Related papers: Mittag-Leffler functions and their applications in…

In this article, we quantify the functional convergence of the rescaled random walk with heavy tails to a stable process.This generalizes the Generalized Central Limit Theorem for stable random variables infinite dimension. We show that…

Network models have been widely used to study diverse systems and analyze their dynamic behaviors. Given the structural variability of networks, an intriguing question arises: Can we infer the type of system represented by a network based…

The representation of complex systems as networks is inappropriate for the study of certain problems. We show several examples of social, biological, ecological and technological systems where the use of complex networks gives very limited…

In this paper we define the class of matrix Mittag-Leffler distributions and study some of its properties. We show that it can be interpreted as a particular case of an inhomogeneous phase-type distribution with random scaling factor, and…

This paper proposes a family of network centralities called fixed-point centralities. This centrality family is defined via the fixed point of permutation equivariant mappings related to the underlying network. Such a centrality notion is…

Traditional measures of closeness and betweenness centrality in networks rely on the shortest paths between nodes. Many standard metrics fail to accurately reflect the physical or probabilistic characteristics of nodal centrality and…

The main purpose of this note is to point out the relevance of the Mittag-Leffler probability distribution in the so-called thinning theory for a renewal process with a queue of power law type. This theory, formerly considered by Gnedenko…

This article introduces a model for interacting vertex-reinforced random walks, each taking values on a complete sub-graph of a locally finite undirected graph. The transition probability for a walk to a given vertex depends on the…

This is an extensive survey of the techniques used to formulate generalizations of the Mittag-Leffler Theorem from complex analysis. With the techniques of the theory of differential forms, sheaves and cohomology, we are able to define the…

We show how a rescaling of fractional operators with bounded kernels may help circumvent their documented deficiencies, for example, the inconsistency at zero or the lack of inverse integral operator. On the other hand, we build a novel…

Multi-layered social networks reflect complex relationships existing in modern interconnected IT systems. In such a network each pair of nodes may be linked by many edges that correspond to different communication or collaboration user…

We study the ergodic theory of a one-parameter family of interval maps T_alpha arising from generalized continued fraction algorithms. First of all, we prove the dependence of the metric entropy of T_alpha to be Hoelder-continuous in the…

We consider the alternating zeta function and the alternating $L$-function of a graph $G$, and express them by using the Ihara zeta function of $G$. Next, we define a generalized alternating zeta function of a graph, and express the…

The problem of assigning centrality values to nodes and edges in graphs has been widely investigated during last years. Recently, a novel measure of node centrality has been proposed, called k-path centrality index, which is based on the…

Graph neural networks are prominent models for representation learning over graph-structured data. While the capabilities and limitations of these models are well-understood for simple graphs, our understanding remains incomplete in the…

Two concepts of centrality have been defined in complex networks. The first considers the centrality of a node and many different metrics for it has been defined (e.g. eigenvector centrality, PageRank, non-backtracking centrality, etc). The…

The structure of many complex networks includes edge directionality and weights on top of their topology. Network analysis that can seamlessly consider combination of these properties are desirable. In this paper, we study two important…

Many complex systems have natural representations as multi-layer networks. While these formulations retain more information than standard single-layer network models, there is not yet a fully developed theory for computing network metrics…

Graphlets are induced subgraph patterns that are crucial to the understanding of the structure and function of a large network. A lot of efforts have been devoted to calculating graphlet statistics where random walk based approaches are…

Network theory is a useful framework for studying interconnected systems of interacting entities. Many networked systems evolve continuously in time, but most existing methods for the analysis of time-dependent networks rely on discrete or…