The vertex version of PI index is a molecular structure descriptor which is similar to vertex version of Szeged index. In this paper, we compute the vertex-PI index of TUC4C8(S), TUC4C8(R) and HAC5C7[r, p].

background: co-authorship is one of the most tangible forms of research collaboration. a co-authorship network is a social network in which the authors through participation in one or more publication through an indirect path have linked to each other. the present research using the social network analysis studied co-authorship network of 681 articles published in journal of research in medical...

Introduction. Functional magnetic resonance data acquired in a task-absent condition (``resting state'') require new data analysis techniques that do not depend on an activation model. Standard methods use either correlations with pre-specified seed regions or independent component analysis, both of which require assumptions about the source (seed-based) or validity (ICA) of a network. In this ...

Centrality of a node measures its relative importance within a network. There are a number of applications of centrality, including inferring the influence or success of an individual in a social network, and the resulting social network dynamics. While we can compute the centrality of any node in a given network snapshot, a number of applications are also interested in knowing the potential im...

Effective online interaction is beyond interacting with whomever. The quality of social interconnectivity matters. Social presence plays a vital role in building an effective learning community. This study empirically examined: how will predict various aspects students’ interconnectivities (i.e., in-degree, out-degree, betweenness centrality, closeness eigenvector reciprocated vertex pair ratio...

Numerous centrality measures have been developed to quantify the importances of nodes in time-independent networks, and many of them can be expressed as the leading eigenvector of some matrix. With the increasing availability of network data that changes in time, it is important to extend such eigenvector-based centrality measures to time-dependent networks. In this paper, we introduce a princi...

Given a social network, which of its nodes are more central? This question has been asked many times in sociology, psychology and computer science, and a whole plethora of centrality measures (a.k.a. centrality indices, or rankings) were proposed to account for the importance of the nodes of a network. In this paper, we try to provide a mathematically sound survey of the most important classic ...