A typical feature of huge, random network topologies is that they are too large to allow a fully detailed description. Such enormous, complex network topologies are encountered in numerous settings and have generated many research investigations. Well-known examples are the Internet and its logical overlay networks, such as the World Wide Web as well as online social networks. At the same time, extensive and rapidly growing wireless ad hoc and sensor networks also lead to hard topology modeling questions. In the current paper, we primarily focus on large, random wireless networks but also consider Web and Internet models. We survey a number of existing models that aim at describing the network topology. We also exhibit common generalizations of various sets of models that cover a number of known constructions as special cases. We demonstrate that higher levels of abstraction, despite their very general nature, can still be meaningfully analyzed and offers quite useful and unique help in solving certain hard networking problems. We believe that this research area can and will generate further significant contributions to the analysis of very large networks. 1. Introduction Many of the communication networks that we use today, or expect to use in the future, have enormous size. This applies not only to the physical networks, including the Internet as well as emerging ubiquitous wireless networks and large scale sensor networks, but also, or even more, to logical overlay networks, such as the World Wide Web. For example, the number of web pages, according already to a 2006 article [1], was as high as 53.7 billion, already at the time of writing that study. Out of the 53.7 billion, 34.7 billion web pages were indexed by Google. Since then, these numbers grew even further. Beyond the sheer size, the usage of these networks is also expected to be extremely heterogeneous, encompassing a huge number of different applications, traffic patterns, diverse requirements, and areas, including business, science, learning, entertainment, and social networking. At the same time, their physical basis is also heterogeneous, including wired, wireless, and optical subnetworks. All this is expected to eventually merge into a ubiquitous, global sociotechnical infrastructure. To understand and reason about huge socio-technical networks, including methods for designing/optimizing them, the traditional network analysis and modeling approaches are generally insufficient, due to their limited scalability. Simulation is usually feasible only up to a rather limited network size.
References
[1]
Y. Hirate, S. Kato, and H. Yamana, “Web structure in 2005,” in Proceedings of the Algorithms and Models for the Web Graph (WAW '06), pp. 36–46, Banff, Canada, December 2006.
[2]
S. Basagni, A. Faragó, M. A. Nanni, and D. T. Tran, “Increased connectivity at lower cost: the case for multi-radio nodes in multi-hop wireless networks,” in Proceedings of IEEE Global Telecommunications Conference (GLOBECOM '09), Honolulu, Hawai, USA, December 2009.
[3]
S. Basagni, F. Nidito, and A. Faragó, “The multi-radio advantage,” in Proceedings of IEEE Radio and Wireless Symposium (RWS '09), pp. 478–481, San Diego, Calif, USA, January 2008.
[4]
A. Faragó, “Analysis and modeling of very large network topologies,” Infocommunications Journal, vol. 4, pp. 1–10, 2012.
[5]
A. Faragó, “On the structure of classes of random graphs,” Chicago Journal of Theoretical Computer Science, 2010.
[6]
A. Faragó, “Scalability of node degrees in random wireless network topologies,” IEEE Journal on Selected Areas in Communications, vol. 27, pp. 1238–1244, 2009.
[7]
A. Faragó, “Quantifying the trade-off between the level of connectivity and local complexity in random wireless network topologies,” in Proceedings of the 6th International Conference on the Quantitative Evaluation of Systems (QEST '09), pp. 237–246, Budapest, Hungary, September 2009.
[8]
A. Faragó, “On the fundamental limits of topology control in ad hoc networks,” Algorithmica, vol. 49, no. 4, pp. 337–356, 2007.
[9]
A. Faragó, “Analysis of fundamental limits for partial connectivity in wireless networks,” in Proceedings of IEEE Global Telecommunications Conference (GLOBECOM '09), Honolulu, Hawai, USA, December 2009.
[10]
A. Faragó, “Asymptotically optimal trade-off between local and global connectivity in wireless networks,” Performance Evaluation, vol. 68, no. 2, pp. 142–156, 2011.
[11]
A. Faragó, “Random graph models and the limits of scalability in Ad Hoc and sensor networks,” in Proceedings of the International Workshop on Theoretical and Algorithmic Aspects of Sensor and Ad-hoc Networks (WTASA '07), pp. 1–12, Miami, Fla, USA, June 2007.
