Dear colleagues,

This is a reminder that tomorrow (Thursday 25) at 16:00, prof. Tiandong Wang (Texas A&M) will give a virtual seminar “in Florence”, to which you are all invited. You can find title and abstract below this message.

The seminar will be on Zoom, and the information to join is:

Topic: Tiandong Wang - Reciprocity in a Preferential Attachment Network Time: Mar 25, 2021 04:00 PM Rome

https://us02web.zoom.us/j/82762436142?pwd=MW45SWN6NTBqV0VWbVJWREhESmtaZz09 https://us02web.zoom.us/j/82762436142?pwd=MW45SWN6NTBqV0VWbVJWREhESmtaZz09

Meeting ID: 827 6243 6142 Passcode: 897951

If you know of someone who might be interested and is not subscribed to the random mailing list, please do not hesitate to forward this announcement to them.

Kind regards, Gianmarco

Title: Reciprocity in a Preferential Attachment Network

Abstract: Empirical studies show that online social networks have not only in- and out-degree distributions with Pareto-like tails, but also a high proportion of reciprocal edges. A classical directed preferential attachment (PA) model generates in- and out-degree distribution with power-law tails, but theoretical properties of the reciprocity feature in this model have not yet been studied. We derive the asymptotic results on the number of reciprocal edges between two fixed nodes, as well as the proportion of reciprocal edges in the entire PA network. We see that with certain choices of parameters, the proportion of reciprocal edges in a directed PA network is close to 0, which differs from the empirical observation. This points out one potential problem of fitting a classical PA model to a given network dataset with high reciprocity, and indicates alternative models need to be considered.

---------------------------------------------------------------------- Gianmarco Bet (he/him) Junior researcher

https://gianmarco.bet Phone: (+39) 055 2751491

Department of Mathematics and Informatics "U. Dini" University of Florence Viale Morgagni, 65 50134 Firenze, Italy Office 64 ----------------------------------------------------------------------