We consider a growing network in which an incoming node gets attached to the [Formula presented] existing node with the probability [Formula presented], where [Formula presented] is the degree of the [Formula presented] node and [Formula presented] its present age. The phase diagram in the [Formula presented] plane is obtained. The network shows scale-free behavior, i.e., the degree distribution [Formula presented] with [Formula presented] only along a line in this plane. Small world property, on the other hand, exists over a large region in the phase diagram. © 2004 The American Physical Society.

PARONGAMA SEN

Physics

K B HAJRA

Fulltext

University of Calcutta (informally known as Calcutta University or CU) is a collegiate public state university located in Kolkata, West Bengal, India.&nbsp;Within India it is recognized as a &quot;Five-Star University&quot; and accredited &quot;A&quot; Grade by National Assessment and Accreditation Council.

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The University of Calcutta has secured the Fifth position among the Universities of India in the prestigious &quot;Indian University Ranking 2019&quot; list, released by the NIRF of the Ministry of Human Resource Development, Government of India.

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It was established on 24 January 1857, and was one of the first institutions in Asia to be established as a multidisciplinary and Western-style university. Its alumni and faculty include several heads of state, heads of government, social reformers, prominent artists, only academy award winner and Dirac medal winner in India, many Fellows of the Royal Society and five Nobel laureates as of 2019 which is highest in South Asia.

University Of Calcutta

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

In two different classes of network models, namely, the Watts Strogatz type and the Euclidean type, subtle changes have been introduced in the randomness. In the Watts Strogatz type network, rewiring has been done in different ways and although the qualitative results remain the same, finite differences in the exponents are observed. In the Euclidean type networks, where at least one finite phase transition occurs, two models differing in a similar way have been considered. The results show a possible shift in one of the phase transition points but no change in the values of the exponents. The WS and Euclidean type models are equivalent for extreme values of the parameters; we compare their behaviour for intermediate values. © 2010 Elsevier B.V. All rights reserved.

Physica A: Statistical Mechanics and its Applications

Complex networks: Effect of subtle changes in nature of randomness

We consider a one-dimensional Euclidean network which is grown using a preferential attachment. Here the jth incoming node gets attached to the ith existing node with the probability , where lij is the Euclidean distance between them and ki the degree of the ith node. This network is known to have a static phase transition point at . On this network, we employ three different searching strategies based on degrees or distances or both, where the possibility of termination of search chains is allowed. A detailed analysis shows that these strategies are significantly affected by the presence of the static critical point. The distributions of the search path lengths and the success rates are also estimated and compared for the different strategies. These distributions appear to be marginally affected by the static phase transition. © IOP Publishing Ltd.

Journal of Statistical Mechanics: Theory and Experiment

The effect of a static phase transition on searching dynamics

Growing network models with preferential attachment dependent on both age and degree are proposed to simulate certain features of citation network noted in [Redner, arXiv: physics/0407137 (2004)]. In this directed network, a new node gets attached to an older node with the probability ∼ K (k) f (t) where the degree and age of the older node are k and t, respectively. Several functional forms of K (k) and f (t) have been considered. The desirable features of the citation network can be reproduced with K (k) ∼ k- β and f (t) ∼ exp (α t) with β = 2.0 and α = - 0.2 and with simple modifications in the growth scheme. © 2006 Elsevier B.V. All rights reserved.

Modelling aging characteristics in citation networks

A growing network in the Euclidean space where the link attachment probability is controlled jointly by two competing factors, namely, the preferential attachment and the magnitude of the link length, was studied. Numerical simulations on a one-dimensional system indicate that on the critical boundary the network crosses over from a BA universality class to a universal scale-free behavior. The calculation of the exponents a and b for the clustering coefficient show that their values are nonuniversal in the region α>-0.5 on the phase boundary, with an indication that a coverges to zero and b coverges to unity as α approaches large negative values.

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Clustering properties of a generalized critical Euclidean network

A random network is grown by introducing at unit rate randomly selected nodes on the Euclidean space. A node is randomly connected to its [formula presented] predecessor of degree [formula presented] with a directed link of length [formula presented] using a probability proportional to [formula presented] Our numerical study indicates that the network is scale free for all values of [formula presented] and the degree distribution decays stretched exponentially for the other values of [formula presented] The link length distribution follows a power law: [formula presented] where [formula presented] is calculated exactly for the whole range of values of [formula presented]. © 2002 The American Physical Society.

Journal	Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Publisher	AMER PHYSICAL SOC
ISSN	1063-651X
Open Access	No