Skip to main content

Connectivity of Dynamic Graphs

Encyclopedia of Systems and Control

Abstract

Dynamic networks have recently emerged as an efficient way to model various forms of interaction within teams of mobile agents, such as sensing and communication. This article focuses on the use of graphs as models of wireless communications. In this context, graphs have been used widely in the study of robotic and sensor networks and have provided an invaluable modeling framework to address a number of coordinated tasks ranging from exploration, surveillance, and reconnaissance to cooperative construction and manipulation. In fact, the success of these stories has almost always relied on efficient information exchange and coordination between the members of the team, as seen, e.g., in the case of distributed state agreement where multi-hop communication has been proven necessary for convergence and performance guarantees.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Bibliography

  • Ajorlou A, Aghdam AG (2010) A class of bounded distributed controllers for connectivity preservation of unicycles. In: Proceedings of the 49th IEEE conference on decision and control, Atlanta, pp 3072–3077

    Google Scholar 

  • Ajorlou A, Momeni A, Aghdam AG (2010) A class of bounded distributed control strategies for connectivity preservation in multi-agent systems. IEEE Trans Autom Control 55(12):2828–2833

    Article  MathSciNet  Google Scholar 

  • Anderson SO, Simmons R, Goldberg D (2003) Maintaining line-of-sight communications networks between planetray rovers. In: Proceedings of the 2003 IEEE/RSJ international conference on intelligent robots and systems, Las Vegas, pp 2266–2272

    Google Scholar 

  • Ando H, Oasa Y, Suzuki I, Yamashita M (1999) Distributed memoryless point convergence algorithm for mobile robots with limited visibility. IEEE Trans Robot Autom 15(5):818–828

    Article  Google Scholar 

  • Arkin RC, Diaz J (2002) Line-of-sight constrained exploration for reactive multiagent robotic teams. In: Proceedings of the 7th international workshop on advanced motion control, Maribor, pp 455–461

    Google Scholar 

  • Bullo F, Cortes J, Martinez S (2009) Distributed control of robotic networks. Applied Mathematics Series. Princeton University Press, Princeton

    MATH  Google Scholar 

  • Cornejo A, Lynch N (2008) Connectivity service for mobile ad-hoc networks. In: Proceedings of the 2nd IEEE international conference on self-adaptive and self-organizing systems workshops, pp 292–297

    Google Scholar 

  • Cortes J, Martinez S, Bullo F (2006) Robust rendezvous for mobile autonomous agents via proximity graphs in arbitrary dimensions. IEEE Trans Autom Control 51(8):1289–1298

    Article  MathSciNet  Google Scholar 

  • DeCouto D, Aguayo D, Bicket J, Morris R (2006) A high-throughput path metric for multihop wireless routing. In: Proceedings of the international ACM conference on mobile computing and networking, San Diego, pp 134–146

    Google Scholar 

  • DeGennaro MC, Jadbabaie A (2006) Decentralized control of connectivity for multi-agent systems. In: Proceedings of the 45th IEEE conference on decision and control, San Diego, pp 3628–3633

    Google Scholar 

  • Dimarogonas DV, Johansson KH (2008) Decentralized connectivity maintenance in mobile networks with bounded inputs. In Proceedings of the IEEE international conference on robotics and automation, Pasadena, pp 1507–1512

    Google Scholar 

  • Dimarogonas DV, Kyriakopoulos KJ (2008) Connectedness preserving distributed swarm aggregation for multiple kinematic robots. IEEE Trans Robot 24(5):1213–1223

    Article  Google Scholar 

  • Fax A, Murray RM (2004) Information flow and cooperative control of vehicle formations. IEEE Trans Autom Control 49:1465–1476

    Article  MathSciNet  Google Scholar 

  • Fiedler M (1973) Algebraic connectivity of graphs. Czechoslovak Math J 23(98):298–305

    MathSciNet  Google Scholar 

  • Flocchini P, Prencipe G, Santoro N, Widmayer P (2005) Gathering of asynchronous oblivious robots with limited visibility. Theor Comput Sci 337(1–3):147–168

