There are a number of "graphs" that Google might use to try to understand relationships, connections, and meanings between things.
For example, there's a concept graph or ontology that came to Google via the Applied Semantics merger as described in the CIRCLA technology  they developed, and a number of pending and granted patents  that apply this semantic technology to both advertising and Web search.
Part of building the creating of the tokens within this concept graph includes understanding entities:The next stage of processing, Named Entity Recognition and Regular Pattern Identification, is responsible for identifying a series of tokens that should potentially be treated as a unit, and that can be recognized as corresponding to a specific semantic type. This module recognizes email addresses, URLs, phone numbers, and dates as well as embodying heuristics for identifying “named entities” such as personal names, locations, and company names.
Under that approach, there are many different types of relationships between concepts (and levels of strength involving those relationships) that are mapped by this concept graph.
Under Phrase-Based Indexing , Google attempts to identify "good" phrases and the other phrases that tend to co-occur with them in a top number of search results for that phrase. Those phrases are considered to be related semantically under that approach. A specific person, place, or thing may be considered a phrase that there are related phrases for. This is another semantic graph that can play a role in how entities might be connected with concepts.
Under a Knowledge Graph approach , Google might first look at knowledge bases such as Wikipedia, Freebases, Amazon.com, IMDB, NetFlix, WordNet, to learn about specific named entities (people, places, and things - including brands and even concepts like "democracy") and aspects or attributes of those entities. Google may then look at its query log files see see how searches that include those entities might be both combined with other terms in queries, and refined in a query session.
So a Knowledge Base might create a unique identifier for a specific named entity to distinguish between different named entities that might share a name, and to cluster together information about a specific entity that might be known by multiple names. It may then use different knowledge bases to identify different aspects or attributes related to those entities, as well as query log information to see what aspects or attributes related to those entities that people tend to search for.
The idea behind Agent Rank  is to create an association between a specific entity (as author or editor or publisher or commentator or social sharer/endorser/annotator or combinations of all of those) and a unique identifier (like the string of numbers in the URL within your profile) so that Google can collect information explicitly stated in a profile and implicitly expressed in social contributions and interactions with others, as well as content associated with that Agent via authorship markup, and possibly some future third party comment system as well. This information can help define facts behind aspects and attributes associated with an individual such as school attended, place employed, hobbies, interests, expertise, topics written about, topics commented upon.
Agent Rank provides Google with unique identifiers for specific individuals, and assign multiple reputation scores to them based upon different concepts or topics that they are associated with. An endorsement (or +1) from a specific agent may carry different weights based upon those different reputation scores.
So, someone like Stephen King, the horror writer, who decides to +1 an article about the history of horror films might carry a lot of weight with his endorsement. If he also endorses (+1) a news article about the habits of prairie dogs in Montana, and he's never written about them before on the Web at pages he has associated himself with via authorship markup, never interacted with others on the topic in Google Plus (or other social networks he has pointed to his profile for in his Google Account), his endorsement might not carry any weight at all.
Note that the endorsements don't count towards increasing the "value" of the content being endorsed, but rather the "reputation" of the author of that content. It's a ranking of Agents.
The credential scores that both +Jeff Jockisch
and I mention above also describe a way of increasing a reputation score for an "Agent" by determining quality scores for both contributions to social networks, and the meaningfulness of interactions with others in those networks. Those scores might be based in part upon a number of features associated with the content itself, and reputation features associated with the people who are being responded to, who respond, who share, who endorse, and so on.
A social graph looks at individuals and their relationships with others. They might be directly connected with each other as friends or connections or people you've circled. They might not be directly connected, but may have interacted in some way (endorsed, shared content, mentioned, etc.) This graph is a different layer of understanding relationships between entities, and those relationships might be topically based, or affinity based or defined in other ways as well.
Google also looks at other graphs, such as the link graph described in PageRank. The PageRank patents also describe a personalized PageRank which might be used to personalize results by being concerned about the topics that might be related to links and might be seen as something that a person searching might be interested in.
The calculation mentioned in Gideon's comment probably isn't quite as simple as:
Agent Rank + Knowledge Graph + Social Graph = "Influence Graph"
When we search while logged into Google, we may see search results from people who we are connected to via a social graph, but those results need to be relevant to our query, and the decision to show something in particular from a person we are connected to is likely going to be based in part upon their reputation score for a topic or concept related to that query.
When we see a knowledge base result, it's possible that the social graph we are part of might have nothing to do with the content that appears as part of that knowledge base result.
We may see both knowledge base information, and social graph information in a sidebar of a set of search results. There may be some connection between them, but there doesn't have to be.
We may see some "personalized" results within our search results that are influenced by what Google knows about our previous search and browsing history and other signals. Those might use information that Google has learned about us from our social interactions and reputation scores and so on at some point in the future, but probably aren't at this point.
When we are logged out of Google, we could potentially continue to see knowledge base results that have nothing to do with our social interactions with others.
When we are logged out of Google, we can still see author badges associated with content that appears in results. It's possible at some point that those results might use credential scores to rank content at some point, and since you're logged out, your social connections with that author aren't directly a reason why content they authored is something that you are seeing.
The content that we create will still be ranked on the words contained within it, and how well it meets an informational or situational of a searcher. But it may also be ranked differently depending upon whether a searcher is logged into Google or not, and it might be partially ranked in the future based upon oan author's "reputation" regardless of whether a searcher is logged in or not.
1. CIRCA Technology: Applying Meaning to Information Management,http://static.twoday.net/blackcat/files/applying%20meaning%20to%20information%20management.pdf
2. Editing a network of interconnected conceptshttp://patft.uspto.gov/netacgi/nph-Parser?Sect1=PTO2&Sect2=HITOFF&p=1&u=%2Fnetahtml%2FPTO%2Fsearch-adv.htm&r=1&f=G&l=50&d=PALL&S1=08051104&OS=PN/08051104&RS=PN/08051104
3. 10 Most Important SEO Patents, Part 5 - Phrase Based Indexinghttp://www.seobythesea.com/2011/12/10-most-important-seo-patents-part-5-phrase-based-indexing/
4. Google and Metaweb: Named Entities and Mashup Search Results?http://www.seobythesea.com/2010/08/google-and-metaweb-named-entities-and-mashup-search-results/
5. Google’s Agent Rank Patent Applicationhttp://searchengineland.com/googles-agent-rank-patent-application-10487