Multi-layered networks

Multi-layered networks consist of layers of several networks, where nodes appear in at least one of these layers. The networks are both connected by intra-layer links (links in one layer) as well as inter-layer links (links between layers). This can be seen in social networks, where multiple types of social ties exist at the same time (private or professional). In real communication networks, such as a peer-to-peer network, one can draw a logical network (the connectedness of peers with each other) as well as a physical network (the way peers are connected through cables, hubs and data centres).

The research on single layer networks is mostly a simplification of the real-world: a social network is multi-layered since we have different networks based on the type of relation with other individuals. Although different layers of a network are mostly partly separated, it is interesting to estimate diffusion and failures propagation between nodes, based on the properties of intra-layer and inter-layer links.

Furthermore, we have developed Multinet.js, a visualization framework for large, dynamic and multi-layered graphs, that works directly in the browser. The source code is also available on Github.

Besides actively doing research in this field, we have prepared a volume with a collection of works, edited by Antonios Garas, which highlights and summarizing recent developments on network theory with respect to multi-layered networks. The book is titled "Interconnected Networks", and appeared in Springer's "Complexity" series.

Here follows the Table of Contents, summarizing the list of contributions.  

  1. A tipping point in the structural formation of interconnected networks
    Alex Arenas and Filippo Radicchi
  2. Multilayer networks: metrics and spectral properties
    Emanuele Cozzo, Guilherme Ferraz de Arruda, Francisco A.Rodrigues and Yamir Moreno
  3. An ensemble perspective on multi-layer networks
    Nicolas Wider, Antonios Garas, Ingo Scholtes, Frank Schweitzer
  4. Interconnecting networks: the role of connector links
    J. M. Buldu, R. Sevilla-Escoboza, J. Aguirre, D. Papo and R. Gutierrez
  5. Vulnerability of interdependent networks and networks of networks
    Michael M. Danziger, Louis M. Shekhtman, Amir Bashan, Yehiel Berezin and Shlomo Havlin
  6. A unified approach to percolation processes on multiplex networks
    G. J. Baxter, D. Cellai, S. N. Dorogovtsev, A. V. Goltsev and J.F. F. Mendes
  7. How much interconnected should networks be for cooperation to thrive?
    Zhen Wang, Attila Szolnoki, Matjaz Perc
  8. The Cacophony of Interconnected Networks
    V. H. P. Louzada, N. A. M. Araujo, J. S. Andrade Jr, and H. J. Herrmann
  9. Several multiplexes in the same city: The role of socioeconomic differences in urban mobility
    Laura Lotero, Alessio Cadillo, Rafael Hurtado and Jesus Gomez-Gardenes
  10. The weak core and the structure of elites in social multiplex networks
    Bernat Corominas-Murtra and Stefan Thurner
  11. Interbank markets and multiplex networks: centrality measures and statistical null models
    Leonardo Bargigli, Giovanni di Iasio, Luigi Infante, Fabrizio Lillo and Federico Pierobon
  12. The financial system as a nexus of interconnected networks
    Stefano Battiston, Guido Caldarelli, Marco D’Errico


Selected Publications

Multiplex Network Regression: How do relations drive interactions?

Casiraghi, Giona

arXiv e-print pages: 1-17


Systemic risk in multiplex networks with asymmetric coupling and threshold feedback

Burkholz, Rebekka; Leduc, Matt; Garas, Antonios; Schweitzer, Frank

Physica D, pages: 64--72, volume: 323-324


Value of peripheral nodes in controlling multilayer scale-free networks

Zhang, Yan; Garas, Antonios; Schweitzer, Frank

Physical Review E, pages: 012309, volume: 93


Generalized Hypergeometric Ensembles: Statistical Hypothesis Testing in Complex Networks

Casiraghi, Giona; Nanumyan, Vahan; Scholtes, Ingo; Schweitzer, Frank

ArXiv e-prints


An ensemble perspective on multi-layer networks

Wider, Nicolas; Garas, Antonios; Scholtes, Ingo; Schweitzer, Frank

Interconnected Networks


Reaction-Diffusion Processes on Interconnected Scale-Free Networks

Garas, Antonios

Physical Review E, pages: 020801(R), volume: 92


Predicting Scientific Success Based on Coauthorship Networks

Sarigol, Emre; Pfitzner, Rene; Scholtes, Ingo; Garas, Antonios; Schweitzer, Frank

EPJ Data Science, pages: 9, volume: 3


Engineering and Mastering Interwoven Systems

Tomforde, Sven; Hähner, Jörg; Seebach, Hella; Reif, W. - E.; Sick, Bernhard; Wacker, Arno; Scholtes, Ingo

Proceedings of ARCS 2014 - 27th International Conference on Architecture of Computing


The Social Dimension of Information Ranking: A Discussion of Research Challenges and Approaches

Schweitzer, Frank; Scholtes, Ingo; Pfitzner, Rene

Socioinformatics - The Social Impact of Interactions between Humans and IT