We address the question of finding the community structure of a complex network. In an earlier effort [H. Zhou, Phys. Rev. E 67, 041908 (2003)], the concept of network random walking is introduced and a distance measure defined. Here we calculate, based on this distance measure, the dissimilarity index between nearest-neighboring vertices of a network and design an algorithm to partition these ...

Let λ1, λ2, · · · , λn be the eigenvalues of the distance matrix of a connected graph G. The distance Estrada index of G is defined as DEE(G) = ∑ n i=1 ei . In this note, we present new lower and upper bounds for DEE(G). In addition, a Nordhaus-Gaddum type inequality for DEE(G) is given. MSC 2010: 05C12, 15A42.

A new topological index J (based on distance sums s i as graph invariants) is proposed. For unsaturated or aromatic compounds, fractional bond orders are used in calculating s i. The degeneracy of J is lowest among all single topological indices described so far. The asymptotic behaviour of J is discussed, e.g. when n ~ ~ in CnH2n+2, J ~ ~r for linear alkanes, and J ~ ** for highly branched ones.

let g be a connected simple (molecular) graph. the distance d(u, v) between two vertices u and v of g is equal to the length of a shortest path that connects u and v. in this paper we compute some distance based topological indices of h-phenylenic nanotorus. at first we obtain an exactformula for the wiener index. as application we calculate the schultz index and modified schultz index of this ...

We present a unified approach to the design of social index numbers. Our starting point is model that employs an exogenously given partition population into subgroups. Three classes group-dependent measures deprivation are characterized. The three groups nested and, beginning with largest these, we narrow them down by successively adding two additional axioms. This leads parameterized class mem...

As highly discriminant distance-based topological indices, the Balaban index and the sum-Balaban index of a graph $G$ are defined as $J(G)=frac{m}{mu+1}sumlimits_{uvin E} frac{1}{sqrt{D_{G}(u)D_{G}(v)}}$ and $SJ(G)=frac{m}{mu+1}sumlimits_{uvin E} frac{1}{sqrt{D_{G}(u)+D_{G}(v)}}$, respectively, where $D_{G}(u)=sumlimits_{vin V}d(u,v)$ is the distance sum of vertex $u$ in $G$, $m$ is the n...