### Concept: Shortest path problem

#### 245

Traditional fact checking by expert journalists cannot keep up with the enormous volume of information that is now generated online. Computational fact checking may significantly enhance our ability to evaluate the veracity of dubious information. Here we show that the complexities of human fact checking can be approximated quite well by finding the shortest path between concept nodes under properly defined semantic proximity metrics on knowledge graphs. Framed as a network problem this approach is feasible with efficient computational techniques. We evaluate this approach by examining tens of thousands of claims related to history, entertainment, geography, and biographical information using a public knowledge graph extracted from Wikipedia. Statements independently known to be true consistently receive higher support via our method than do false ones. These findings represent a significant step toward scalable computational fact-checking methods that may one day mitigate the spread of harmful misinformation.

#### 42

##### To each according to its degree: the meritocracy and topocracy of embedded markets

- OPEN
- Scientific reports
- Published over 5 years ago
- Discuss

A system is said to be meritocratic if the compensation and power available to individuals is determined by their abilities and merits. A system is topocratic if the compensation and power available to an individual is determined primarily by her position in a network. Here we introduce a model that is perfectly meritocratic for fully connected networks but that becomes topocratic for sparse networks-like the ones in society. In the model, individuals produce and sell content, but also distribute the content produced by others when they belong to the shortest path connecting a buyer and a seller. The production and distribution of content defines two channels of compensation: a meritocratic channel, where individuals are compensated for the content they produce, and a topocratic channel, where individual compensation is based on the number of shortest paths that go through them in the network. We solve the model analytically and show that the distribution of payoffs is meritocratic only if the average degree of the nodes is larger than a root of the total number of nodes. We conclude that, in the light of this model, the sparsity and structure of networks represents a fundamental constraint to the meritocracy of societies.

#### 15

##### Resting-brain functional connectivity predicted by analytic measures of network communication

- OPEN
- Proceedings of the National Academy of Sciences of the United States of America
- Published over 5 years ago
- Discuss

The complex relationship between structural and functional connectivity, as measured by noninvasive imaging of the human brain, poses many unresolved challenges and open questions. Here, we apply analytic measures of network communication to the structural connectivity of the human brain and explore the capacity of these measures to predict resting-state functional connectivity across three independently acquired datasets. We focus on the layout of shortest paths across the network and on two communication measures-search information and path transitivity-which account for how these paths are embedded in the rest of the network. Search information is an existing measure of information needed to access or trace shortest paths; we introduce path transitivity to measure the density of local detours along the shortest path. We find that both search information and path transitivity predict the strength of functional connectivity among both connected and unconnected node pairs. They do so at levels that match or significantly exceed path length measures, Euclidean distance, as well as computational models of neural dynamics. This capacity suggests that dynamic couplings due to interactions among neural elements in brain networks are substantially influenced by the broader network context adjacent to the shortest communication pathways.

#### 10

We introduce a methodology to efficiently exploit natural-language expressed biomedical knowledge for repurposing existing drugs towards diseases for which they were not initially intended. Leveraging on developments in Computational Linguistics and Graph Theory, a methodology is defined to build a graph representation of knowledge, which is automatically analysed to discover hidden relations between any drug and any disease: these relations are specific paths among the biomedical entities of the graph, representing possible Modes of Action for any given pharmacological compound. We propose a measure for the likeliness of these paths based on a stochastic process on the graph. This measure depends on the abundance of indirect paths between a peptide and a disease, rather than solely on the strength of the shortest path connecting them. We provide real-world examples, showing how the method successfully retrieves known pathophysiological Mode of Action and finds new ones by meaningfully selecting and aggregating contributions from known bio-molecular interactions. Applications of this methodology are presented, and prove the efficacy of the method for selecting drugs as treatment options for rare diseases.

#### 10

It is conventional in labor economics to treat all workers who are seeking new jobs as belonging to a labor pool, and all firms that have job vacancies as an employer pool, and then match workers to jobs. Here we develop a new approach to study labor and firm dynamics. By combining the emerging science of networks with newly available employment micro-data, comprehensive at the level of whole countries, we are able to broadly characterize the process through which workers move between firms. Specifically, for each firm in an economy as a node in a graph, we draw edges between firms if a worker has migrated between them, possibly with a spell of unemployment in between. An economy’s overall graph of firm-worker interactions is an object we call the labor flow network (LFN). This is the first study that characterizes a LFN for an entire economy. We explore the properties of this network, including its topology, its community structure, and its relationship to economic variables. It is shown that LFNs can be useful in identifying firms with high growth potential. We relate LFNs to other notions of high performance firms. Specifically, it is shown that fewer than 10% of firms account for nearly 90% of all employment growth. We conclude with a model in which empirically-salient LFNs emerge from the interaction of heterogeneous adaptive agents in a decentralized labor market.

