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## 1Capacity Scaling of Wireless Social Networks

### Citations

3183 | The capacity of wireless networks
- Gupta, Kumar
- 2000
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Citation Context ... of the throughput capacity in the limit when the size of network gets large, have been extensively studied in depth from both theoretical and practical perspectives, [6]– [12], since Gupta and Kumar =-=[13]-=- took the lead to study the unicast capacity for homogeneous wireless random and arbitrary networks. In wireless social networks, source-destination associations depend on their social relationships t... |

1252 | The small world problem - Milgram - 1992 |

1064 | Foundations of Statistical Natural Language Processing.
- Manning, Schütze
- 1999
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Citation Context ...the following procedure: 1. Zipf’s Degree Distribution of Social Relations: Assume that the number of friends (or followers) of a particular node vk ∈ V , denoted by qk, follows a Zipf’s distribution =-=[26]-=-, i.e., Pr(qk = l) = (∑n−1 j=1 j−γ )−1 · l−γ . (1) From Eq.(1), we can observe that the degree distribution above depends on the specific network size (the number of users n). Please see a numerical v... |

934 | What is twitter, a social network or a news media
- Kwak, Lee, et al.
- 2010
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Citation Context ...nts a specific interdependency, such as co-authorship, citationship, or friendship, and so on. Based on massive datasets of large-scale real-world online social networks, such as Myspace [1], Twitter =-=[2]-=-, Flickr [3], LiveJournal [4], and Facebook [5], extensive studies validate respectively that these two most representative features of complex networks, i.e., the small-world phenomenon and scale-fre... |

679 | Measurement and analysis of online social networks
- MISLOVE, AL
- 2007
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Citation Context ...y, such as co-authorship, citationship, or friendship, and so on. Based on massive datasets of large-scale real-world online social networks, such as Myspace [1], Twitter [2], Flickr [3], LiveJournal =-=[4]-=-, and Facebook [5], extensive studies validate respectively that these two most representative features of complex networks, i.e., the small-world phenomenon and scale-free degree distribution, nearly... |

283 |
Navigation in a Small World
- Kleinberg
- 2000
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Citation Context ...el acts as the precondition for the session formation model. Some theoretical models have been advanced to model the social relationship formation depending on geography in social networks. Kleinberg =-=[17]-=- initiated a distance-based social model relating geographical distance and social friendship, in which the probability of befriending a particular user is inversely proportional to the positive power... |

262 | Hierarchical cooperation achieves optimal capacity scaling in ad hoc networks,”
- Ozgur, Leveque, et al.
- 2007
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Citation Context ...eneral Scaling Models In the research of network capacity scaling laws, there are two typical models in terms of scaling patterns of network: dense scaling model and extended scaling model [6], [30], =-=[33]-=-. They have different engineering implications related to the classical notions of interference-limitedness and coverage-limitedness [33]: The former is only interference-limited; while, the latter is... |

253 | Analysis of topological characteristics of huge online social networking services
- AHN, AL
- 2007
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Citation Context ...tices represents a specific interdependency, such as co-authorship, citationship, or friendship, and so on. Based on massive datasets of large-scale real-world online social networks, such as Myspace =-=[1]-=-, Twitter [2], Flickr [3], LiveJournal [4], and Facebook [5], extensive studies validate respectively that these two most representative features of complex networks, i.e., the small-world phenomenon ... |

234 | Closing the gap in the capacity of wireless networks via percolation theory,”
- Franceschetti, Dousse, et al.
- 2007
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Citation Context ...eless networks, i.e., the scaling of the throughput capacity in the limit when the size of network gets large, have been extensively studied in depth from both theoretical and practical perspectives, =-=[6]-=-– [12], since Gupta and Kumar [13] took the lead to study the unicast capacity for homogeneous wireless random and arbitrary networks. In wireless social networks, source-destination associations depe... |

224 | Geograph routing in social networks - Liben-Nowell, Novak, et al. - 2005 |

164 | An experimental study of search in global social networks
- Dodds, Muhamad, et al.
- 2003
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Citation Context ...ould be necessarily relevant to the geography. On the other hand, some classical experiments showed or implied that social relationships among users strongly depend on their geographic location, [14]–=-=[16]-=-. Thus, under the assumption that a 2Physical Layer Social Layer Session Layer Between Physically Connected Pairs From Sources to Friends From Sources to Destinations Fig. 1. Layered System Model. ses... |