[12]
A. Faragó and S. Basagni, “The effect of multi-radio nodes on network connectivity—a graph theoretic analysis,” in Proceedings of the IEEE International Workshop on Wireless Distributed Networks (WDN '08), Cannes, France, September 2008.
[13]
A. Faragó, “Algorithmic challenges in Ad Hoc networks,” in Mobile Ad Hoc Networking, S. Basagni, M. Conti, S. Giordano, and I. Stojmenovic, Eds., pp. 427–445, IEEE Press and Wiley-Interscience, 2004.
[14]
A. Faragó, “Efficient blocking probability computation of complex traffic flows for network dimensioning,” Computers and Operations Research, vol. 35, no. 12, pp. 3834–3847, 2008.
[15]
A. Faragó, “Algorithmic challenges in learning path metrics from observed choices,” Applied Artificial Intelligence, vol. 22, no. 7-8, pp. 749–760, 2008.
[16]
A. Faragó, “A general tractable density concept for graphs,” Mathematics in Computer Science, vol. 1, no. 4, pp. 689–699, 2008.
[17]
A. Faragó, “Random graph models and the limits of scalability in Ad Hoc and sensor networks,” in Sensor and ad Hoc Networks, Theoretical and Algorithmic Aspects, S. K. Makki, X. Y. Li, and N. Pissinou, Eds., pp. 19–42, Springer, 2008.
[18]
A. Faragó, “On the typical case complexity of graph optimization,” Discrete Applied Mathematics, vol. 153, no. 1–3, pp. 73–88, 2005.
[19]
A. Faragó and V. R. Syrotiuk, “MERIT: a scalable approach for protocol assessment,” Mobile Networks and Applications, vol. 8, no. 5, pp. 567–577, 2003.
[20]
A. Faragó and S. Basagni, “Connecting two worlds: physical models and graph models of wireless network topologies,” in Proceedings of the 13th IEEE International Workshop on Future Trends of Distributed Computing Systems (FTDCS '11), pp. 739–744, Banff, Canada, September 2011.
[21]
A. Faragó and D. T. Tran, “The multigraph advantage and its application in network analysis,” in Proceedings of the EURO 24th Conference on Operations Research, Session 6.2.52, (Telecommunications), Paper 1, Lisbon, Portugal, July 2010.
[22]
A. Faragó, “Structural properties of random graph models,” in Proceedings of the Computing: The Australasian Theory Symposium (CATS '09), Wellington, New Zealand, January 2009.
[23]
A. Faragó and S. Basagni, “The effect of multi-radio nodes on network connectivity—a graph theoretic analysis,” in Proceedings of the IEEE International Workshop on Wireless Distributed Networks (WDM '08), Cannes, France, September 2008.
[24]
A. Faragó, “Graph theoretic analysis of Ad Hoc network vulnerability,” in Proceedings of the Workshop on Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks (WiOpt '03), pp. 171–180, INRIA Sophia-Antipolis, France, March 2003.
[25]
N. Meghanathan and A. Faragó, “On the stability of paths, Steiner trees and connected dominating sets in mobile ad hoc networks,” Ad Hoc Networks, vol. 6, no. 5, pp. 744–769, 2008.
[26]
C. Wang, M. A. Park, J. Willson, Y. Cheng, A. Faragó, and W. Wu, “On approximate optimal dual power assignment for biconnectivity and edge-biconnectivity,” Theoretical Computer Science, vol. 396, no. 1–3, pp. 180–190, 2008.
[27]
R. Kumar, P. Raghavan, S. Rajagopalan, and A. Tomkins, “Trawling the web for emerging cyber communities,” in Proceedings of the 8th World Wide Web Conference, Toronto, Canada, 1999.
[28]
A. L. Barabási and R. Albert, “Emergence of scaling in random networks,” Science, vol. 286, no. 5439, pp. 509–512, 1999.
[29]
A. L. Barabási, R. Albert, and H. Jeong, “Scale-free characteristics of random networks: the topology of the world-wide web,” Physica A, vol. 281, no. 1, pp. 69–77, 2000.
[30]
A. Broder, R. Kumar, F. Maghoul, et al., “Graph structure in the web,” in Proceedings of the 9th World Wide Web Conference, Amsterdam, The Netherland, May 2000.
