Related papers: Scaling of internode distances in weighted complex…
We consider the self organizing process of merging and regeneration of vertices in complex networks and demonstrate that a scale-free degree distribution emerges in a steady state of such a dynamics. The merging of neighbor vertices in a…
The Erdos-Renyi classical random graph is characterized by a fixed linking probability for all pairs of vertices. Here, this concept is generalized by drawing the linking probability from a certain distribution. Such a procedure is found to…
This paper establishes a relation between scale-free networks and Markov chains, and proposes a computation framework for degree distributions of scale-free networks. We first find that, under the BA model, the degree evolution of…
A scale-free network is grown in the Euclidean space with a global directional bias. On a vertical plane, nodes are introduced at unit rate at randomly selected points and a node is allowed to be connected only to the subset of nodes which…
Scaling behavior of scale-free evolving networks arising in communications, citations, collaborations, etc. areas is studied. We derive universal scaling relations describing properties of such networks and indicate limits of their…
Real world complex networks are scale free and possess meso-scale properties like core-periphery and community structure. We study evolution of the core over time in real world networks. This paper proposes evolving models for both…
We show that the load at each node in a preferential attachment network scales as a power of the degree of the node. For a network whose degree distribution is p(k) ~ k^(-gamma), we show that the load is l(k) ~ k^eta with eta = gamma - 1,…
The topology of many real complex networks has been conjectured to be embedded in hidden metric spaces, where distances between nodes encode their likelihood of being connected. Besides of providing a natural geometrical interpretation of…
In this work we make an attempt to understand social networks from a mathematical viewpoint. In the first instance we consider a network where each node representing an individual can connect with a neighbouring node with a certain…
All networks can be analyzed at multiple scales. A higher scale of a network is made up of macro-nodes: subgraphs that have been grouped into individual nodes. Recasting a network at higher scales can have useful effects, such as decreasing…
In this paper, we propose a new model that allows us to investigate this competitive aspect of real networks in quantitative terms. Through theoretical analysis and numerical simulations, we find that the competitive network have the…
Complex network theory has been used to study complex systems. However, many real-life systems involve multiple kinds of objects . They can't be described by simple graphs. In order to provide complete information of these systems, we…
We present a statistical mechanics approach for the description of complex networks. We first define an energy and an entropy associated to a degree distribution which have a geometrical interpretation. Next we evaluate the distribution…
Network growth is currently explained through mechanisms that rely on node prestige measures, such as degree or fitness. In many real networks those who create and connect nodes do not know the prestige values of existing nodes, but only…
Topology of exponential and scale-free trees and simple graphs is investigated numerically. The numbers of the nearest neighbors, the next-nearest neighbors, the next-next-nearest neighbors, the 4-th and the 5-th neighbors are calculated.…
What is the underlying mechanism leading to power-law degree distributions of many natural and artificial networks is still at issue. We consider that scale-free networks emerges from self-organizing process, and such a evolving model is…
Geometric constraints impact the formation of a broad range of spatial networks, from amino acid chains folding to proteins structures to rearranging particle aggregates. How the network of interactions dynamically self-organizes in such…
A spatial scale-free network is introduced and studied whose motivation has been originated in the growing Internet as well as the Airport networks. We argue that in these real-world networks a new node necessarily selects one of its…
A finite graph embedded in the plane is called a series-parallel map if it can be obtained from a finite tree by repeatedly subdividing and doubling edges. We study the scaling limit of weighted random two-connected series-parallel maps…
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…