Continuous Homophily and Clustering in Random Networks

42 Pages Posted: 24 Jul 2014 Last revised: 9 Oct 2016

See all articles by Florian Gauer

Florian Gauer

Bielefeld University - Center for Mathematical Economics

Jakob Landwehr

Bielefeld University - Center for Mathematical Economics

Date Written: August 2016

Abstract

We propose a random network model incorporating heterogeneity of agents and a continuous notion of homophily. Unlike the vast majority of the corresponding economic literature, we capture homophily in terms of similarity rather than equality by assuming that the probability of linkage between two agents continuously decreases in the distance of their characteristics. A homophily parameter directly determines the strength of this effect. As a main result, we show that for any positive level of homophily our model exhibits clustering, that is an increased probability of linkage given a common neighbor. As opposed to this, the seminal Bernoulli Random Graph model à la Erdős and Rényi (1959) is comprised as the limit case of no homophily. Moreover, simulations indicate that, although the average distance between agents increases in homophily, the well-known small-world phenomenon is preserved even at high homophily levels. We finally provide a possible application in form of a stylized labor market model, where a firm can hire a new employee via the social network.

Keywords: Random Graphs, Homophily, Clustering, Small-World Phenomenon, Network Formation, Labor Market Search

JEL Classification: D85, J64, Z13

Suggested Citation

Gauer, Florian and Landwehr, Jakob, Continuous Homophily and Clustering in Random Networks (August 2016). Center for Mathematical Economics Working Paper No. 515, Available at SSRN: https://ssrn.com/abstract=2470176 or http://dx.doi.org/10.2139/ssrn.2470176

Florian Gauer (Contact Author)

Bielefeld University - Center for Mathematical Economics ( email )

Postfach 10 01 31
Bielefeld, D-33501
Germany
+49 (0) 521 106 4918 (Phone)

Jakob Landwehr

Bielefeld University - Center for Mathematical Economics ( email )

Postfach 10 01 31
Bielefeld, D-33501
Germany

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