Estimation of Cliques in a Random Graph
نویسندگان
چکیده
This paper examines methods for predicting and estimating the number of maximal cliques in a random graph. A clique is a subgraph where each vertex is connected to every other vertex in the subgraph. A maximal clique is a clique which is not a proper subgraph of another clique. There are many algorithms that enumerate all maximal cliques in a graph, but since the task can take exponential time, there are practical limits on the size of the input. In this paper, we examine three methods that could be used to estimate the number of cliques in a random graph. One method is based on sampling, another on probability arguments and the third uses curve fitting. We compare the methods for accuracy and efficiency.
منابع مشابه
Cohen-Macaulay $r$-partite graphs with minimal clique cover
In this paper, we give some necessary conditions for an $r$-partite graph such that the edge ring of the graph is Cohen-Macaulay. It is proved that if there exists a cover of an $r$-partite Cohen-Macaulay graph by disjoint cliques of size $r$, then such a cover is unique.
متن کاملConditional Random Fields for XML Trees
We present xml Conditional Random Fields (xcrfs), a framework for building conditional models to label xml data. xcrfs are Conditional Random Fields over unranked trees (where every node has an unbounded number of children). The maximal cliques of the graph are triangles consisting of a node and two adjacent children. We equip xcrfs with efficient dynamic programming algorithms for inference an...
متن کاملA Markov Random Field Model for Bilevel Cutset Reconstruction
A bilevel image can be modeled by the Markov random field (MRF). Let G = (V,E) be an 8-connected graph, where V and E denote the nodes (vertices) and edges, modeling the pixels and the connectivities in an image, respectively. The MRF with 2-point cliques is defined on the 8-connected graph. The 2-point cliques consist of horizontal, vertical and diagonal neighboring nodes (Figure 1a). A node i...
متن کاملCounting cliques and clique covers in random graphs
We study the problem of counting the number of isomorphic copies of a given template graph, say H , in the input base graph, say G. In general, this is (provably) very hard to solve efficiently. So, a lot of work has gone into designing efficient approximation schemes, especially, when H is a perfect matching. In this work, we present schemes to count k-cliques and k-clique covers. Our embeddin...
متن کاملNumber of cliques in random scale-free network ensembles
In this paper we calculate the average number of cliques in random scale-free networks. We consider first the hidden variable ensemble and subsequently the Molloy Reed ensemble. In both cases we find that cliques, i.e. fully connected subgraphs, appear also when the average degree is finite. This is in contrast to what happens in Erdös and Renyi graphs in which diverging average degree is requi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2010