Machine learning on graphs is an important and ubiquitous task with applications ranging from drug design to friendship recommendation in social networks. The primary challenge in this domain is finding a way to represent, or encode, graph structure so that it can be easily exploited by machine learning models. Traditionally, machine learning approaches relied on user-defined heuristics to extr...

Online social networks (OSNs) are becoming increasingly popular in recent years, which have generated great interest in studying the influence diffusion and influence maximization with applications to online viral marketing. Existing studies focus on social networks with only friendship relations, whereas the foe or enemy relations that commonly exist in many OSNs, e.g., Epinions and Slashdot, ...

Large graphs are prevalent in social networks, traffic networks, and biology. These graphs are often inexact. For example, in a friendship network, an edge between two nodesu andv indicates that users u and v have a close relationship. This edge may only exist with a probability. To model such information, the uncertain graph model has been proposed, in which each edge e is augmented with a pro...

Many real-world problems are represented by using graphs. For example, given a graph of a chemical compound, we want do determine whether it causes a gene mutation or not. As another example, given a graph of a social network, we want to predict a potential friendship that does not exist but it is likely to appear soon. Many of these questions can be answered by using machine learning methods i...

Social networks and collaborative tagging systems are rapidly gaining popularity as a primary means for storing and sharing data among friends, family, colleagues, or perfect strangers as long as they have common interests. del.icio.us is a social network where people store and share their personal bookmarks. Most importantly, users tag their bookmarks for ease of information dissemination and ...

We examine the simultaneous embedding with fixed edges problem for two planar graphs G1 and G2 with the focus on their intersection S = G1∩G2. In particular, we will present the complete set of intersection graphs S that guarantee a simultaneous embedding with fixed edges for (G1, G2). More formally, we define the subset ISEFE of all planar graphs as follows: A graph S lies in ISEFE if every pa...

We prove that the unique decomposition of connected graphs defined by Tutte is definable by formulas of Monadic Second-Order Logic. This decomposition has two levels: every connected graph is a tree of "2-connected components" called blocks ; every 2-connected graph is a tree of so-called 3-blocks. Our proof uses 2dags which are certain acyclic orientations of the considered graphs. We obtain a...

The rank-width is a graph parameter related in terms of fixed functions to cliquewidth but more tractable. Clique-width has nice algorithmic properties, but no good “minor” relation is known analogous to graph minor embedding for tree-width. In this paper, we discuss the vertex-minor relation of graphs and its connection with rank-width. We prove a relationship between vertex-minors of bipartit...

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