[31]
M. Faloutsos, P. Faloutsos, and C. Faloutsos, “On power-law relationships of the Internet topology,” in Proceedings of the Conference on Applications, Technologies, Architectures, and Protocols for Computer Communication (SIGCOMM '99), pp. 251–262, New York, NY, USA, 1999.
[32]
A. Bonato, A Course on the Web Graph, American Mathematical Society, 2008.
[33]
S. Bornholdt and H. G. Schuster, Handbook of Graphs and Networks, Wiley-VCH, 2003.
[34]
G. Caldarelli, Scale-Free Networks, Oxford University Press, 2007.
[35]
F. Chung and L. Lu, Complex Graphs and Networks, American Mathematical Society, 2006.
[36]
M. Newman, A. L. Barabási, and D. J. Watts, The Structure and Dynamics of Networks, Princeton University Press, 2006.
[37]
L. Li, D. Alderson, J. C. Doyle, and W. Willinger, “Towards a theory of scale-free graphs: definition, properties, and implications,” Internet Mathematics, vol. 2, pp. 431–523, 2005.
[38]
D. Alderson, L. Li, W. Willinger, and J. C. Doyle, “Understanding internet topology: principles, models, and validation,” IEEE/ACM Transactions on Networking, vol. 13, no. 6, pp. 1205–1218, 2005.
[39]
B. Bollobás, O. Riordan, J. Spencer, and G. Tusnády, “The degree sequence of a scale-free random graph process,” Random Structures and Algorithms, vol. 18, no. 3, pp. 279–290, 2001.
[40]
W. Aiello, F. Chung, and L. Lu, “Random evolution in massive graphs,” in Handbook on Massive Data Sets, J. Abello, P. M. Pardalos, and M. G. C. Resende, Eds., pp. 97–122, Kluwer Academic Publishers, 2002.
[41]
J. Kleinberg, R. Kumar, P. Raghavan, et al., “The web as a graph: measurements, models and methods,” in Proceedings of the International Conference on Combinatorics and Computing, 1999.
[42]
F. Chung and L. Lu, “Coupling off-line and on-line analysis of random power law graphs,” Internet Mathematics, vol. 1, pp. 409–461, 2004.
[43]
J. Leskovec, D. Chakrabarti, J. Kleinberg, and C. Faloutsos, “Realistic, mathematically tractable graph generation and evolution, using Kronecker multiplication,” in Proceedings of the Knowledge Discovery in Databases (PKDD '05), vol. 3721 of Lecture Notes in Computer Science, pp. 133–145, Springer, 2005.
[44]
F. Chierichetti, R. Kumar, S. Lattanzi, A. Panconesi, and P. Raghavan, “Models for the compressible web,” in Proceedings of the 50th Annual Symposium on Foundations of Computer Science (FOCS '09), pp. 331–340, October 2009.
[45]
J. Leskovec, J. Kleinberg, and C. Faloutsos, “Graphs over time: densification laws, shrinking diameters and possible explanations,” in Proceedings of the 11th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 177–187, Chicago, Ill, USA, August 2005.
[46]
A. D. Flaxman, A. M. Frieze, and J. Vera, “A geometric preferential attachment model of networks,” International Workshop on Algorithms and Models for the Web-Graph, vol. 3243, pp. 44–55, 2004.
[47]
W. Aiello, A. Bonato, C. Cooper, J. Janssen, and P. Pralat, “A spatial web graph model with local influence,” Internet Mathematics, vol. 5, pp. 175–196, 2009.
[48]
A. D. Flaxman, “Expansion and lack thereof in randomly perturbed graphs,” Microsoft Research Technical Report TR-2006-118, Web Algorithms Workshop, 2006.
[49]
F. Chung and L. Lu, “The average distance in a random graph with given expected degrees,” Internet Mathematics, vol. 1, pp. 91–114, 2003.
[50]
P. Gupta and P. R. Kumar, “The capacity of wireless networks,” IEEE Transactions on Information Theory, vol. 46, no. 2, pp. 388–404, 2000.
[51]
S. Toumpis and A. Goldsmith, “Ad hoc network capacity,” in Proceedings of the 34th Asilomar Conference on Signals, Systems and Computers, pp. 1265–1269, November 2000.
[52]
P. Gupta and P. Kumar, “Internets in the sky: the capacity of three dimensional wireless networks,” Communications in Information and Systems, vol. 1, pp. 39–49, 2001.