    Article  MATH  MathSciNet  Google Scholar 

  • Franceschelli M, Gasparri A, Giua A, Seatzu C (2013) Decentralized estimation of laplacian eigenvalues in multi-agent systems. Automatica 49(4):1031–1036

    Article  MathSciNet  Google Scholar 

  • Ganguli A, Cortes J, Bullo F (2009) Multirobot rendezvous with visibility sensors in nonconvex environments. IEEE Trans Robot 25(2):340–352

    Article  Google Scholar 

  • Ghaffarkhah A, Mostofi Y (2011) Communication-aware motion planning in mobile networks. IEEE Trans Autom Control Spec Issue Wirel Sens Actuator Netw 56(10):2478–248

    Article  MathSciNet  Google Scholar 

  • Godsil C, Royle G (2001) Algebraic graph theory, Graduate Texts in Mathematics, vol 207. Springer, Berlin

    Book  Google Scholar 

  • Gustavi T, Dimarogonas DV, Egerstedt M, Hu X (2010) Sufficient conditions for connectivity maintenance and rendezvous in leader-follower networks. Automatica 46(1):133–139

    Article  MATH  MathSciNet  Google Scholar 

  • Hollinger G, Singh S (2010) Multi-robot coordination with periodic connectivity. In: Proceedings of the IEEE international conference on robotics and automation, Anchorage, Alaska, pp 4457–4462

    Google Scholar 

  • Hsieh MA, Cowley A, Kumar V, Taylor C (2008) Maintaining network connectivity and performance in robot teams. J Field Robot 25(1–2):111–131

    Article  Google Scholar 

  • Ji M, Egerstedt M (2007) Coordination control of multi-agent systems while preserving connectedness. IEEE Trans Robot 23(4):693–703

    Article  Google Scholar 

  • Kempe D, McSherry F (2008) A decentralized algorithm for spectral analysis. J Comput Syst Sci 74(1):70–83

    Article  MATH  MathSciNet  Google Scholar 

  • Kim Y, Mesbahi M (2006) On maximizing the second smallest eigenvalue of a state-dependent graph laplacian. IEEE Trans Autom Control 51(1):116–120

    Article  MathSciNet  Google Scholar 

  • Knorn F, Stanojevic R, Corless M, Shorten R (2009) A framework for decentralized feedback connectivity control with application to sensor networks. Int J Control 82(11):2095–2114

    Article  MATH  MathSciNet  Google Scholar 

  • Lundgren H, Nordstrom E, Tschudin C (2002) The gray zone problem in ieee 802.11b based ad hoc networks. ACM SIGMOBILE Mobile Comput Commun Rev 6(3):104–105

    Article  Google Scholar 

  • Lynch N (1997) Distributed algorithms. Morgan Kaufmann, San Francisco

    Google Scholar 

  • Merris R (1994) Laplacian matrices of a graph: a survey. Linear Algebra Appl 197:143–176

    Article  MathSciNet  Google Scholar 

  • Michael N, Zavlanos MM, Kumar V, Pappas GJ (2009) Maintaining connectivity in mobile robot networks. In: Experimental robotics. Tracts in advanced robotics. Springer, Berlin/Heidelberg, pp 117–126

    Google Scholar 

  • Mohar B (1991) The laplacian spectrum of graphs. In: Alavi Y, Chartrand G, Ollermann O, Schwenk A (Eds) Graph theory, combinatorics, and applications. Wiley, New York, pp 871–898

    Google Scholar 

  • Montijano E, Montijano JI, Sagues C (2011) Adaptive consensus and algebraic connectivity estimation in sensor networks with chebyshev polynomials. In: Proceedings of the 50th IEEE conference on decision and control, Orlando, pp 4296–4301

    Google Scholar 

  • Mostofi Y (2009) Decentralized communication-aware motion planning in mobile networks: an information-gain approach. J Intell Robot Syst 56(1–2):233–256

    Article  MATH  Google Scholar 

  • Neely MJ (2010) Universal scheduling for networks with arbitrary traffic, channels, and mobility. In: Proceedings of the 49th IEEE conference on decision and control, Altanta, pp 1822–1829

