arXiv subjects

Kamalika Basu Hajra

Publications and source records attributed to Kamalika Basu Hajra.

8 recordsLinked to original sources

arXiv2010

Coevolution of Glauber-like Ising dynamics on typical networks

We consider coevolution of site status and link structures from two different initial networks: a one dimensional Ising chain and a scale free network. The dynamics is governed by a preassigned stability parameter $S$, and a rewiring factor $ϕ$, that determines whether the Ising spin at the chosen site flips or whether the node gets rewired to another node in the system. This dynamics has also been studied with Ising spins distributed randomly among nodes which lie on a network with preferential attachment. We have observed the steady state average stability and magnetisation for both kinds of systems to have an idea about the effect of initial network topology. Although the average stability shows almost similar behaviour, the magnetisation depends on the initial condition we start from. Apart from the local dynamics, the global effect on the dynamics has also been studied. These parameters show interesting variations for different values of $S$ and $ϕ$, which helps in determining the steady-state condition for a given substrate.

physics.soc-ph↗

arXiv2007

Effect of a static phase transition on searching dynamics

We consider a one dimensional Euclidean network which is grown using a preferential attachment. Here the $j$th incoming node gets attached to the $i$th existing node with the probability $Π_i \propto k_i {l}_{ij}^α$, where ${l}_{ij}$ is the Euclidean distance between them and $k_i$ the degree of the $i$th node. This network is known to have a static phase transition point at $α_c \simeq 0.5$. 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.

cond-mat.stat-mech↗

arXiv2006

Modelling temporal and spatial features of collaboration network

The collaboration network is an example of a social network which has both non-trivial temporal and spatial dependence. Based on the observations of collaborations in Physical Review Letters, a model of collaboration network is proposed which correctly reproduces the time evolution of the link length distributions, clustering coefficients, degree distributions and assortative property of real data to a large extent.

physics.soc-ph↗

arXiv2006

Earthquake aftershock networks generated on Euclidean spaces of different fractal geometry

According to some recent analysis (M. Baiesi and M. Paczuski, Phys. Rev. E {\bf 69}, 066106, 2004 \cite{maya1}) of earthquake data, aftershock epicenters can be considered to represent the nodes of a network where the linking scheme depends on several factors. In the present paper a model network of earthquake aftershock epicenters is proposed based on this scheme and studied on fractals of different dimensions. The various statistical features of this network, like degree, link length, frequency and correlation distributions are evaluated and compared to the observed data. The results are also found to be independent of the fractal geometry.

cond-mat.stat-mech↗

arXiv2006

Time evolution of link length distribution in PRL collaboration network

An important aspect of a Euclidean network is its link length distribution, studied in a few real networks so far. We compute the distribution of the link lengths between collaborators whose papers appear in the PhysicalReview Letters (PRL) in several years within a range of four decades. The distribution is non-monotonic; there is a peak at nearest neighbour distances followed by a sharp fall and a subsequent rise at larger distances. The behaviour of the statistical properties of the distribution with time indicates that collaborations might become distance independent in about thirty to forty years.

physics.soc-ph↗

arXiv2005

Modelling Aging Characteristics in Citation Networks

Growing network models with preferential attachment dependent on both age and degree are proposed to simulate certain features of citation network noted in \cite{red2}. In this directed network, a new node gets attached to an older node with the probability $\sim K(k)f(t)$ 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 $K(k) \sim k^{-β}$ and $f(t) \sim \exp(αt)$ with $β=2.0$ and $α= -0.2$ and with simple modifications in the growth scheme.

physics.soc-ph↗

arXiv2004

Aging in Citation Networks

In many growing networks, the age of the nodes plays an important role in deciding the attachment probability of the incoming nodes. For example, in a citation network, very old papers are seldom cited while recent papers are usually cited with high frequency. We study actual citation networks to find out the distribution $T(t)$ of $t$, the time interval between the published and the cited paper. For different sets of data we find a universal behaviour: $T(t) \sim t^{-0.9}$ for $t \leq t_c$ and $T(t) \sim t^{-2}$ for $t>t_c$ where $t_c \sim O(10)$.

cond-mat.other↗

arXiv2004

Phase Transitions in an Aging Network

We consider a growing network in which an incoming node gets attached to the $i^{th}$ existing node with the probability $Π_i \propto {k_i}^βτ_i^α$, where $k_{i}$ is the degree of the $i^{th}$ node and $τ_i$ its present age. The phase diagram in the ${α-β}$ plane is obtained. The network shows scale-free behaviour, i.e., the degree distribution $P(k) \sim k^{-γ}$ with $γ=3$ only along a line in this plane. Small world property, on the other hand, exists over a large region in the phase diagram.

cond-mat.stat-mech↗