[53]
S. Yi, Y. Pei, and S. Kalyanamaran, “On the capacity improvement of Ad Hoc wireless networks using directional antennas,” in Proceedings of the ACM International Symposium on Mobile Ad Hoc Networking and Computing (MOBIHOC '03), pp. 108–116, Annapolis, Md, USA, June 2003.
[54]
C. Peraki and S. D. Servetto, “On the maximum satble throughput problem in random networks with directional antennas,” in Proceedings of the ACM International Symposium on Mobile Ad Hoc Networking and Computing (MOBIHOC '03), pp. 76–87, Annapolis, Md, USA, June 2003.
[55]
U. C. Kozat and L. Tassiulas, “Throughput capacity of random Ad Hoc networks with infrastructure support,” in Proceedings of the 9th Annual International Conference on Mobile Computing and Networking (MobiCom '03), pp. 55–65, San Diego, Calif, USA, September 2003.
[56]
B. Liu, Z. Liu, and D. Towsley, “On the capacity of hybrid wireless networks,” in Proceedings of the 22nd Annual Joint Conference on the IEEE Computer and Communications Societies (INFOCOM '03), pp. 1543–1552, San Francisco, Calif, USA, April 2003.
[57]
S. Toumpis, “Capacity bounds for three classes of wireless networks: asymetirc, cluster and hybrid,” in Proceedings of the ACM International Symposium on Mobile Ad Hoc Networking and Computing (MOBIHOC '04), pp. 133–144, Roppongi, Japan, May 2004.
[58]
M. Grossglauser and D. N. C. Tse, “Mobility increases the capacity of ad hoc wireless networks,” IEEE/ACM Transactions on Networking, vol. 10, no. 4, pp. 477–486, 2002.
[59]
A. El Gamal, J. Mammen, B. Prabhakar, and D. Shah, “Throughput-delay trade-off in wireless networks,” in Proceedings of IEEE Conference on Computer Communications (INFOCOM '04), pp. 464–475, Hong Kong, March 2004.
[60]
A. ？zgür, O. Lévêque, and D. Tse, “Hierarchical cooperation achieves optimal capacity scaling in Ad Hoc networks,” IEEE Transactions on Information Theory archive, vol. 53, no. 10, pp. 3549–3572, 2007.
[61]
P. Gupta and P. R. Kumar, “Critical power for asymptotic connectivity in wireless networks,” in Stochastic Analysis, Control, Optimization and Applications: A Volume in Honor of W.H. Fleming, W. M. McEneany, G. Yin, and Q. Zhang, Eds., pp. 547–566, Birkhauser, Boston, Mass, USA, 1998.
[62]
J. Li, C. Blake, D. S. J. De Couto, H. I. Lee, and R. Morris, “Capacity of Ad Hoc wireless networks,” in Proceedings of the ACM 7th Annual International Conference on Mobile Computing and Networking (MOBICOM '01), pp. 61–69, Rome, Italy, 2001.
[63]
O. Dousse, P. Thiran, and M. Franceschetti, “On the throughput scaling of wireless relay networks,” IEEE Transactions on Information Theory, vol. 52, no. 6, pp. 2756–2761, 2006.
[64]
M. Franceschetti and R. Meester, Random Networks for Communication, Cambridge University Press, 2007.
[65]
M. Penrose, Random Geometric Graphs, Oxford University Press, 2003.
[66]
B. Bollobás and O. Riordan, “Mathematical results on scale-free random graphs,” in Handbook of Graphs and Networks, S. Bornholdt and H. G. Schuster, Eds., pp. 1–34, Wiley-VCH, 2003.
[67]
B. N. Clark, C. J. Colbourn, and D. S. Johnson, “Unit disk graphs,” Discrete Mathematics, vol. 86, no. 1–3, pp. 165–177, 1990.
[68]
S. Schmid and R. Wattenhofer, “Modeling sensor networks,” in Algorithms and Protocols for Wireless Sensor Networks, A. Boukerche, Ed., John Wiley & Sons, 2008.
[69]
F. Kuhn, R. Wattenhofer, and A. Zollinger, “Ad hoc networks beyond unit disk graphs,” Wireless Networks, vol. 14, no. 5, pp. 715–729, 2008.
