Fractal and Multifractal Analysis of Complex Networks

Dear Colleagues,

We are surrounded by systems that are complex. Interactions between particles of matter, social phenomena being the results of cooperation between billions of individuals, communication and cooperation, the activity of billions of neurons in brains of living beings, the structure and dynamics of financial markets or the structure of the mountain ridges are just a few examples of the real-world complexity. To a greater or lesser extent, these systems play a significant role in both our private and professional lives. Therefore, their fullest understanding, description, and prediction of their future behaviors is a very interesting scientific challenge.

One of the tools that contributes to a more complete description of complex phenomena is the language of complex networks developed for more than two decades.

Complex networks are an approach to studying different real systems through graph-based representation, which allows their observation with different graph measures, such as, among others, degree distribution, clustering coefficient, betweenness or assortativity.

However, these measures are local in nature; thus, the global structures that compose the network are hidden. To study these global structures in the networks, the right approach seems to be multifractal analysis (MFA), which consists in the measure of fractal dimensions in different scales of the network.

Today’s level of technology development allows for an empirical analysis of large-scale and complex dynamical networks generated by nature, as well as enables the construction and verification of more sophisticated models.

Currently, we know many interesting properties of real complex networks. These are, among others, scale-free, small-world, and also self-similarity, which is closely related to the (multi-)fractality of the complex system.

Fractal and (in general) multifractal analysis allows identifying and better understanding the nonlinear properties, hierarchical structure, and spatial heterogeneity of both real-word and synthetic systems.

The challenge is therefore to build tools (methods) that reliably identify the possible multifractal nature of the networks. Some algorithms have been proposed for MFA both for weighted and unweighted complex networks in the past few years. However, as it often happens in research, the issue of creating new methods and ideas, especially in this field, has certainly not been exhausted yet.

This Special Issue will accept original ideas in the form of unpublished original manuscripts focused on topics arising from the broadly understood field of quantitative analysis of “complex networks”, in particular, their multiscale nature.

Dr. Rafał Rak
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.