"Invalid URI: The format of the URI could not be determined" Error in C#

You are getting the error of Invalid URI because you are passing a string here, which may or may not have complete URL with https or http (with protocol) string

string href = m.Groups[1].Value;

So you need to change the above code and use it like

public static List<Uri> FetchLinksFromSource(string htmlSource)
        {
            List<Uri> links = new List<Uri>();
            string regexImgSrc = @"<img[^>]*?src\s*=\s*[""']?([^'"" >]+?)[ '""][^>]*?>";
            MatchCollection matchesImgSrc = Regex.Matches(htmlSource, regexImgSrc, RegexOptions.IgnoreCase | RegexOptions.Singleline);
            foreach (Match m in matchesImgSrc)
            {
                string href = m.Groups[1].Value; 
                 //get Request Context
                var request = HttpContext.Current.Request; 

                // Get url scheme with domain name(Auhtority) https://foo.com
                Uri serverUri = new Uri(request.Url.Scheme+"://"+ request.Url.Authority);

                // get the relative uri (/test.html)
                Uri relativeUri = new Uri(href, UriKind.Relative);

                // Get complete URi details
                Uri fullUri = new Uri(serverUri, relativeUri);

                //Now add it in Link
                links.Add(fullUri);
            }
            return links;
        }

I have commented out the code, to explain its meaning, I hope this helps, thanks

You may need to put the protocol infront of your URI if you are passing a string like

string server = "www.myserver.com";

it may throw this error, so use proper string for URI

System.Uri uri = new Uri("http://"+"example.com");

OR

Use different URI constructor 

// this works, because the protocol is included in the string
Uri serverUri = new Uri(yourServer);

// needs UriKind arg, or UriFormatException is thrown
Uri relativeUri = new Uri(YourServerRelativePath, UriKind.Relative); 

// Uri(Uri, Uri) is the preferred constructor in this case
Uri fullUri = new Uri(serverUri, relativeUri);

Where yourServer = "https://example.com" and YourServerRelativePath="/category/some-url"