[70]
I. F. Akyildiz, W. Y. Lee, and K. R. Chowdhury, “Spectrum management in cognitive radio ad hoc networks,” IEEE Network, vol. 23, no. 4, pp. 6–12, 2009.
[71]
F. Kuhn, T. Moscibroda, and R. Wattenhofer, “On the locality of bounded growth,” in Proceedings of the 24th Annual ACM Symposium on Principles of Distributed Computing (PODC '05), pp. 60–68, New York, NY, USA, July 2005.
[72]
T. K. Philips, S. S. Panwar, and A. N. Tantawi, “Connectivity properties of a packet radio network model,” IEEE Transactions on Information Theory, vol. 35, no. 5, pp. 1044–1047, 1989.
[73]
P. J. Wan and C. W. Yi, “Asymptotic critical transmission radius and critical neighbor number for k-connectivity in wireless ad hoc networks,” in Proceedings of the 5th ACM International Symposium on Mobile Ad Hoc Networking and Computing (MoBiHoc '04), pp. 1–8, Roppongi, Japan, May 2004.
[74]
M. D. Penrose, “The longest edge of the random minimal spanning tree,” Annals of Applied Probability, vol. 7, no. 2, pp. 340–361, 1997.
[75]
M. D. Penrose, “A strong law for the longest edge of the minimal spanning tree,” Annals of Probability, vol. 27, no. 1, pp. 246–260, 1999.
[76]
F. Xue and P. R. Kumar, “The number of neighbors needed for connectivity of wireless networks,” Wireless Networks, vol. 10, no. 2, pp. 169–181, 2004.
[77]
M. D. Penrose, “On k-connectivity for a geometric random graph,” Random Structures and Algorithms, vol. 15, no. 2, pp. 145–164, 1999.
[78]
M. J. B. Appel and R. P. Russo, “The minimum vertex degree of a graph on uniform points in [0, 1]d,” Advances in Applied Probability, vol. 29, no. 3, pp. 582–594, 1997.
[79]
H. Dette and N. Henze, “The limit distribution of the largest nearest neighbour link in the Unit d-Cube,” Journal of Applied Probability, vol. 26, pp. 67–80, 1989.
[80]
B. Bollobás, Random Graphs, Cambridge University Press, 2001.
[81]
S. Janson, T. Luczak, and A. Rucinski, Random Graphs, John Wiley & Sons, 2000.
[82]
K. Pahlavan and P. Krishnamurthy, Principles of Wireless Networks, Prentice Hall, 2002.
[83]
J. E. Yukich, Probability Theory of Classical Euclidean Optimization Problems, vol. 1675 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 1998.
[84]
C. Avin, Y. Emek, E. Kantor, Z. Lotker, D. Peleg, and L. Roditty, “SINR diagrams: towards algorithmically usable SINR models of wireless networks,” in Proceedings of the 28th Symposium on Principles of Distributed Computing (PODC '09), pp. 200–209, Calgary, Alberta, Canada, August 2009.
[85]
C. Yan, Y. Xiang, and F. F. Dragan, “Compact and low delay routing labeling scheme for unit disk graphs,” in Proceedings of the Workshop on Algorithms and Data Structures (WADS '09), vol. 5664 of Lecture Notes in Computer Science, pp. 566–577, 2009.
[86]
I. F. Akyildiz, X. Wang, and W. Wang, “Wireless mesh networks: a survey,” Computer Networks, vol. 47, no. 4, pp. 445–487, 2005.
[87]
R. Bruno, M. Conti, and E. Gregori, “Mesh networks: commodity multihop ad hoc networks,” IEEE Communications Magazine, vol. 43, no. 3, pp. 123–131, 2005.
[88]
B. Awerbuch, D. Holmer, and H. Rubens, “High throughput route selection in multi-rate ad hoc wireless networks,” in Proceedings of the 1st Working Conference on Wireless On-demand Networks Systems (WONS '04), R. Battiti, M. Conti, and E. Lo Cigno, Eds., vol. 2998 of Lecture Notes in Computer Science, pp. 253–270, Madonna di Campiglio, TN, Italy, January 2004.
[89]
J. Tang, G. Xue, and W. Zhang, “Interference-aware topology control and QoS routing in multi-channel wireless mesh networks,” in Proceedings of 6th ACM International Symposium on Mobile Ad Hoc Networking and Computing (MOBIHOC '05), pp. 68–77, Urbana-Champaign, Ill, USA, May 2005.
