Topological analysis of numerosity-constrained social networks

Nicole Abaid, Maurizio Porfiri

Research output: Chapter in Book/Report/Conference proceedingConference contribution


In this study, we present a class of directed graphs with bounded degree sequences, which embodies the physical phenomenon of numerosity found in the collective behavior of large animal groups. Behavioral experiments show that an animal's perception of number is capped by a critical limit, above which an individual perceives a nonspecific "many". This species-dependent limit plays a pivotal role in the decision making process of large groups, such as fish schools and bird flocks. Here, we consider directed graphs whose edges model information-sharing between individual vertices. We incorporate the numerosity phenomenon as a critical limit on the intake of information by bounding the degree sequence and include the variability of cognitive processes by using a random variable in the network construction. We analytically compute measures of the expected structure of this class of graphs based on cycles, clustering, and sorting among vertices. Theoretical results are verified with numerical simulation.

Original languageEnglish (US)
Title of host publicationASME 2010 Dynamic Systems and Control Conference, DSCC2010
Number of pages7
StatePublished - 2010
EventASME 2010 Dynamic Systems and Control Conference, DSCC2010 - Cambridge, MA, United States
Duration: Sep 12 2010Sep 15 2010

Publication series

NameASME 2010 Dynamic Systems and Control Conference, DSCC2010


OtherASME 2010 Dynamic Systems and Control Conference, DSCC2010
Country/TerritoryUnited States
CityCambridge, MA

ASJC Scopus subject areas

  • Control and Systems Engineering


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