# Network interpolation

## TL;DR

This paper introduces a Markov chain-based network interpolation method that generates plausible sequences of graphs between snapshots, with analytical estimates and validation on synthetic and real data showing its effectiveness.

## Contribution

The paper presents a novel Markov chain model for network interpolation that analytically estimates transition properties and outperforms common growth models.

## Key findings

- The model accurately interpolates between network snapshots.
- It provides analytical estimates of hitting times and long-term behavior.
- It outperforms preferential attachment and triadic closure models.

## Abstract

Given a set of snapshots from a temporal network we develop, analyze, and experimentally validate a so-called network interpolation scheme. Our method allows us to build a plausible, albeit random, sequence of graphs that transition between any two given graphs. Importantly, our model is well characterized by a Markov chain, and we leverage this representation to analytically estimate the hitting time (to a predefined distance to the target graph) and long term behavior of our model. These observations also serve to provide interpretation and justification for a rate parameter in our model. Lastly, through a mix of synthetic and real-world data experiments we demonstrate that our model builds reasonable graph trajectories between snapshots, as measured through various graph statistics. In these experiments, we find that our interpolation scheme compares favorably to common network growth models, such as preferential attachment and triadic closure.