Studies on some graph operators and related topics

Department of Mathematics, Cochin University of Science and Technology

Studies on Some Graph Classes

Department of Mathematics, Cochin University of Science and Technology

Studies on some generalizations of line graph and the power domination problem in graphs

Department of Mathematics, Cochin University of Science and Technology

Strongly distance-balanced graphs and graph products

A graph G is strongly distance-balanced if for every edge uv of G and every i 0 the number of vertices x with d.x; u/ D d.x; v/ 1 D i equals the number of vertices y with d.y; v/ D d.y; u/ 1 D i. It is proved that the strong product of graphs is strongly distance-balanced if and only if both factors are strongly distance-balanced. It is also proved that connected components of the direct product of two bipartite graphs are strongly distancebalanced if and only if both factors are strongly distance-balanced. Additionally, a new characterization of distance-balanced graphs and an algorithm of time complexity O.mn/ for their recognition, wheremis the number of edges and n the number of vertices of the graph in question, are given

Median Sets and Median Number of a Graph

A profile is a finite sequence of vertices of a graph. The set of all vertices of the graph which minimises the sum of the distances to the vertices of the profile is the median of the profile. Any subset of the vertex set such that it is the median of some profile is called a median set. The number of median sets of a graph is defined to be the median number of the graph. In this paper, we identify the median sets of various classes of graphs such as Kp − e, Kp,q forP > 2, and wheel graph and so forth. The median numbers of these graphs and hypercubes are found out, and an upper bound for the median number of even cycles is established.We also express the median number of a product graph in terms of the median number of their factors.

On The Center Sets and Center Numbers of Some Graph Classes

For a set S of vertices and the vertex v in a connected graph G, max x2S d(x, v) is called the S-eccentricity of v in G. The set of vertices with minimum S-eccentricity is called the S-center of G. Any set A of vertices of G such that A is an S-center for some set S of vertices of G is called a center set. We identify the center sets of certain classes of graphs namely, Block graphs, Km,n, Kn −e, wheel graphs, odd cycles and symmetric even graphs and enumerate them for many of these graph classes. We also introduce the concept of center number which is defined as the number of distinct center sets of a graph and determine the center number of some graph classes

Content aggregation on knowledge bases using graph clustering

Recently, research projects such as PADLR and SWAP have developed tools like Edutella or Bibster, which are targeted at establishing peer-to-peer knowledge management (P2PKM) systems. In such a system, it is necessary to obtain provide brief semantic descriptions of peers, so that routing algorithms or matchmaking processes can make decisions about which communities peers should belong to, or to which peers a given query should be forwarded. This paper proposes the use of graph clustering techniques on knowledge bases for that purpose. Using this clustering, we can show that our strategy requires up to 58% fewer queries than the baselines to yield full recall in a bibliographic P2PKM scenario.

Understanding Subsystems in Biology through Dimensionality Reduction, Graph Partitioning and Analytical Modeling

Biological systems exhibit rich and complex behavior through the orchestrated interplay of a large array of components. It is hypothesized that separable subsystems with some degree of functional autonomy exist; deciphering their independent behavior and functionality would greatly facilitate understanding the system as a whole. Discovering and analyzing such subsystems are hence pivotal problems in the quest to gain a quantitative understanding of complex biological systems. In this work, using approaches from machine learning, physics and graph theory, methods for the identification and analysis of such subsystems were developed. A novel methodology, based on a recent machine learning algorithm known as non-negative matrix factorization (NMF), was developed to discover such subsystems in a set of large-scale gene expression data. This set of subsystems was then used to predict functional relationships between genes, and this approach was shown to score significantly higher than conventional methods when benchmarking them against existing databases. Moreover, a mathematical treatment was developed to treat simple network subsystems based only on their topology (independent of particular parameter values). Application to a problem of experimental interest demonstrated the need for extentions to the conventional model to fully explain the experimental data. Finally, the notion of a subsystem was evaluated from a topological perspective. A number of different protein networks were examined to analyze their topological properties with respect to separability, seeking to find separable subsystems. These networks were shown to exhibit separability in a nonintuitive fashion, while the separable subsystems were of strong biological significance. It was demonstrated that the separability property found was not due to incomplete or biased data, but is likely to reflect biological structure.

Web Graph

Slides and an essay on the Web Graph, search engines and how Google calculates Page Rank

Graph Theory and Social Networks Tutorial

For COMP60

Social Media Analytics: Trust and Power

In this lecture for a second year interdisciplinary course (part of the curriculum innovation programme) We explore the scope of social media analytics and look at two aspects in depth: Analysing for influence (looking at factors such as network structure, propagation of content and interaction), and analysing for trust (looking at different methods including policy, provenance and reputation - both local and global). The lecture notes include a number of short videos, which cannot be included here for copy-write reasons.

WAIS seminar: Provenance Analytics and Crowdsourcing

Wednesday 26th March 2014 Speaker(s): Dr Trung Dong Huynh Organiser: Dr Tim Chown Time: 26/03/2014 11:00-11:50 Location: B32/3077 File size: 349Mb Abstract Understanding the dynamics of a crowdsourcing application and controlling the quality of the data it generates is challenging, partly due to the lack of tools to do so. Provenance is a domain-independent means to represent what happened in an application, which can help verify data and infer their quality. It can also reveal the processes that led to a data item and the interactions of contributors with it. Provenance patterns can manifest real-world phenomena such as a significant interest in a piece of content, providing an indication of its quality, or even issues such as undesirable interactions within a group of contributors. In this talk, I will present an application-independent methodology for analysing provenance graphs, constructed from provenance records, to learn about such patterns and to use them for assessing some key properties of crowdsourced data, such as their quality, in an automated manner. I will also talk about CollabMap (www.collabmap.org), an online crowdsourcing mapping application, and show how we applied the approach above to the trust classification of data generated by the crowd, achieving an accuracy over 95%.

Web Science and Data Analytics Course

Resources from the Singapore Summer School 2014 hosted by NUS. ws-summerschool.comp.nus.edu.sg

Scalable real-time crisis mapping and analytics of social media streams for disaster management and breaking news

Real-time geoparsing of social media streams (e.g. Twitter, YouTube, Instagram, Flickr, FourSquare) is providing a new 'virtual sensor' capability to end users such as emergency response agencies (e.g. Tsunami early warning centres, Civil protection authorities) and news agencies (e.g. Deutsche Welle, BBC News). Challenges in this area include scaling up natural language processing (NLP) and information retrieval (IR) approaches to handle real-time traffic volumes, reducing false positives, creating real-time infographic displays useful for effective decision support and providing support for trust and credibility analysis using geosemantics. I will present in this seminar on-going work by the IT Innovation Centre over the last 4 years (TRIDEC and REVEAL FP7 projects) in building such systems, and highlights our research towards improving trustworthy and credible of crisis map displays and real-time analytics for trending topics and influential social networks during major news worthy events.