相关论文: Entropy distribution and condensation in random ne…

Most real world dynamic networks are evolved very fast with time. It is not feasible to collect the entire network at any given time to study its characteristics. This creates the need to propose local algorithms to study various properties…

Due to their conceptual and mathematical simplicity, Erd\"os-R\'enyi or classical random graphs remain as a fundamental paradigm to model complex interacting systems in several areas. Although condensation phenomena have been widely…

The degree distribution, referred to as the delta-sequence of a network is studied. Using the non-normalized Lorenz curve, we apply a generalized form of the classical majorization partial order. Next, we introduce a new class of small…

We derive a message passing method for computing the spectra of locally tree-like networks and an approximation to it that allows us to compute closed-form expressions or fast numerical approximates for the spectral density of random graphs…

We study Erd\"{o}s-R\'enyi random graphs with random weights associated with each link. We generate a new ``Supernode network'' by merging all nodes connected by links having weights below the percolation threshold (percolation clusters)…

The connectivity of a network contains information about the relationships between nodes, which can denote interactions, associations, or dependencies. We show that this information can be analyzed by measuring the uncertainty (and…

We consider large networks of theta neurons and use the Ott/Antonsen ansatz to derive degree-based mean field equations governing the expected dynamics of the networks. Assuming random connectivity we investigate the effects of varying the…

A central task in analyzing complex dynamics is to determine the loci of information storage and the communication topology of information flows within a system. Over the last decade and a half, diagnostics for the latter have come to be…

Investigation of divisibility properties of natural numbers is one of the most important themes in the theory of numbers. Various tools have been developed over the centuries to discover and study the various patterns in the sequence of…

This article investigates emergence and complexity in complex systems that can share information on a network. To this end, we use a theoretical approach from information theory, computability theory, and complex networks. One key studied…

A problem closely related to epidemiology, where a subgraph of 'infected' links is defined inside a larger network, is investigated. This subgraph is generated from the underlying network by a random variable, which decides whether a link…

We provide a framework for determining the centralities of agents in a broad family of random networks. Current understanding of network centrality is largely restricted to deterministic settings, but practitioners frequently use random…

We give an intuitive though general explanation of the finite-size effect in scale-free networks in terms of the degree distribution of the starting network. This result clarifies the relevance of the starting network in the final degree…

Represented as graphs, real networks are intricate combinations of order and disorder. Fixing some of the structural properties of network models to their values observed in real networks, many other properties appear as statistical…

We study an opinion formation model by the means of a co-evolving complex network where the vertices represent the individuals, characterised by their evolving opinions, and the edges represent the interactions among them. The network…

The logarithm of the number of Eulerian orientations, normalised by the number of vertices, is known as the residual entropy in studies of ice-type models on graphs. The spanning tree entropy depends similarly on the number of spanning…

Random graphs have played an instrumental role in modelling real-world networks arising from the internet topology, social networks, or even protein-interaction networks within cells. Percolation, on the other hand, has been the fundamental…

Complex networks have gained more attention from the last few years. The size of real-world complex networks, such as online social networks, WWW network, collaboration networks, is increasing exponentially with time. It is not feasible to…

This article introduces a new class of models for multiple networks. The core idea is to parametrize a distribution on labelled graphs in terms of a Fr\'{e}chet mean graph (which depends on a user-specified choice of metric or graph…

Affiliation network is one kind of two-mode social network with two different sets of nodes (namely, a set of actors and a set of social events) and edges representing the affiliation of the actors with the social events. Although a number…