Terminal-set-enhanced community detection in social networks

Tong, Guangmo; Cui, Lei; Wu, Weili; Liu, Cong; Du, Ding‐Zhu

doi:10.1109/infocom.2016.7524473

Cited by 7 publications

(6 citation statements)

References 28 publications

(44 reference statements)

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“…(6) Each planar graph without intersecting 3-cycles has va(G) 2 in [15]. (7) Every planar graph without intersecting 5-cycles has va(G) 2 in [16]. We generalize the results in [10] and [12], and get the following results.…”

Section: Introductionmentioning

confidence: 70%

“…The configuration which is shown in Fig. 1(3) is going to be used in the following R v 1.3(4) to R v 1.3 (7). For the 5-vertex v in Fig.…”

Section: Proof Of Theoremmentioning

confidence: 99%

“…Let v be a 6-vertex of G. We have f 3 (v) ≤ 3 clearly. If f 3 (v) = 3, then there are some cases due to the vertex rules as follows: c (v) = 6−3× 7 5 −3×…”

Section: Proof Of Theoremmentioning

confidence: 99%

“…• • • , n 3 b (s)) by R v 1(4)-(5), R v 2(4)x, R v 2(5)x, R v 2(6)x, R v 2(7)x, R v 2(8)x, R v 3, and R v 4(3). Suppose the vertex like v 4 in Fig.1(1) is a 5+ -vertex.…”

mentioning

confidence: 99%

“…If n 6 + (s) > 1, then τ (s → sb i ) = 1, 2, • • • , n 3 b (s)) by R v 1(4)-(5), R v 3(5)-(8), and R v 4(3). Suppose no one 6-vertex satisfies R v 3(5)-(7). Then τ (s → sb i ) 1, 2, • • • , n 3 b (s)) by R v 1(4)-(5), R v 3(8), and R v 4(3).…”

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confidence: 99%

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Social Structure Decomposition With Security Issue

et al. 2019

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Social structure decomposition has been a valuable research topic in the study of social networks, and it still has many unresolved problems. At the same time, an increasing number of people pays attention to the security issue that is worth considering and researching. With security consideration, we study a new social structure decomposition problem that can be formulated as a minimization problem in graph theory as follows: given a social network with formulation as a graph G, partition the vertex set of G into the minimum number of subsets, such that each subset induces an acyclic graph called a forest. This minimum number is called the vertex arboricity, denoted by va(G). It is well known that the vertex arboricity va(G) ≤ 3 for each planar graph G in the graph theory. In this paper, we prove that for the planar graph G, if no 3-cycle intersects a 4-cycle or no 3-cycle intersects a 5-cycle, then va(G) ≤ 2.INDEX TERMS Cycles, intersecting, planar graph, vertex arboricity.

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Section: Introductionmentioning

confidence: 70%

“…The configuration which is shown in Fig. 1(3) is going to be used in the following R v 1.3(4) to R v 1.3 (7). For the 5-vertex v in Fig.…”

Section: Proof Of Theoremmentioning

confidence: 99%

“…Let v be a 6-vertex of G. We have f 3 (v) ≤ 3 clearly. If f 3 (v) = 3, then there are some cases due to the vertex rules as follows: c (v) = 6−3× 7 5 −3×…”

Section: Proof Of Theoremmentioning

confidence: 99%

“…• • • , n 3 b (s)) by R v 1(4)-(5), R v 2(4)x, R v 2(5)x, R v 2(6)x, R v 2(7)x, R v 2(8)x, R v 3, and R v 4(3). Suppose the vertex like v 4 in Fig.1(1) is a 5+ -vertex.…”

mentioning

confidence: 99%

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confidence: 99%

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