Graphs can be used to represent and reason about systems a variety of metrics have been devised quantify their global characteristics. However, little is currently known how construct graph or improve an existing one given target objective. In this work, we formulate the construction as decision-making process in which central agent creates topologies by trial error receives rewards proportiona...

It is well-known that any nite simple graph ? is an induced sub-graph of some exponentially larger strongly regular graph ? (e.g. 2, 8]). No general polynomial-size construction has been known. For a given-nite simple graph ? on v vertices we present a construction of a strongly regular graph ? on O(v 4) vertices that contains ? as its induced sub-graph. A discussion is included of the size of ...

For a family F of graphs, a graph U is induced-universal for F if every graph in F is an induced subgraph of U . We give a construction for an induceduniversal graph for the family of graphs on n vertices with degree at most r, which has Cnb(r+1)/2c vertices and Dn2b(r+1)/2c−1 edges, where C and D are constants depending only on r. This construction is nearly optimal when r is even in that such...

Given a directed graph, there exists a universal operator algebra and universal C-algebra associated to the directed graph. In this paper we give intrinsic constructions of these objects. We provide an explicit construction for the maximal C-algebra of an operator algebra. We also discuss uniqueness of the universal algebras for finite graphs, showing that for finite graphs the graph is an isom...

A recent trend in health-related machine learning proposes the use of Graph Neural Networks (GNN’s) to model biomedical data. This is justified due complexity healthcare data and modelling power graph abstractions. Thus, GNN’s emerge as natural choice learn from increasing amounts While formulating problem, however, there are usually multiple design choices decisions that can affect final perfo...

Semi-Supervised Learning (SSL) techniques have become very relevant since they require a small set of labeled data. In this scenario, graph-based SSL algorithms provide a powerful framework for modeling manifold structures in high-dimensional spaces and are effective for the propagation of the few initial labels present in training data through the graph. An important step in graph-based SSL me...

As a powerful model to represent the data, graph has been widely applied to many machine learning tasks. More notably, to address the problems associated with the traditional graph construction methods, sparse representation has been successfully used for graph construction, and one typical work is L1graph. However, since L1-graph often establishes only part of all the valuable connections betw...