arXiv subjects
Publications and source records attributed to Divya Sindhu Lekha.
The median $M$ of a graph $G$ is the set of vertices with a minimum total distance to all other vertices in the graph. In this paper, we determine the median of Sierpiński triangle graphs. Sierpiński triangle graphs, also known as Sierpiński gasket graphs of order $n$ are graphs formed by contracting all non-clique edges from the Sierpiński graphs of order ($n+1$).
In this work, we analyse and predict the stability of communities in complex networks. We use a variant of closeness centrality, known as profile closeness, to measure the loyalty of a member towards its community. We show that the profile closeness is an adequate indicator of how communities evolve in a network. We investigate this in static as well as dynamic (temporal) networks and establish the relevance of profile closeness in predicting the evolution of a complex network. Keywords: Small world networks , Centrality , Community , Closeness , Clustering
Central nodes are critical in establishing structural connectivity in a complex network. Attacking such nodes can create real havoc in a complex system. We propose attack strategies based on four types of centers, namely betweenness center, degree center, median, and center. We study the vulnerability of synthetic as well as real-world networks in these center-based attacks. These attacks are node-removal attacks which involve identifying the central node set and removing them from the network. We observed that the attacks based on recalculated network information are more efficient than ones based on initial network information. This work shows that the median-based attack, which is a novel strategy proposed in this work, is highly destructive in real as well as synthetic networks.
In this paper, we introduce a generalized concept of vertex transitivity in graphs called generalized vertex transitivity. We put forward a new invariant called transitivity number of a graph. The value of this invariant in different classes of graphs is explored. Also, different results showing the importance of this concept is established.