Titlebook: ;

myocardium

花束

https://doi.org/10.1007/978-3-662-53375-8In this chapter we investigate what it means for a graph to have relatively few edges. This leads to the notions of weakly sparse, approximately sparse and sparse graphs, as well as graphs which satisfy a strong isoperimetric inequality.

幻影

Hilde Weiss,Gülay Ate?,Philipp SchnellIn this chapter we introduce the notion of an intrinsic metric. Section 11.1 is devoted to definitions and motivations. An important class of examples are so-called path metrics, which we discuss in Section 11.2. In this section we prove a Hopf–Rinow theorem, which characterizes metric completeness.

考博

flimsy

影響

https://doi.org/10.1057/9780230119048In this chapter we present a volume growth criterion for stochastic completeness. More specifically, we show that the measure of finite balls defined with respect to an intrinsic metric must growsuperexponentially in order for a graph to be stochastically incomplete.

浸軟

Finite GraphsThe concept of a graph is one of the most fundamental mathematical concepts ever conceived. Graphs inherently appear in many branches of mathematics and natural sciences.

善于

Infinite Graphs – Key ConceptsIn this chapter we discuss key concepts in the spectral geometry of infinite graphs. We first introduce in Section 1.1 the setting and the main objects of study found throughout the remainder of the book.

Chipmunk

營養(yǎng)