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# 13th Seminar of the “D2 Seminar Series” – Florence Center for Data Science

## March 11, 2022 @ 14:00 - 15:00

The Florence Center for Data Science is happy to present the 13th Seminar of the “D2 Seminar Series” launched by the FDS. The Seminar will be held online Friday **11th **of **March **2021, from **2-3 pm.**

The seminar on *“* *Paths and flows for centrality measures in networks” *will be held by Daniela Bubboloni from the Department of Mathematics and Computer Science “Ulisse Dini” of the University of Florence.

Register in advance for this webinar:

https://us02web.zoom.us/webinar/register/WN_KFoLkeSfT3-kzWLK2mwHPA

After registering, you will receive a confirmation email containing information about joining the webinar.

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**Speaker**: Daniela Bubboloni – Department of Mathematics and Computer Science “Ulisse Dini”, University of Florence

**Title**: Paths and flows for centrality measures in networks

**Abstract**: Consider the number of paths that must pass through a subset X of vertices of a capacitated network N in a maximum sequence of arc-disjoint paths connecting two vertices y and z. Consider then the difference between the maximum flow value from y to z in N and the maximum flow value from y to z in the network obtained by N by setting to zero the capacities of all the arcs incident to X. When X is a singleton, those quantities are involved in defining and computing the flow betweenness centrality and are commonly identified without any rigorous proof justifying the identification. That surprising gap in the literature is the starting point of our research. On the basis of a deep analysis of the interplay between paths and flows, we prove that, when X is a singleton, those quantities coincide. On the other hand, when X has at least two elements, those quantities may be different from each other. By means of the considered quantities, two conceptually different group centrality measures, respectively based on paths and flows, can be naturally defined. Such group centrality measures both extend the flow betweenness centrality to groups of vertices and satisfy a desirable form of monotonicity.