TY - CHAP

T1 - Random walks on stochastic temporal networks

AU - Hoffmann, T.

AU - Porter, M.A.

AU - Lambiotte, R.

PY - 2013/1/1

Y1 - 2013/1/1

N2 - In the study of dynamical processes on networks, there has been intense focus on network structure-i.e., the arrangement of edges and their associated weights-but the effects of the temporal patterns of edges remains poorly understood. In this chapter, we develop a mathematical framework for random walks on temporal networks using an approach that provides a compromise between abstract but unrealistic models and data-driven but non-mathematical approaches. To do this, we introduce a stochastic model for temporal networks in which we summarize the temporal and structural organization of a system using a matrix of waiting-time distributions. We show that random walks on stochastic temporal networks can be described exactly by an integro-differentialmaster equation and derive an analytical expression for its asymptotic steady state. We also discuss how our work might be useful to help build centrality measures for temporal networks.

AB - In the study of dynamical processes on networks, there has been intense focus on network structure-i.e., the arrangement of edges and their associated weights-but the effects of the temporal patterns of edges remains poorly understood. In this chapter, we develop a mathematical framework for random walks on temporal networks using an approach that provides a compromise between abstract but unrealistic models and data-driven but non-mathematical approaches. To do this, we introduce a stochastic model for temporal networks in which we summarize the temporal and structural organization of a system using a matrix of waiting-time distributions. We show that random walks on stochastic temporal networks can be described exactly by an integro-differentialmaster equation and derive an analytical expression for its asymptotic steady state. We also discuss how our work might be useful to help build centrality measures for temporal networks.

UR - http://www.scopus.com/inward/record.url?scp=84883514054&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-36461-7-15

DO - 10.1007/978-3-642-36461-7-15

M3 - Chapter

AN - SCOPUS:84883514054

SN - 9783642364600

SP - 295

EP - 313

BT - Understanding Complex Systems

ER -