Doctors and clients sometimes experience interactive clashes during hospital meetings in South-western Nigerian hospitals because of their divergent culture-constrained orientation to politeness cues. The goal of this paper is to unpack the discursive elements that characterize interactive confluence and divergence in selected consultative encounters in the hospitals. The findings indicate that...

A digraph Γ is called n-Cayley digraph over a group G, if there exists a semiregular subgroup RG of Aut(Γ) isomorphic to G with n orbits. In this paper, we represent the adjacency matrix of Γ as a diagonal block matrix in terms of irreducible representations of G and determine its characteristic polynomial. As corollaries of this result we find: the spectrum of semi-Cayley graphs over abelian g...

The total graph is built by joining the to its line means of incidences. We introduce a similar construction for signed graphs. Under two defnitions graph, we defne corresponding and show that it stable under switching. consider balance, frustration index number, largesteigenvalue. In regular case compute spectrum adjacency matrix spectra certain compositions, determine some with exactly main e...

A graph G is divisible by a H if the characteristic polynomial of that H. In this paper, necessary and sufficient condition for recursive graphs to be path used show H-shape P2,2;n−42,n−7, known (for n large enough) minimizer spectral radius among order diameter n−5, determined its adjacency spectrum only n≠10,13,15.

Common techniques in collaborative filtering rely on finding low-rank matrix approximations to the adjacency matrix (ratings that users assign to items), essentially representing users and items as a collection of a small number of latent features. One issue that arises in many real world datasets for collaborative filtering is that the number of observed entries per row/column follows a heavy-...

Community structure analysis is a powerful tool for complex networks, which can simplify their functional analysis considerably. Many approaches have recently been proposed to the communities in complex networks, but a method to characterize the node importance to communities is still lacking. In this paper a centrality metric is proposed to measure the importance of network nodes to community ...

A mixed graph means a graph containing both oriented edges and undirected edges. The nullity of the Hermitian-adjacency matrix of a mixed graph G, denoted by ηH(G), is referred to as the multiplicity of the eigenvalue zero. In this paper, for a mixed unicyclic graph G with given order and matching number, we give a formula on ηH(G), which combines the cases of undirected and oriented unicyclic ...

Mean-field approximations (MFAs) are frequently used in physics. When a process (such as an epidemic or a synchronization) on a network is approximated by MFA, a major hurdle is the determination of those graphs for which MFA is reasonably accurate. Here, we present an accuracy criterion for Markovian susceptible-infected-susceptible (SIS) epidemics on any network, based on the spectrum of the ...

Notation: λ1(A) = largest eigenvalue of A. Motivation: The largest eigenvalue tells us the spectrum of a matrix and thus can be somewhat useful. More crucially for the adjacency matrix of a graph, we know exactly that the all one’s vector is the largest eigenvector, and thus by working orthogonal to this vector we can approximate the second largest eigenvalue of the graph, which tells us how we...

Let G be a graph on n vertices. Its Laplacian matrix is the n-by-n matrix L(G) = D(G) A(G), where A(G) is the familiar (0, 1) adjacency matrix, and D(G) is the diagonal matrix of vertex degrees. This is primarily an expository article surveying some of the many results known for Laplacian matrices. Its six sections are: Introduction, The Spectrum, The Algebraic Connectivity, Congruence and Equi...