Abstract

Abstract
With recent advances in high-throughput cell biology, the amount of cellular biological data has grown drastically. Such data is often modeled as graphs (also called networks) and studying them can lead to new insights intomolecule-level organization. A possible way to understand their structure is by analyzing the smaller components that constitute them, namely network motifs and graphlets. Graphlets are particularly well suited to compare networks and to assess their level of similarity due to the rich topological information that they offer but are almost always used as small undirected graphs of up to five nodes, thus limiting their applicability in directed networks. However, a large set of interesting biological networks such asmetabolic, cell signaling, or transcriptional regulatory networks are intrinsically directional, and using metrics that ignore edge direction may gravely hinder information extraction. Our main purpose in this work is to extend the applicability of graphlets to directed networks by considering their edge direction, thus providing a powerful basis for the analysis of directed biological networks. We tested our approach on two network sets, one composed of synthetic graphs and another of real directed biological networks, and verified that they were more accurately grouped using directed graphlets than undirected graphlets. It is also evident that directed graphlets offer substantially more topological information than simple graph metrics such as degree distribution or reciprocity. However, enumerating graphlets in large networks is a computationally demanding task. Our implementation addresses this concern by using a state-of-the-art data structure, the g-trie, which is able to greatly reduce the necessary computation. We compared our tool to other state-of-the art methods and verified that it is the fastest general tool for graphlet counting.

Abstract
Computing the frequency of small subgraphs on a large network is a computationally hard task. This is, however, an important graph mining primitive, with several applications, and here we present a novel multicore parallel algorithm for this task. At the core of our methodology lies a state-of-the-art data structure, the g-trie, which represents a collection of subgraphs and allows for a very efficient sequential search. Our implementation was done using Pthreads and can run on any multicore personal computer. We employ a diagonal work sharing strategy to dynamically and effectively divide work among threads during the execution. We assess the performance of our Pthreads implementation on a set of representative networks from various domains and with diverse topological features. For most networks, we obtain a speedup of over 50 for 64 cores and an almost linear speedup up to 32 cores, showcasing the flexibility and scalability of our algorithm. This paves the way for the usage of such counting algorithms on larger subgraph and network sizes without the obligatory access to a cluster.

Abstract
This paper introduces a novel ranking system for competitive sports based around the notion of subgraphs. Although the system is targeted specifically to professional tennis it could be applied to any dominance network due to its generality. The results of about 140,000 tennis matches played between Top-100 players are used to create a colored directed network where colors represent different surfaces and edge direction depends on head-to-read results between players. The main contribution of this work is a ranking system which relies on the occurrences of 4-node directed subgraphs and the positions (or orbits) where the players appear on them. Since the concept of orbit is intrinsically connected with node dominance, appearing frequently in dominant orbits indicates that the player himself is dominant. Even in a very sparse network and without any background knowledge on the tournaments or stages of the matches, our proposal is able to extract meaningful rankings which capture the intricate competitive relationships between players from different eras.

Abstract
Counting the occurrences of small subgraphs in large networks is a fundamental graph mining metric with several possible applications. Computing frequencies of those subgraphs is also known as the subgraph census problem, which is a computationally hard task. In this paper we provide a parallel multicore algorithm for this purpose. At its core we use FaSE, an efficient network-centric sequential subgraph census algorithm, which is able to substantially decrease the number of isomorphism tests needed when compared to past approaches. We use one thread per core and employ a dynamic load balancing scheme capable of dealing with the highly unbalanced search tree induced by FaSE and effectively redistributing work during execution. We assessed the scalability of our algorithm on a varied set of representative networks and achieved near linear speedup up to 32 cores while obtaining a high efficiency for the total 64 cores of our machine.

Abstract
Given a set of temporal networks, from different domains and with different sizes, how can we compare them? Can we identify evolutionary patterns that are both (i) characteristic and (ii) meaningful? We address these challenges by introducing a novel temporal and topological network fingerprint named Graphlet-orbit Transitions (GoT). We demonstrate that GoT provides very rich and interpretable network characterizations. Our work puts forward an extension of graphlets and uses the notion of orbits to encapsulate the roles of nodes in each subgraph. We build a transition matrix that keeps track of the temporal trajectory of nodes in terms of their orbits, therefore describing their evolution. We also introduce a metric (OTA) to compare two networks when considering these matrices. Our experiments show that networks representing similar systems have characteristic orbit transitions. GoT correctly groups synthetic networks pertaining to well-known graph models more accurately than competing static and dynamic state-of-the-art approaches by over 30%. Furthermore, our tests on real-world networks show that GoT produces highly interpretable results, which we use to provide insight into characteristic orbit transitions.