Graphlet analysis is an approach to network analysis that is particularly popular in bioinformatics. We show how to set up a system of linear equations that relate the orbit counts and can be used in an algorithm that is significantly faster than the existing approaches based on direct enumeration of graphlets. The algorithm requires existence of a vertex with certain properties; we show that such vertex exists for graphlets of arbitrary size, except for complete graphs and @math , which are treated separately. Empirical analysis of running time agrees with the theoretical results.
Vassilevska and Williams @cite_4 studied the problem of finding and counting individual non-induced subgraphs. Their results depend on the size @math of the independent set in the pattern graph and rely on efficient computations of matrix permanents and not on fast matrix multiplication techniques like some other approaches. If we restrict the problem to counting small patterns and therefore treat @math and @math as small constants, their approach counts a non-induced pattern in @math time. This is an improvement over a simple enumeration when @math . Kowaluk @cite_10 also improved on the result of Vassilevska and Williams when @math . @cite_3 developed algorithms for counting non-induced cycles with 3 to 7 nodes in @math , where @math represents the exponent of matrix multiplication algorithms.
@cite_10 @cite_4 @cite_3
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We present a general technique for detecting and counting small subgraphs. It consists of forming special linear combinations of the numbers of occurrences of different induced subgraphs of fixed size in a graph. These combinations can be efficiently computed by rectangular matrix multiplication. Our two main results utilizing the technique are as follows. Let @math be a fixed graph with @math vertices and an independent set of size @math 1. Detecting if an @math -vertex graph contains a (not necessarily induced) subgraph isomorphic to @math can be done in time @math , where @math is the exponent of fast arithmetic matrix multiplication of an @math matrix by an @math matrix. 2. When @math counting the number of (not necessarily induced) subgraphs isomorphic to @math can be done in the same time, i.e., in time @math It follows in particular that we can count the nu... The role of self-relevance has been somewhat neglected in static face processing paradigms but may be important in understanding how emotional faces impact on attention, cognition and affect. The aim of the current study was to investigate the effect of self-relevant primes on processing emotional composite faces. Sentence primes created an expectation of the emotion of the face before sad, happy, neutral or composite face photos were viewed. Eye movements were recorded and subsequent responses measured the cognitive and affective impact of the emotion expressed. Results indicated that primes did not guide attention, but impacted on judgments of valence intensity and self-esteem ratings. Negative self-relevant primes led to the most negative self-esteem ratings, although the effect of the prime was qualified by salient facial features. Self-relevant expectations about the emotion of a face and subsequent attention to a face that is congruent with these expectations strengthened the affective impact of viewing the face.