Related papers: Pattern detection in ordered graphs
Network motif algorithms have been a topic of research mainly after the 2002-seminal paper from Milo \emph{et al}, that provided motifs as a way to uncover the basic building blocks of most networks. In Bioinformatics, motifs have been…
Visualization of the adjacency matrix enables us to capture macroscopic features of a network when the matrix elements are aligned properly. Community structure, a network consisting of several densely connected components, is a…
Design patterns being applied more and more to solve the software engineering difficulties in the object oriented software design procedures. So, the design pattern detection is widely used by software industries. Currently, many solutions…
Detecting which nodes in graphs are outliers is a relatively new machine learning task with numerous applications. Despite the proliferation of algorithms developed in recent years for this task, there has been no standard comprehensive…
We revisit the algorithmic problem of finding a triangle in a graph: We give a randomized combinatorial algorithm for triangle detection in a given $n$-vertex graph with $m$ edges running in $O(n^{7/3})$ time, or alternatively in…
Network detection is an important capability in many areas of applied research in which data can be represented as a graph of entities and relationships. Oftentimes the object of interest is a relatively small subgraph in an enormous,…
The class of closed graphs by a linear ordering on their sets of vertices is investigated. A recent characterization of such a class of graphs is analyzed by using tools from the proper interval graph theory.
Over the years, much research involving mobile computational entities has been performed. From modeling actual microscopic (and smaller) robots, to modeling software processes on a network, many important problems have been studied in this…
The three-in-a-tree problem is to determine if a simple undirected graph contains an induced subgraph which is a tree connecting three given vertices. Based on a beautiful characterization that is proved in more than twenty pages,…
Many real-world applications give rise to large heterogeneous networks where nodes and edges can be of any arbitrary type (e.g., user, web page, location). Special cases of such heterogeneous graphs include homogeneous graphs, bipartite,…
In this paper, we present two main results. First, by only one conjecture (Conjecture 2.9) for recognizing a vertex symmetric graph, which is the hardest task for our problem, we construct an algorithm for finding an isomorphism between two…
This work examines the problem of graph learning over a diffusion network when data can be collected from a limited portion of the network (partial observability). The main question is to establish technical guarantees of consistent…
We study the first-order (FO) model checking problem of dense graphs, namely those which have FO interpretations in (or are FO transductions of) some sparse graph classes. We give a structural characterization of the graph classes which are…
Understanding how a vertex relates to a set of vertices is a fundamental task in graph analysis. Given a graph $G$ and a vertex set $X \subseteq V(G)$, consider the collection of subsets of the form $N(u) \cap X$ where $u$ ranges over all…
Identifying frequent subgraphs, also called network motifs, is crucial in analyzing and predicting properties of real-world networks. However, finding large commonly-occurring motifs remains a challenging problem not only due to its NP-hard…
In the age of social computing, finding interesting network patterns or motifs is significant and critical for various areas such as decision intelligence, intrusion detection, medical diagnosis, social network analysis, fake news…
We introduce the class of interval $H$-graphs, which is the generalization of interval graphs, particularly interval bigraphs. For a fixed graph $H$ with vertices $a_1,a_2,\dots,a_k$, we say that an input graph $G$ with given partition…
Let H be a connected bipartite graph with n nodes and m edges. We give an O(nm) time algorithm to decide whether H is an interval bigraph. The best known algorithm has time complexity O(nm^6(m + n) \log n) and it was developed in 1997 [18].…
We provide a fast distributed algorithm for detecting $h$-cycles in the \textsf{Congested Clique} model, whose running time decreases as the number of $h$-cycles in the graph increases. In undirected graphs, constant-round algorithms are…
In the graph clustering problem with a planted solution, the input is a graph on $n$ vertices partitioned into $k$ clusters, and the task is to infer the clusters from graph structure. A standard assumption is that clusters induce…