Property testing is a relaxation of decision problems
in which it is required to distinguish {\sc yes}-instances
(i.e., objects having a predetermined property) from instances
that are far from any {\sc yes}-instance.
We presents three theorems regarding testing graph
properties in the adjacency matrix representation.
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In this paper we consider two refined questions regarding
the query complexity of testing graph properties
in the adjacency matrix model.
The first question refers to the relation between adaptive
and non-adaptive testers, whereas the second question refers to
testability within complexity that
is inversely proportional to ... more >>>

We initiate a systematic study of a special type of property testers.
These testers consist of repeating a basic test
for a number of times that depends on the proximity parameters,
whereas the basic test is oblivious of the proximity parameter.
We refer to such basic tests ... more >>>

Referring to the query complexity of property testing,
we prove the existence of a rich hierarchy of corresponding
complexity classes. That is, for any relevant function $q$,
we prove the existence of properties that have testing
complexity Theta(q).
Such results are proven in three standard
domains often considered in property ... more >>>

Detecting and counting the number of copies of certain subgraphs (also known as {\em network motifs\/} or {\em graphlets\/}), is motivated by applications in a variety of areas ranging from Biology to the study of the World-Wide-Web. Several polynomial-time algorithms have been suggested for counting or detecting the number of ... more >>>

The aim of this article is to introduce the reader to the study
of testing graph properties, while focusing on the main models
and issues involved. No attempt is made to provide a
comprehensive survey of this study, and specific results
are often mentioned merely as illustrations of general ... more >>>