101 | Growth of the flickr social network
- MISLOVE, AL
- 2008
(Show Context)
Citation Context ...ic interdependency, such as co-authorship, citationship, or friendship, and so on. Based on massive datasets of large-scale real-world online social networks, such as Myspace [1], Twitter [2], Flickr =-=[3]-=-, LiveJournal [4], and Facebook [5], extensive studies validate respectively that these two most representative features of complex networks, i.e., the small-world phenomenon and scale-free degree dis... |

94 | Growth rates of Euclidean minimal spanning trees with power weighted edges,” The Annals of Probability - Steele - 1988 |

68 | Multicast capacity for large scale wireless ad hoc networks
- Li, Tang, et al.
- 2007
(Show Context)
Citation Context ...e advantages of this model. Challenge II: Bounding Sum of Distances for All Sessions. The sum of transport distances for all sessions is the prerequisite for bounding the capacity scaling laws, [13], =-=[22]-=-. The long-tailed property of both the destination number (Zipf’s Distribution) and destination distribution (Power Law Distribution) causes the transport distances of resulted sessions to be signific... |

47 | Capacity of large scale wireless networks under gaussian channel model
- Li, Liu, et al.
- 2008
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Citation Context ...points/positions, which leads that the distances of sessions are dependent and then causes analysis difficulty in bounding the sum of transport distances of sessions with multiple destinations, [13], =-=[21]-=-. Then, for addressing the capacity scaling laws of wireless networks, it should be the first step to introduce a new distance&density-aware social formation model that is suitable for capacity analys... |

45 | The reverse small world experiment - Killworth, Bernard |

44 |
A strong law for the longest edge of the minimal spanning tree
- Penrose
- 1999
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Citation Context ....(7), which completes the proof. Note that we deliberately relax the upper bound of L as in Eq.(7) in order to ensure Eq.(6) to hold with uniformly high probability for Θ(n) Euclidean spanning trees, =-=[29]-=-. 4 SOCIAL-BROADCAST CAPACITY FOR HOMOGENEOUS PHYSICAL LAYER In this work, we specifically reduce the complexity from three dimensions (δ, γ, β) ∈ [0,∞)3 to two dimensions (γ, β) ∈ [0,∞)2 by letting δ... |

43 | Optimal delay–throughput tradeoffs in mobile ad hoc networks - Ying, Yang, et al. - 2008 |

43 |
Distance matters: Physical space and social impact
- Latane, Liu, et al.
- 1995
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Citation Context ... a larger socialbroadcast capacity. Importantly, we notice that we only take account of the case that δ = 0, where the population-based model degenerates to that similar to distance-based model [17], =-=[31]-=-. The advantages 7of population-based model cannot be sufficiently highlighted for such a special model, indeed. This work can act as the first step of investigating the capacity under the general pop... |

39 |
On the evolution of user interaction
- Viswanath, Mislove, et al.
(Show Context)
Citation Context ...orship, citationship, or friendship, and so on. Based on massive datasets of large-scale real-world online social networks, such as Myspace [1], Twitter [2], Flickr [3], LiveJournal [4], and Facebook =-=[5]-=-, extensive studies validate respectively that these two most representative features of complex networks, i.e., the small-world phenomenon and scale-free degree distribution, nearly hold in online so... |

39 | Manycast: exploring the space between anycast and multicast in ad hoc networks
- Carter, Yi, et al.
- 2003
(Show Context)
Citation Context ...eets in Twitter and posts in Facebook. Accordingly, we can define other session patterns based on the definitions of corresponding non-social sessions, such as social-anycast [27] and social-manycast =-=[28]-=-. In this work, we mainly study social-broadcast sessions. 2.4 Communication Model We mainly adopt the generalized physical model [6], [21] due to its generality and practicality compared to other mod... |

36 | Shot noise Cox processes
- Møller
(Show Context)
Citation Context ... be fully embodied by this simple model. To model the clustering behavior of node distribution with ω(1) centers in real-life applications of wireless networks, the shotnoise Cox process (SNCP, [23], =-=[32]-=-) can be introduced, where M center points generate their respective point processes, and the conditional local intensity at X is determined by the superposition of the individual processes, i.e., d(X... |

30 | Probability with Martingales; Cambridge University Press - Williams - 1991 |

23 | Capacity and delay of hybrid wireless broadband access networks - Li, Zhang, et al. - 2009 |

22 | Evolution of social-attribute networks: measurements, modeling, and implications using google - Gong, Xu, et al. |

