Generative models of simultaneously heavy-tailed distributions of interevent times on nodes and edges.

Elohim Fonseca Dos Reis,Naoki Masuda,Aming Li

doi:10.1103/physreve.102.052303

Elohim Fonseca Dos Reis, Naoki Masuda + Show 1 more

Open Access

https://doi.org/10.1103/physreve.102.052303

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Abstract

Intervals between discrete events representing human activities, as well as other types of events, often obey heavy-tailed distributions, and their impacts on collective dynamics on networks such as contagion processes have been intensively studied. The literature supports that such heavy-tailed distributions are present for interevent times associated with both individual nodes and individual edges in networks. However, the simultaneous presence of heavy-tailed distributions of interevent times for nodes and edges is a nontrivial phenomenon, and its origin has been elusive. In the present study, we propose a generative model and its variants to explain this phenomenon. We assume that each node independently transits between a high-activity and low-activity state according to a continuous-time two-state Markov process and that, for the main model, events on an edge occur at a high rate if and only if both end nodes of the edge are in the high-activity state. In other words, two nodes interact frequently only when both nodes prefer to interact with others. The model produces distributions of interevent times for both individual nodes and edges that resemble heavy-tailed distributions across some scales. It also produces positive correlation in consecutive interevent times, which is another stylized observation for empirical data of human activity. We expect that our modeling framework provides a useful benchmark for investigating dynamics on temporal networks driven by non-Poissonian event sequences.

Highlights

Dynamic contacts as well as the static structure of social contact networks govern how humans or animals gather, communicate, and act
We expect that our modeling framework provides a useful benchmark for investigating dynamics on temporal networks driven by non-Poissonian event sequences
We propose a model of time-stamped event sequences on networks that is based on a latent state dynamics of nodes

Summary

INTRODUCTION

Dynamic contacts as well as the static structure of social contact networks govern how humans or animals gather, communicate, and act. The time between two consecutive contacts, called the interevent time (IET), is a key quantity to characterize temporal networks and dynamics on them Myriad human activities, such as online chats, email correspondence, mobility, web browsing, and broker trading, have heavy-tailed distributions of IETs [1,4,6,7]. This observation implies that sequences of discrete events that an individual node or edge in a network experiences obey non-Poissonian statistics. At each time step, activated nodes are uniformly randomly selected to communicate with simultaneously activated neighbors By construction, this model produces a heavy-tailed distribution of IETs for individual nodes. We show that our model produces distributions of IETs with large dispersions for both single nodes and edges, resembling empirical data

SIMULTANEOUSLY LARGE VARIABILITY OF INTEREVENT TIMES ON NODES AND EDGES IS

RESULTS

Analytical evaluation of the CV of interevent times

Correlation between consecutive interevent times

Variants of the model

DISCUSSION