    Google Scholar 

  • Neskovic A, Neskovic N, Paunovic G (2000) Modern approaches in modeling of mobile radio systems propagation environment. IEEE Commun Surv 3(3):1–12

    Article  Google Scholar 

  • Notarstefano G, Savla K, Bullo F, Jadbabaie A (2006) Maintaining limited-range connectivity among second-order agents. In: Proceedings of the 2006 American control conference, Minneapolis, pp 2124–2129

    Google Scholar 

  • Olfati-Saber R, Murray RM (2004) Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans Autom Control 49:1520–1533

    Article  MathSciNet  Google Scholar 

  • Oreshkin BN, Coates MJ, Rabbat MG (2010) Optimization and analysis of distributed averaging with short node memory. IEEE Trans Signal Process 58(5):2850–2865

    Article  MathSciNet  Google Scholar 

  • Pahlavan K, Levesque AH (1995) Wireless information networks. Willey, New York

    Google Scholar 

  • Parsons JD (2000) The mobile radio propagation channel. Willey, Chichester

    Book  Google Scholar 

  • Pecora L, Carrollg T (1998) Master stability functions for synchronized coupled systems. Phys Rev Lett 80:2109–2112

    Article  Google Scholar 

  • Powers M, Balch T (2004) Value-based communication preservation for mobile robots. In: Proceedings of the 7th international symposium on distributed autonomous robotic systems, Toulouse

    Google Scholar 

  • Preciado V (2008) Spectral analysis for stochastic models of large-scale complex dynamical networks. Ph.D. dissertation, Department of Electrical Engineering and Computer Science, MIT

    Google Scholar 

  • Preciado V, Verghese G (2005) Synchronization in generalized erdös-rényi networks of nonlinear oscillators. In: 44th IEEE conference on decision and control, Seville, Spain, pp 4628–463

    Google Scholar 

  • Ribeiro A, Luo Z-Q, Sidiropoulos ND, Giannakis GB (2007) Modelling and optimization of stochastic routing for wireless multihop networks. In: Proceedings of the 26th annual joint conference of the IEEE Computer and Communications Societies (INFOCOM), Anchorage, pp 1748–1756

    Google Scholar 

  • Ribeiro A, Sidiropoulos ND, Giannakis GB (2008) Optimal distributed stochastic routing algorithms for wireless multihop networks. IEEE Trans Wirel Commun 7(11):4261–4272

    Article  Google Scholar 

  • Sabattini L, Chopra N, Secchi C (2011) On decentralized connectivity maintenance for mobile robotic systems. In: Proceedings of the 50th IEEE conference on decision and control, Orlando, pp 988–993

    Google Scholar 

  • Schuresko M, Cortes J (2009a) Distributed tree rearrangements for reachability and robust connectivity. In: Hybrid systems: computetation and control. Lecture notes in computer science, vol 5469. Springer, Berlin/New York, pp 470–474

    Google Scholar 

  • Schuresko M, Cortes J (2009b) Distributed motion constraints for algebraic connectivity of robotic networks. J Intell Robot Syst 56(1–2):99–126

    Article  MATH  Google Scholar 

  • Simonetto A, Kaviczky T, Babuska R (2013) Constrained distributed algebraic connectivity maximization in robotic networks. Automatica 49(5):1348–1357

    Article  MathSciNet  Google Scholar 

  • Spanos DP, Murray RM (2004) Robust connectivity of networked vehicles. In: Proceedings of the 43rd IEEE conference on decision and control, Bahamas, pp 2893–2898

    Google Scholar 

  • Spanos DP, Murray RM (2005) Motion planning with wireless network constraints. In: Proceedings of the 2005 American control conference, Portland, pp 87–92

    Google Scholar 

  • Srivastava K, Spong MW (2008) Multi-agent coordination under connectivity constraints. In: Proceedings of the 2008 American control conference, Seattle, pp 2648–2653

    Google Scholar 

  • Stump E, Jadbabaie A, Kumar V (2008) Connectivity management in mobile robot teams. In: Proceedings of the IEEE international conference on robotics and automation, Pasadena, pp 1525–1530