[90]
R. Chandra, P. Bahl, and P. Bahl, “Multinet: connecting to multiple IEEE 802.11 networks using a single wireless card,” in Proceedings of IEEE Conference on Computer Communications (INFOCOM '04), pp. 882–893, Hong Kong, March 2004.
[91]
P. Kyasanur and N. H. Vaidya, “Capacity of multi-channel wireless networks: impact of number of channels and interfaces,” in Proceedings of the 11th Annual International Conference on Mobile Computing and Networking (MobiCom '05), pp. 43–57, Cologne, Germany, September 2005.
[92]
M. Kodialam and T. Nandagopal, “Characterizing achievable rates in multi-hop wireless mesh networks with orthogonal channels,” IEEE/ACM Transactions on Networking, vol. 13, no. 4, pp. 868–880, 2005.
[93]
M. Kodialam and T. Nandagopal, “Characterizing achievable rates in wireless multi-hop networks: the joint routing and scheduling problem,” in Proceedings of the 9th Annual International Conference on Mobile Computing and Networking (MobiCom '03), pp. 42–54, San Diego, Calif, USA, September 2003.
[94]
“Wireless community network,” http://en.wikipedia.org/wiki/Wireless_community_network.
[95]
R. Draves, J. Padhye, and B. Zill, “Routing in multi-radio, multi-hop wireless mesh networks,” in Proceedings of the 10th Annual International Conference on Mobile Computing and Networking (MobiCom '04), pp. 114–128, Philadelphia, Pa, USA, October 2004.
[96]
P. Bahl, A. Adya, J. Padhye, and A. Wolman, “Reconsidering wireless systems with multiple radios,” ACM SIGCOMM Computer Communications Review, vol. 34, no. 5, pp. 39–46, 2004.
[97]
A. Miu, H. Balakrishnan, and C. E. Koksal, “Improving loss resilience with multi-radio diversity in wireless networks,” in Proceedings of the 11th Annual International Conference on Mobile Computing and Networking (MobiCom '05), pp. 16–30, Cologne, Germany, September 2005.
[98]
J. Shin, H. Choi, P. G. Traynor, and T. F. La Porta, “Network formation schemes for dynamic multi-radio, multi-hop wireless celluar systems,” Tech. Rep. NAS-TR-0005-2005, The Pennsylvania State University, University Park, Pa, USA, 2005.
[99]
J. Shin, P. Kishen, and T. F. La Porta, “Dynamic multi-frequency, multi-hop wireless cellular networks,” in Proceedings of the IFIP Mediterranean Ad Hoc Networking Workshop, Lipari, Italy, June 2006.
[100]
M. Alicherry, R. Bhatia, and L. Li, “Joint channel assignment and routing for throughput optimization in multi-radio wireless mesh networks,” in Proceedings of the 11th Annual International Conference on Mobile Computing and Networking (MobiCom '05), pp. 58–72, Cologne, Germany, September 2005.
[101]
M. Shin, S. Lee, and Y. A. Kim, “Distributed channel assignment for multi-radio wireless networks,” in Proceedings of IEEE International Conference on Mobile Ad Hoc and Sensor Sysetems (MASS '06), pp. 417–426, October 2006.
[102]
K. N. Ramachandran, E. M. Belding, K. C. Almeroth, and M. M. Buddhikot, “Interference-aware channel assignment in multi-radio wireless mesh networks,” in Proceedings of the 25th IEEE International Conference on Computer Communications (INFOCOM '06), pp. 1–12, Barcelona, Spain, April 2006.
[103]
A. Adya, P. Bahl, J. Padhye, A. Wolman, and L. Zhou, “A multi-radio unification protocol for IEEE 802.11 wireless networks,” in Proceedings of the 1st International Conference on Broadband Networks (BroadNets '04), pp. 344–354, San Jose, Calif, USA, October 2004.
[104]
R. Hekmat and P. Van Mieghem, “Connectivity in wireless ad-hoc networks with a log-normal radio model,” Mobile Networks and Applications, vol. 11, no. 3, pp. 351–360, 2006.
[105]
R. Gowaikar, B. Hochwald, and B. Hassibi, “Communication over a wireless network with random connections,” IEEE Transactions on Information Theory, vol. 52, no. 7, pp. 2857–2871, 2006.
