한 응용

학위논문(박사) - 한국과학기술원 : 전산학과, 1992.2, [ ix, 104 p. ]In this thesis, network metrics of circulant graphs are investigated, and a new topology of communication networks is proposed. We consider diameters of circulant graphs with degree four of less and diameters of circulant graphs which are isomorphic to the product of two nontrivial circulant graphs. We present a necessary and sufficient condition for a strongly connected circulant digraph with two jumps to have a directed hamiltonian cycle. The problems of constructing circulant minimal broadcast digraphs and regular minimal broadcast digraphs with as small degree as possible are considered. We propose a construction of circulant graphs with the property that every circulant graph can be obtained by applying the constructions repeatedly to trivial graphs, and give a generalization of the construction by relaxing some constraints posed on the construction. Many graphs including hypercubes with the maximum connectivity and edge connectivity can be obtained by applying the generalized constructions repeatedly to trivial graphs. The connectivity and edge connectivity of graphs obtained by applying the generalized construction to d connected graphs are considered. We also consider the connectivity and edge connectivity of digraphs obtained by applying the digraph-form generalized construction to d strongly connected digraphs. A new topology of communication networks is proposed. The network G (N, d), d≥2, is a circulant graph with N nodes and jumps $d^i$, $0 \le i \le [log_{d}N]-1$. The network is vertex transitive (not edge transitive), and has a hamiltonian cycle. The connectivity and edge connectivity, diameter, mean intemode distance, and node visit ratio and edge visit ratio (under the uniform message distribution) of G($cd^m$, d), 1≤c <d, are analyzed, and a shortest path routing algorithm in G($cd^m$, d) is developed. Compared with a hypercube $\mathcal{Q}_m$, G($2^m$, 4) achieves noticeable improvements in diameter, mean internode distance, and node vi...한국과학기술원 : 전산학과