In computer networks, toughness is an important parameter which is used to measure the vulnerability of the network. Zhou et al. [24] obtains a toughness condition for a graph to be fractional (k,m)–deleted and presents an example to show the sharpness of the toughness bound. In this paper we remark that the previous example does not work and inspired by this fact, we present a new toughness co...

We describe a simple, fast computing and easy to implement method for finding relatively good clusterings of software systems. Our method relies on the ability to compute the strength of an edge in a graph by applying a straightforward metric defined in terms of the neighborhoods of its end vertices. The metric is used to identify the weak edges of the graph, which are momentarily deleted to br...

We investigate the relative complexity of the graph isomorphism problem (GI) and problems related to the reconstruction of a graph from its vertex-deleted or edge-deleted subgraphs (in particular, deck checking (DC) and legitimate deck (LD) problems). We show that these problems are closely related for all amounts c ≥ 1 of deletion: 1. GI ≡iso VDCc, GI ≡iso EDCc, GI ≤m LVDc, and GI ≡iso LEDc. 2...

Ambivalent data structures are presented for several problems on undirected graphs. They are used in finding the k smallest spanning trees of a weighted undirected graph in Oem log [3(m, n)+min{p/2, km1/ 2 }) time, where m is the number of edges and n the number of vertices in the graph. The techniques can be extended to find the k smallest spanning trees in an embedded planar graph in O(n + k(...

Abstract: In this paper we focus on the problem of the degree sequence for the following random graph process. At any time-step t, one of the following three substeps is executed: with probability α1, a new vertex xt and m edges incident with xt are added; or, with probability α− α1, m edges are added; or finally, with probability 1 − α, m random edges are deleted. Note that in any case edges a...

20 Background. Electronic Health Record (EHR)-based sepsis alert systems have failed to 21 demonstrate improvements in clinically meaningful endpoints. However, the effect of 22 implementation barriers on the success of new sepsis alert systems is rarely explored. 23 Objective. To test the hypothesis time to severe sepsis alert acknowledgement by critical care 24 clinicians in the ICU setting w...

In an information graph situation, a finite set of agents and source are the nodes undirected with property that two adjacent can share at no cost. The has some (or technology), in same component as reach this for free. other components, agent must pay unitary cost to obtain information. We prove core derived game is von Neumann-Morgenstern stable if only cycle-complete, or equivalently concave...

An ecard of a graph G is a subgraph formed by deleting an edge. A da-ecard specifies the degree of the deleted edge along with the ecard. The degree associated edge reconstruction number of a graph G, dern(G), is the minimum number of da-ecards that uniquely determines G. The adversary degree associated edge reconstruction number of a graph G, adern(G), is the minimum number k such that every c...

The core number of a vertex is a basic index depicting cohesiveness of a graph, and has been widely used in large-scale graph analytics. In this paper, we study the update of core numbers of vertices in dynamic graphs with edge insertions/deletions, which is known as the core maintenance problem. Different from previous approaches that just focus on the case of single-edge insertion/deletion an...