The ontogeny of large-scale functional organization of the human brain is not well understood. Here we use network analysis of intrinsic functional connectivity to characterize the organization of brain networks in 23 children (ages 7-9 y) and 22 young-adults (ages 19-22 y). Comparison of network properties, including path-length, clustering-coefficient, hierarchy, and regional connectivity, re...

By blocking dopamine and norepinephrine transporters, methylphenidate affects cognitive performance and regional brain activation in healthy individuals as well as those with neuropsychiatric disorders. Resting-state connectivity evaluates the functional integrity of a network of brain regions. Here, we examined how methylphenidate effects resting-state functional connectivity of the dorsal str...

A graph is said to be P 4-connected if for every partition of its vertex-set into two nonempty disjoint sets, some P 4 in the graph has vertices from both sets in the partition. A P 4-chain is a sequence of vertices such that every four consecutive ones induce a P 4. The main result of this work states that a graph is P 4-connected if and only if each pair of vertices is connected by a P 4-chai...

We prove that, if M is a weakly 4-connected matroid with |E(M)| 7 and neither M nor M∗ is isomorphic to the cycle matroid of a ladder, then M has a proper minor M ′ such that M ′ is weakly 4-connected and |E(M ′)| |E(M)| − 2 unless M is some 12-element matroid with a special structure. © 2007 Elsevier Inc. All rights reserved.

Let G be a simple connected graph and t be a given real number. The zero-order general Randić index αt(G) of G is defined as ∑ v∈V (G) d(v) t , where d(v) denotes the degree of v. In this paper, for any t , we characterize the graphs with the greatest and the smallest αt within two subclasses of connected unicyclic graphs on n vertices, namely, unicyclic graphs with k pendant vertices and unicy...

The Randić index R(G) of a graph G is defined as the sum of 1 √dudv over all edges uv of G, where du and dv are the degrees of vertices u and v, respectively. Let D(G) be the diameter of Gwhen G is connected. Aouchiche et al. (2007) [1] conjectured that among all connected graphs G on n vertices the path Pn achieves the minimum values for both R(G)/D(G) and R(G) − D(G). We prove this conjecture...

A graph G is weakly 4-connected if it is 3-connected, has at least five vertices, and for every pair (A,B) such that A ∪ B = V (G), |A ∩ B| = 3 and no edge has one end in A − B and the other in B − A, one of the induced subgraphs G[A], G[B] has at most four edges. We describe a set of constructions that starting from a weakly 4-connected planar graph G produce a finite list of non-planar weakly...

Let G be a connected graph, suppose that v is a vertex of G, and denote the subgraph formed from G by deleting vertex v by G \ v. Denote the algebraic connectivities of G and G \ v by α(G) and α(G \ v), respectively. In this paper, we consider the functions φ(v) = α(G) − α(G \ v) and κ(v) = α(G\v) α(G) , provide attainable upper and lower bounds on both functions, and characterise the equality ...

Amnestic mild cognitive impairment (aMCI) is a transitional stage between normal cognitive aging and Alzheimer's disease. Previous studies have found that neuronal activity and functional connectivity impaired in many functional networks, especially in the default mode network (DMN), which is related to significantly impaired cognitive and memory functions in aMCI patients. However, few studies...

We study the connectivity properties of an ad hoc network consisting of a given number of nodes each moving according to the Random Waypoint mobility model. Connectivity properties of networks with uniformly distributed nodes are well known, but the movement in the RWP model results in a spatial node distribution which is not uniform. Approximations are provided for the probability that the net...