Node similarity as a basic principle behind connectivity in complex networks

Matthias Scholz

doi:10.46298/jdmdh.33

Abstract

How are people linked in a highly connected society? Since in many networks a power-law (scale-free) node-degree distribution can be observed, power-law might be seen as a universal characteristics of networks. But this study of communication in the Flickr social online network reveals that power-law node-degree distributions are restricted to only sparsely connected networks. More densely connected networks, by contrast, show an increasing divergence from power-law. This work shows that this observation is consistent with the classic idea from social sciences that similarity is the driving factor behind communication in social networks. The strong relation between communication strength and node similarity could be confirmed by analyzing the Flickr network. It also is shown that node similarity as a network formation model can reproduce the characteristics of different network densities and hence can be used as a model for describing the topological transition from weakly to strongly connected societies.

Highlights

In an increasingly interconnected world, it must be of huge interest to understand the topology of a highly connected society; important, for example, for predicting the spread of epidemic diseases [Pastor-Satorras and Vespignani, 2001]
By analyzing the Flickr R social online network, this study shows that communication strength is directly related to tag similarity
This work demonstrates that the frequently observed scale-free power-law distribution can be well reproduced by a model which is purely based on the idea of node similarity

Summary

INTRODUCTION

In an increasingly interconnected world, it must be of huge interest to understand the topology of a highly connected society; important, for example, for predicting the spread of epidemic diseases [Pastor-Satorras and Vespignani, 2001]. ‘To be in the right place at the right time’ works often as the basic principle for getting connected, but beside fitting in space and time additional properties are important: for instance similar surfaces of molecules, or similar interests of people. Online social networks are an ideal source for investigating complex networks because of the often huge number of users, their link and communication profiles, and the availability of additional metadata such as tags (keywords). By analyzing the Flickr R social online network, this study shows that communication strength is directly related to tag (keyword) similarity. It turns out that more densely connected networks show an increasing divergence from the power-law distribution This characteristic can be reproduced by a network formation model based on similarity, as shown by the Euclidean distance model proposed in this work

SIMILARITY IN THE FLICKR NETWORK

FROM SPARSE TO DENSE NETWORKS

CONCLUSION