Académie serbe des sciences et des arts-2004 Classe des sciences mathématiques et naturelles sciences mathématiques, N o 29 A b s t r a c t. The generalized inverse L † of the Laplacian matrix of a connected graph is examined and some of its properties are established. In some physical and chemical considerations the quantity r ij = (L †) ii + (L †) jj − (L †) ij − (L †) ji is encountered; it i...

We propose a new graph metric and study its properties. In contrast to the standard distance in connected graphs [5], it takes into account all paths between vertices. Formally, it is defined as d(i, j) = qii+qjj−qij−qji [11], where qij is the (i, j)-entry of the relative forest accessibility matrix Q(ε) = (I + εL)−1, L is the Laplacian matrix of the (weighted) (multi)graph, and ε is a positive...

We propose a new graph metric and study its properties. In contrast to the standard distance in connected graphs [5], it takes into account all paths between vertices. Formally, it is defined as d(i, j) = qii+qjj−qij−qji [11], where qij is the (i, j)-entry of the relative forest accessibility matrix Q(ε) = (I + εL)−1, L is the Laplacian matrix of the (weighted) (multi)graph, and ε is a positive...

In data analysis, there is a strong demand for graph metrics that differ from the classical shortest path and resistance distances. Recently, several new classes of graph metrics have been proposed. This paper presents some of them featuring the cutpoint additive distances. These include the path distances, the reliability distance, the walk distances, and the logarithmic forest distances among...

We propose a new graph metric and study its properties. In contrast to the standard distance in connected graphs [5], it takes into account all paths between vertices. Formally, it is defined as d(i, j) = qii+qjj−qij−qji [11], where qij is the (i, j)-entry of the relative forest accessibility matrix Q(ε) = (I + εL)−1, L is the Laplacian matrix of the (weighted) (multi)graph, and ε is a positive...

protein structural flexibility is important for catalysis, binding, protein design, and allostery. some simple methods have recently been introduced to compute protein flexibility directly from the protein structure without any mechanical models. for example the atomic mean square displacement (or b-factor) is related to the number of neighboring atoms. the protein structure can be modeled as a...