21 | Capacity scaling of wireless networks with inhomogeneous node density: Lower bounds
- Alfano, Garetto, et al.
- 2010
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Citation Context ...t ourselves to the kernel κ(O, ·) that is invariant under both translation and rotation, i.e., κ(O,X) = κ(|X − O|) depends only on the Euclidean distance |X − O| of point X from the cluster center O, =-=[23]-=-, [24]. Moreover, we assume that κ(O, ·) is a summable, non-increasing, bounded and continuous function, and ∫ O κ(O,X)dX = 1. Following a common normalizing method, the kernel can be specified by fir... |

15 |
Multicast performance with hierarchical cooperation
- Wang, Fu, et al.
- 2012
(Show Context)
Citation Context ...-dimensional Torus O. To simplify the description, we assume that the number of nodes is exactly n, and denote the set of nodes by V = {vk}nk=1, without changing our results in order sense, [6], [7], =-=[11]-=-. To emulate the clustering behavior of users distribution in wireless networks, we construct the center-clustering random model (CCRM) by the following procedure: First, making a center of O as the c... |

14 |
Capacity and delay analysis for social-proximity urban vehicular networks
- Lu, Luan, et al.
- 2012
(Show Context)
Citation Context ... networks, i.e., the scaling of the throughput capacity in the limit when the size of network gets large, have been extensively studied in depth from both theoretical and practical perspectives, [6]– =-=[12]-=-, since Gupta and Kumar [13] took the lead to study the unicast capacity for homogeneous wireless random and arbitrary networks. In wireless social networks, source-destination associations depend on ... |

8 | Density-based anycast: a robust routing strategy for wireless ad hoc networks
- Lenders, May, et al.
(Show Context)
Citation Context ...l its friends, such as tweets in Twitter and posts in Facebook. Accordingly, we can define other session patterns based on the definitions of corresponding non-social sessions, such as social-anycast =-=[27]-=- and social-manycast [28]. In this work, we mainly study social-broadcast sessions. 2.4 Communication Model We mainly adopt the generalized physical model [6], [21] due to its generality and practical... |

7 | Scaling Laws on Multicast Capacity for Power-Constrained Wireless Networks under Gaussian Channel Model
- Wang, Li, et al.
- 2012
(Show Context)
Citation Context ...lly, we define g(s) := min { 1, s−δ } , where δ ∈ [0,∞) is the clustering exponent of node distribution. Note that when δ = 0, the model degenerates into the homogeneous random extended network, [6], =-=[25]-=-. We introduce an approximate real-world case of CCRM based on Google+ dataset. Please see details in Appendix D.2. 2.1.2 Extending Generality of Physical Layer Model In this paper, we only study the ... |

5 | General capacity scaling of wireless networks
- Wang, Jiang, et al.
- 2011
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Citation Context ...) ∈ [0,∞)3 to two dimensions (γ, β) ∈ [0,∞)2 by letting δ = 0. In this case of extremely weak clustering behavior, the physical layer degenerates into the homogeneous random network model, [6], [13], =-=[30]-=-, where d(Y ) ≡ Θ(1). 4.1 Main Results 4.1.1 Capacity under Generalized Physical Model Theorem 3: Under the population-based social model P(δ = 0, γ, β) and the generalized physical model (GphyM) with... |

5 | Reciprocity in social networks: Measurements, predictions, and implications,” arXiv preprint arXiv:1302.6309 - Gong, Xu, et al. - 2013 |

4 | Heterogeneity Increases Multicast Capacity - Peng, Wang, et al. |

3 | Joint link prediction and attribute inference using a social-attribute network - Gong, Talwalkar, et al. |

1 | Capacity of composite networks: Combining social and wireless ad hoc networks
- Azimdoost, Sadjadpour, et al.
- 2011
(Show Context)
Citation Context ...-based social model relating geographical distance and social friendship, in which the probability of befriending a particular user is inversely proportional to the positive power of the distance. In =-=[18]-=- and [19], the distance-based social model had been adopted in studying the unicast capacity of wireless social networks. Intuitively, such a session pattern leads to a mismatch with the characteristi... |

1 | Capacity of scale free wireless networks
- Azimdoost, Sadjadpour
- 2012
(Show Context)
Citation Context ...cial model relating geographical distance and social friendship, in which the probability of befriending a particular user is inversely proportional to the positive power of the distance. In [18] and =-=[19]-=-, the distance-based social model had been adopted in studying the unicast capacity of wireless social networks. Intuitively, such a session pattern leads to a mismatch with the characteristics of dat... |