ANALYZING SOCIAL NETWORKS STRUCTURALLY USING PETRI NETS
By
Gajendra Pratap Singh1 , Nikita2 , Pooja3 and Riddhi Jangid4,*
1,4School of Computational and Integrative Sciences Jawaharlal Nehru University, New Delhi-110067
2,3Department of Mathematics, Kamla Nehru College, University of Delhi, India-110067
*Corresponding author
Email: gajendra@mail.jnu.ac.in, nikita.mat2325@knc.du.ac.in, poojaa@knc.du.ac.in, riddhijangid97@gmail.com
(Received: August 01, 2025, Revised: February 15, 2026; Accepted: June 18, 2026)
DOI: https://doi.org/10.58250/jnanabha.2026.561P-13
Abstract
Social networks are commonly expressed, modelled and analyzed using discrete mathematics as graph theory. This paper proposes a directed bipartite based model in the framework of Petrinet for behavioral and structurally analysis of social works using places, transitions, directed arcs, and marking vectors. The approach establishes a formal relationship between graph-based social network structures and Peri-nets, enabling the analysis of connectivity, surfaces, P and T- invariants, marked graph, liveness, reachability, and structural properties. Illustrative examples demonstrate the applicability of Petri nets for representing and analyzing social network structures.
2020 Mathematical Sciences Classification: 05C82, 68R10, 68M11, 68Q85
Keywords and Phrases: Social networks, Graph theory, Petri nets, Reachability, Invariants, Firing Rule, Marking Vector.