# Mixed Random Sampling of Frames method for counting number of motifs

## TL;DR

This paper introduces a Monte Carlo-based sampling method for efficiently estimating the frequency of small network motifs in large-scale directed and undirected networks, reducing computational costs.

## Contribution

It presents a novel mixed random sampling approach that controls accuracy and minimizes variance in motif frequency estimation for large networks.

## Key findings

- Effective in large networks with hundreds of thousands of nodes.
- Reduces computational resources compared to exact counting methods.
- Controls estimation accuracy through variance minimization.

## Abstract

The problem of calculating the frequencies of network motifs on three and four nodes in large networks is considered. Telecommunications networks, cell molecular networks are investigated. The sizes of the investigated networks are hundreds of thousands of nodes and connections. These networks are represented in the form of directed and undirected simple graphs. Exact calculating requires huge computational resources for such large graphs. A method for calculating the frequencies of network motifs using the Monte Carlo method with control of the accuracy of calculations is proposed. The proposed effective method minimizes the value of the coefficient of variation.

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Source: https://tomesphere.com/paper/1904.02483