#### 8

##### Cilia-based flow network in the brain ventricles

- Science (New York, N.Y.)
- Published almost 3 years ago
- Discuss

Cerebrospinal fluid conveys many physiologically important signaling factors through the ventricular cavities of the brain. We investigated the transport of cerebrospinal fluid in the third ventricle of the mouse brain and discovered a highly organized pattern of cilia modules, which collectively give rise to a network of fluid flows that allows for precise transport within this ventricle. We also discovered a cilia-based switch that reliably and periodically alters the flow pattern so as to create a dynamic subdivision that may control substance distribution in the third ventricle. Complex flow patterns were also present in the third ventricles of rats and pigs. Our work suggests that ciliated epithelia can generate and maintain complex, spatiotemporally regulated flow networks.

#### 5

Creative exploration is central to science, art and cognitive development. However, research on creative exploration is limited by a lack of high-resolution automated paradigms. To address this, we present such an automated paradigm, the creative foraging game, in which people search for novel and valuable solutions in a large and well-defined space made of all possible shapes made of ten connected squares. Players discovered shape categories such as digits, letters, and airplanes as well as more abstract categories. They exploited each category, then dropped it to explore once again, and so on. Aligned with a prediction of optimal foraging theory (OFT), during exploration phases, people moved along meandering paths that are about three times longer than the shortest paths between shapes; when exploiting a category of related shapes, they moved along the shortest paths. The moment of discovery of a new category was usually done at a non-prototypical and ambiguous shape, which can serve as an experimental proxy for creative leaps. People showed individual differences in their search patterns, along a continuum between two strategies: a mercurial quick-to-discover/quick-to-drop strategy and a thorough slow-to-discover/slow-to-drop strategy. Contrary to optimal foraging theory, players leave exploitation to explore again far before categories are depleted. This paradigm opens the way for automated high-resolution study of creative exploration.

#### 5

Increasingly detailed data on the network topology of neural circuits create a need for theoretical principles that explain how these networks shape neural communication. Here we use a model of cascade spreading to reveal architectural features of human brain networks that facilitate spreading. Using an anatomical brain network derived from high-resolution diffusion spectrum imaging (DSI), we investigate scenarios where perturbations initiated at seed nodes result in global cascades that interact either cooperatively or competitively. We find that hub regions and a backbone of pathways facilitate early spreading, while the shortest path structure of the connectome enables cooperative effects, accelerating the spread of cascades. Finally, competing cascades become integrated by converging on polysensory associative areas. These findings show that the organizational principles of brain networks shape global communication and facilitate integrative function.

#### 4

##### Routes Obey Hierarchy in Complex Networks

- OPEN
- Scientific reports
- Published almost 2 years ago
- Discuss

The last two decades of network science have discovered stunning similarities in the topological characteristics of real life networks (many biological, social, transportation and organizational networks) on a strong empirical basis. However our knowledge about the operational paths used in these networks is very limited, which prohibits the proper understanding of the principles of their functioning. Today, the most widely adopted hypothesis about the structure of the operational paths is the shortest path assumption. Here we present a striking result that the paths in various networks are significantly stretched compared to their shortest counterparts. Stretch distributions are also found to be extremely similar. This phenomenon is empirically confirmed on four networks from diverse areas of life. We also identify the high-level path selection rules nature seems to use when picking its paths.

#### 4

##### Mandala Networks: ultra-small-world and highly sparse graphs

- OPEN
- Scientific reports
- Published about 4 years ago
- Discuss

The increasing demands in security and reliability of infrastructures call for the optimal design of their embedded complex networks topologies. The following question then arises: what is the optimal layout to fulfill best all the demands? Here we present a general solution for this problem with scale-free networks, like the Internet and airline networks. Precisely, we disclose a way to systematically construct networks which are robust against random failures. Furthermore, as the size of the network increases, its shortest path becomes asymptotically invariant and the density of links goes to zero, making it ultra-small world and highly sparse, respectively. The first property is ideal for communication and navigation purposes, while the second is interesting economically. Finally, we show that some simple changes on the original network formulation can lead to an improved topology against malicious attacks.