The persistence of homological features in simplicial complex representations of big datasets in R n resulting from Vietoris-Rips or Čech filtrations is commonly used to probe the topological structure of such datasets. In this paper, the notion of homological persistence in simplicial complexes obtained from power filtrations of graphs is introduced. Specifically, the rth complex, r ≥ 1, in su...

The harmonic in distribution systems becomes an important problem due to an increase in nonlinear loads. This paper presents a new approach based on a graph algorithm for optimum placement of passive harmonic filters in a multi-bus system, which suffers from harmonic current sources. The objective of this paper is to minimize the network loss, the cost of the filter and the total harmonic disto...

In this paper we study the special case of Graphic TSP where the underlying graph is a power law graph (PLG). We give a refined analysis of some of the current best approximation algorithms and show that an improved approximation ratio can be achieved for certain ranges of the power law exponent β. For the value of power law exponent β = 1.5 we obtain an approximation ratio of 1.34 for Graphic ...

Modeling power transmission networks is an important area of research with applications such as vulnerability analysis, study of cascading failures, and location of measurement devices. Graph-theoretic approaches have been widely used to solve these problems, but are subject to several limitations. One of the limitations is the ability to model a heterogeneous system in a consistent manner usin...

The small-world phenomenon includes both small average distance and the clustering effect. Randomly generated graphs with a power law degree distribution are widely used to model large real-world networks, but while these graphs have small average distance, they generally do not exhibit the clustering effect. We introduce an improved hybrid model that combines a global graph (a random power law...

In this paper, we propose a new graph sampling method for online social networks that achieves the following. First, a sample graph should reflect the ratio between the number of nodes and the number of edges of the original graph. Second, a sample graph should reflect the topology of the original graph. Third, sample graphs should be consistent with each other when they are sampled from the sa...

Scale free graphs can be found very often as models of real networks and are characterized by a power law degree distribution, that is, for a constant γ ≥ 1 the number of vertices of degree d is proportional to d−γ . Experimental studies show that the eigenvalue distribution also follows a power law for the highest eigenvalues. Hence it has been conjectured that the power law of the degrees det...

Topology control is the problem of assigning transmission power values to the nodes of an ad hoc network so that the induced graph satisfies some specified property. The most fundamental such property is that the network/graph be connected. For connectivity, prior work on topology control gave a polynomial time algorithm for minimizing the maximum power assigned to any node (such that the induc...