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The largest eigenvalue of the adjacency matrix of a network (referred to as the spectral radius) is an important metric in its own right. Further, for several models of epidemic spread on networks (e.g., the 'flu-like' SIS model), it has been shown that an epidemic dies out quickly if the spectral radius of the graph is below a certain threshold that… (More)

Simple diffusion processes on networks have been used to model, analyze and predict diverse phenomena such as spread of diseases, information and memes. More often than not, the underlying network data is noisy and sampled. This prompts the following natural question: how sensitive are the diffusion dynamics and subsequent conclusions to uncertainty in the… (More)

In this paper we initiate an algorithmic study of Boxicity, a combina-torially well studied graph invariant, from the viewpoint of parameterized algorithms. The boxicity of an arbitrary graph G with the vertex set V (G) and the edge set E(G), denoted by box(G), is the minimum number of interval graphs on the same set of vertices such that the intersection… (More)

Let G(V, E) be a simple, undirected graph where V is the set of vertices and E is the set of edges. A b-dimensional cube is a Cartesian product I1 × I2 × · · · × I b , where each Ii is a closed interval of unit length on the real line. The cubicity of G, denoted by cub(G) is the minimum positive integer b such that the vertices in G can be mapped to axis… (More)

The k-core is commonly used as a measure of importance and well connectedness for nodes in diverse applications in social networks and bioinformatics. Since network data is commonly noisy and incomplete, a fundamental issue is to understand how robust the core decomposition is to noise. Further, in many settings, such as online social media networks,… (More)

The spread of epidemics and malware is commonly modeled by diffusion processes on networks. Protective interventions such as vaccinations or installing anti-virus software are used to contain their spread. Typically, each node in the network has to decide its own strategy of securing itself, and its benefit depends on which other nodes are secure, making… (More)

An axis-parallel b-dimensional box is a Cartesian product R1 × R2 × · · · × R b where Ri is a closed interval of the form [ai, bi] on the real line. For a graph G, its boxicity box(G) is the minimum dimension b, such that G is representable as the intersection graph of boxes in b-dimensional space. Although boxicity was introduced in 1969 and studied… (More)

A k-box B = (R 1 , R 2 ,. .. , R k), where each R i is a closed interval on the real line, is defined to be the Cartesian product R 1 × R 2 × · · · × R k. If each R i is a unit length interval, we call B a k-cube. Boxicity of a graph G, denoted as box(G), is the minimum integer k such that G is an intersection graph of k-boxes. Similarly, the cubicity of G,… (More)