Temporal graph reproduction with RWIG

Our Random Walkers Induced temporal Graphs (RWIG) model generates temporal graph sequences based on M independent, random walkers that traverse an underlying graph as a function of time. Co-location of walkers at a given node and time defines an individual-level contact. RWIG is shown to be a realistic model for temporal human contact graphs.   

A key idea is that a random walk on a Markov graph executes the Markov process. Each of the M walkers traverses the same set of nodes (= states in the Markov graph), but with own transition probabilities (in discrete time) or rates (in continuous time). Hence, the Markov transition probability matrix P_j reflects the policy of motion of walker w_j. RWIG is analytically feasible: we derive closed form solutions for the probability distribution of contact graphs.

Usually, human mobility networks are inferred through measurements of timeseries of contacts between individuals. We also discuss this “inverse RWIG problem”, which aims to determine the parameters in RWIG (i.e. the set of probability transfer matrices P₁, P₂, ..., P_M and the initial probability state vectors s₁[0], ...,s_M[0] of walkers w₁,w₂, ...,w_M in discrete time), given a timeseries of contact graphs.

This talk is based on the article:
Almasan, A.-D., Shvydun, S., Scholtes, I. and P. Van Mieghem, 2025, "Generating Temporal Contact Graphs Using Random Walkers", IEEE Transactions on Network Science and Engineering, to appear.