# Dependence of the average to-node distance on the node degree for random graphs and growing networks

Source: [Dependence of the average to-node distance on the node degree for random graphs and growing networks](<https://www.sota2.com/research/paper/68fa1e677a2b558e29322309>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-23T14:57:13.366Z

Authors: K.Malarz, K.Kulakowski

Published: 2004-02-18T15:54:22.000Z

## Abstract

In a graph, nodes can be characterized locally (with their degree $k$) or globally (e.g. with their average length path $\\xi$ to other nodes). Here we investigate how $\\xi$ depends on $k$. Our earlier algorithm of the construction of the distance matrix is applied to the random graphs. Numerical calculations are performed for the random graphs and the growing networks: the scale-free ones and the exponential ones. The results are relevant for search strategies in different networks.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/cond-mat/0402474>)

[PDF](<https://arxiv.org/pdf/cond-mat/0402474.pdf>)