    Google Scholar 

  • Tardioli D, Mosteo AR, Riazuelo L, Villarroel JL, Montano L (2010) Enforcing network connectivity in robot team missions. Int J Robot Res 29(4):460–480

    Article  Google Scholar 

  • Van Mieghem P, Omic J, Kooij R (2009) Virus spread in networks. IEEE/ACM Trans Networking 17(1):1–14

    Article  Google Scholar 

  • Wagenpfeil J, Trachte A, Hatanaka T, Fujita M, Sawodny O (2009) A distributed minimum restrictive connectivity maintenance algorithm. In: Proceedings of the 9th international symposium on robot control, Gifu

    Google Scholar 

  • Wagner AR, Arkin RC (2004) Communication-sensitive multi-robot reconnaissance. In: Proceedings of the IEEE international conference on robotics and automation, New Orleans, pp 2480–2487

    Google Scholar 

  • Yan Y, Mostofi Y (2012) Robotic router formation in realistic communication environments. IEEE Trans Robot 28(4):810–827

    Article  Google Scholar 

  • Yang P, Freeman RA, Gordon GJ, Lynch KM, Srinivasa SS, Sukthankar R (2010) Decentralized estimation and control of graph connectivity for mobile sensor networks. Automatica 46(2): 390–396

    Article  MATH  MathSciNet  Google Scholar 

  • Yao Z, Gupta K (2009) Backbone-based connectivity control for mobile networks. In: Proceedings IEEE international conference on robotics and automation, Kobe, pp 1133–1139

    Google Scholar 

  • Zavlanos MM (2010) Synchronous rendezvous of very-low-range wireless agents. In: Proceedings of the 49th IEEE conference on decision and control, Atlanta, pp 4740–4745

    Google Scholar 

  • Zavlanos MM, Pappas GJ (2005) Controlling connectivity of dynamic graphs. In: Proceedings of the 44th IEEE conference on decision and control and European control conference, Seville, pp 6388–6393

    Google Scholar 

  • Zavlanos MM, Pappas GJ (2007) Potential fields for maintaining connectivity of mobile networks. IEEE Trans Robot 23(4):812–816

    Article  Google Scholar 

  • Zavlanos MM, Pappas GJ (2008) Distributed connectivity control of mobile networks. IEEE Trans Robot 24(6):1416–1428

    Article  Google Scholar 

  • Zavlanos MM, Jadbabaie A, Pappas GJ (2007) Flocking while preserving network connectivity. In: Proceedings of the 46th IEEE conference on decision and control, New Orleans, pp 2919–2924

    Google Scholar 

  • Zavlanos MM, Tanner HG, Jadbabaie A, Pappas GJ (2009) Hybrid control for connectivity preserving flocking. IEEE Trans Autom Control 54(12):2869–2875

    Article  MathSciNet  Google Scholar 

  • Zavlanos MM, Egerstedt MB, Pappas GJ (2011) Graph theoretic connectivity control of mobile robot networks. Proc IEEE Spec Issue Swarming Nat Eng Syst 99(9):1525–154

    Google Scholar 

  • Zavlanos MM, Ribeiro A, Pappas GJ (2013) Network integrity in mobile robotic networks. IEEE Trans Autom Control 58(1):3–18

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Michael M. Zavlanos .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer-Verlag London

About this entry

Cite this entry

Zavlanos, M.M., Pappas, G.J. (2014). Connectivity of Dynamic Graphs. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, London. https://doi.org/10.1007/978-1-4471-5102-9_213-1

Download citation

  • DOI: https://doi.org/10.1007/978-1-4471-5102-9_213-1

  • Received:

  • Accepted:

  • Published:

  • Publisher Name: Springer, London

  • Online ISBN: 978-1-4471-5102-9

  • eBook Packages: Springer Reference EngineeringReference Module Computer Science and Engineering

Publish with us

Policies and ethics

Chapter history

  1. Latest

    Dynamic Graphs, Connectivity of
    Published:
    20 September 2020

    DOI: https://doi.org/10.1007/978-1-4471-5102-9_213-2

  2. Original

    Connectivity of Dynamic Graphs
    Published:
    07 February 2014

    DOI: https://doi.org/10.1007/978-1-4471-5102-9_213-1