ORIGINAL ARTICLE A significant core structure inside the social network evolutionary process Billel Hamadache 1 • Hassina Seridi-Bouchelaghem 1 • Nadir Farah 1 Received: 11 August 2015 / Revised: 2 June 2016 / Accepted: 8 June 2016 Ó Springer-Verlag Wien 2016 Abstract In social networks, the interaction sustainability and the information sharing needs can produce a subtle and leader phenomenon: a core. Investigations of homeland security in social organizations need to recognize such elite class dominating the network consistency and centraliza- tion. However, dense regions gathering strategic individu- als are not the best realistic structures to represent it in static models. In this paper, we propose an approach based on the social network dynamics to characterize and identify a core identity. We use ‘‘the group’’ as a conceptual mold to explore three key features: cohesion, dominance, and durability. We represent a real-world network by a meta- model based on patterns of overlapped groups between time steps, linked by weighted arcs. The weights determine which overlaps are relevant. By a critical pattern-based research, we detect the critical path covering the most relevant overlaps: large and central. Once a grouping per- sists deep in inside, findings show that it presents a large and durable composition playing a central role the most stable. It is qualified as a significant core where the net- work is shown sensitive throughout the observation period. Keywords Dynamic social network  Underlying structure  Temporal dynamics  Group dynamics  Temporal overlaps  Persistence  Durability  Group centrality  Centrality stability  Deep critical patterns  Significant core identity  Network sensitivity 1 Introduction Nowadays, the computer-mediated interaction among people, institutions, employees, and learners promotes the individual’s socialization. The social media proliferates and invades not just social platforms but different other organizations for innovation. Complex social phenomena are currently discussed from emergent online/organiza- tional social networks (Rosen et al. 2011) (OSNs). The Social Network Analysis and Mining (SNAM) (Memon and Alhajj 2011a, b) is an innovative and successful field for management research and decision making. But, the advances, prospects (Scott 2011), and ambitions exceed nowadays static and structural frameworks. The SN dynamics or semantics (Ereteo et al. 2009, 2011) are becoming indispensable. Within the scope of new SNAM trends, the main purpose of this study was to understand one of the most critical underlying structures: ‘‘A core’’ deep in inside realistic social network (SN) models. How can a core be significantly characterized and identified, specifically in an organizational SN? The investigations need to know more about a core structure (in business, government, organizations of crim- inal conspiracy, mobile phone networks) for feeding busi- ness strategies, decisions, politics, and homeland security. This is a flagship notion and common research topic in the SNs as well as other complex systems. For example, to recognize elites, a core is evoked as a leader class that Electronic supplementary material The online version of this article (doi:10.1007/s13278-016-0344-y) contains supplementary material, which is available to authorized users. & Billel Hamadache Hamadache@labged.net Hassina Seridi-Bouchelaghem seridi@labged.net Nadir Farah farah@labged.net 1 Laboratory of Electronic Document Management LabGED, Badji Mokhtar Annaba-University, P. O. Box 12, 23000 Annaba, Algeria 123 Soc. Netw. Anal. Min. (2016) 6:38 DOI 10.1007/s13278-016-0344-y